Maths : How To Calculate/Multiply Fast in Competitive Exams - Tricks

<div dir="ltr" style="text-align: left;" trbidi="on"><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPNvnn7ltmHPQwWtvIaXvmzMwtCewvR3ArvnE9lfOVdKSHCf3FCFsjjWKwr_GLlJBQEsQip02p4N4A-ae6xw4eLitpBNGoW5ZfTBfrvEarVtKbUHN2R-645_h1ZHoEGWv4uYBNLMBSCgc/s1600/16+Easy+Quantitative+Aptitude+shortcut+tricks+for+all+competitive+exams.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhPNvnn7ltmHPQwWtvIaXvmzMwtCewvR3ArvnE9lfOVdKSHCf3FCFsjjWKwr_GLlJBQEsQip02p4N4A-ae6xw4eLitpBNGoW5ZfTBfrvEarVtKbUHN2R-645_h1ZHoEGWv4uYBNLMBSCgc/s1600/16+Easy+Quantitative+Aptitude+shortcut+tricks+for+all+competitive+exams.jpg" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSdD1RyHGNn4pOyQ8JEdCIe8Nwxg6865j4Rg1chpPF-NpWMT4o1B4dT1HUV4PwW39J59Oa-T5fq-I61xpwX1a3wxCwdfkeTluGqs93N_hI2Os1ka9p5EihSLoPwCVdY8_Mvteib2lylG0/s1600/280px-Tricks-logo.svg.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjSdD1RyHGNn4pOyQ8JEdCIe8Nwxg6865j4Rg1chpPF-NpWMT4o1B4dT1HUV4PwW39J59Oa-T5fq-I61xpwX1a3wxCwdfkeTluGqs93N_hI2Os1ka9p5EihSLoPwCVdY8_Mvteib2lylG0/s1600/280px-Tricks-logo.svg.png" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYeP80nanAS-MIXgUmIzB78456bAzlFi6etiHYvzJdKgg4LSkCR1l7phz2LqUAGsH-wXBQqbArj8ROIML6lMBRWbmhjkx-JVNli3dzhjY1I4vDVcPrr9Dh7a9ZMyuo7WCfFIqtrRqnRkA/s1600/tips.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhYeP80nanAS-MIXgUmIzB78456bAzlFi6etiHYvzJdKgg4LSkCR1l7phz2LqUAGsH-wXBQqbArj8ROIML6lMBRWbmhjkx-JVNli3dzhjY1I4vDVcPrr9Dh7a9ZMyuo7WCfFIqtrRqnRkA/s1600/tips.jpg" /></a></div><div class="MsoNormal" style="background: white; margin-top: 9pt; mso-outline-level: 3;"><br /></div><div class="MsoNormal" style="background: white; margin-top: 9pt; mso-outline-level: 3;"><br /></div><div class="MsoNormal" style="background: white; margin-top: 9pt; mso-outline-level: 3;"><br /></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"><span style="font-size: large;"><b><u><span style="color: purple;">MATHEMATICS</span></u></b><span style="color: #222222;"><o:p></o:p></span></span></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"><br /></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><span style="color: #222222;">Whenever we are going to solve any competitive exam`s  questions  paper we have</span><span style="color: #222222;"> </span><b><u><span style="color: purple;">four subjects to solve: -</span></u></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><b><span style="color: #222222;">1. Computer  </span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><b><span style="color: #222222;">2. English</span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;"> </span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><b><span style="color: #222222;">3. General knowledge   </span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><b><span style="color: #222222;">4. Reasoning</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><b><span style="color: #222222;">5. Mathematics  </span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"><br /></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><span style="color: #222222;">            Dear friends, when we are fighting any competitive exam, whether it is</span><span style="color: #222222;"> </span><span style="color: #222222;"><a href="http://www.ibps.in/"><span style="color: #8866dd; mso-bidi-font-size: 12.0pt; text-decoration: none; text-underline: none;">IBPS</span></a>, <a href="http://www.ssc.nic.in/"><span style="color: #8866dd; mso-bidi-font-size: 12.0pt; text-decoration: none; text-underline: none;">SSC</span></a></span><span style="color: #222222;"> </span><span style="color: #222222;">or any other competitive exam,  the problem comes when we face a shortage of time. That’s why we have all the answers, but we can’t answer.  So how can we solve our problem? Why do not we pay much less time to solve question. Especially this problem comes  in Mathematics where we have to solve a lots of question in short time. Most of our time consumes in calculating the numbers. To solve mathematics in short time firstly we have to learn how to calculate easily.</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><span style="color: #222222;">  Now you will ask how,</span><span style="color: #222222;"> </span><b><span style="color: #222222;">Here I am telling you how to calculate fast in second.</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><br /></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><span style="color: #222222;">                         </span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><span style="color: #222222;">In mathematics addition and subtraction is easy, but multiplication is so time consuming. So why do not we make it simple and easy. How????????? Let’s know…………</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><b><i><u><span style="color: purple;">Multiplication: -</span></u></i></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white;"><span style="font-size: large;"><b><span style="color: #222222;">Multiply the Two Digit numbers:-</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"><b><span style="color: #222222; font-family: Georgia, serif;"><span style="font-size: large;"><br /></span></span></b></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsK5CzTk5n1LKvMX7b005Xe3SbSMdmuHYqcP17ihYT4dyMFb0LRtrs8LeF4majZAzEFX3sWr_2S7WuPBCenhaC8Wow4O4FQ6NNXvW3N863QGuOcRpmNgRB9OZUWMr6zIU310EbbrdPYs0/s1600/www.topnaukrialert.com.png" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: large;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsK5CzTk5n1LKvMX7b005Xe3SbSMdmuHYqcP17ihYT4dyMFb0LRtrs8LeF4majZAzEFX3sWr_2S7WuPBCenhaC8Wow4O4FQ6NNXvW3N863QGuOcRpmNgRB9OZUWMr6zIU310EbbrdPYs0/s1600/www.topnaukrialert.com.png" width="320" /></span></a></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"><span style="font-size: large;"><b><span style="color: #222222; font-family: Georgia, serif;"> </span></b><b><span style="color: #222222; font-family: Georgia, serif;"> </span></b><b><span style="color: #222222;"><span style="color: #8866dd; text-decoration: none; text-underline: none;"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" o:spt="75" o:preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"/> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"/> <v:f eqn="sum @0 1 0"/> <v:f eqn="sum 0 0 @1"/> <v:f eqn="prod @2 1 2"/> <v:f eqn="prod @3 21600 pixelWidth"/> <v:f eqn="prod @3 21600 pixelHeight"/> <v:f eqn="sum @0 0 1"/> <v:f eqn="prod @6 1 2"/> <v:f eqn="prod @7 21600 pixelWidth"/> <v:f eqn="sum @8 21600 0"/> <v:f eqn="prod @7 21600 pixelHeight"/> <v:f eqn="sum @10 21600 0"/> </v:formulas> <v:path o:extrusionok="f" gradientshapeok="t" o:connecttype="rect"/> <o:lock v:ext="edit" aspectratio="t"/></v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" alt="" style='width:150pt; height:112.5pt' o:button="t"> <v:imagedata src="file:///C:\Users\Om\AppData\Local\Temp\msohtmlclip1\01\clip_image001.jpg" o:href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjtr_xN3KTDWfqczxFhhNFPdMYFHIJQ6WVksu1sCqWUKPUFc-kxNBK7soi0yYT0w2Cf3w8wpAJ-MVeISpvPlbVn63EpOTkTLvFqQdN5ke8FrP9QX6QNKgt18-UnKXNIVPpcRrybesjBxuV4/s200/PAINT.BMP"/></v:shape><![endif]--><!--[if !vml]--><!--[endif]--></span></span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222; font-family: Georgia, serif;">     </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">1. First we are taking two two-digit numbers AB and CD.</span></b><span style="color: #222222;"> </span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">      2. Now, the digit of unit of the first number multiplied by the digit of unit of the second number.</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">      3. Then, the ten-digit of the first number multiplied by the first digit of unit of the second number and then the ten-digit of the second number multiplied by the first digit of unit of the first number then plus them.</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">      4. Again, the ten-digit of the first number multiplied by the ten-digit of the second number.</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">     </span><b style="text-indent: -0.25in;"><u><span style="color: purple;">Example:- </span></u></b><b style="text-indent: -0.25in;"><u><span style="color: purple;"> </span></u></b><b style="text-indent: -0.25in;"><span style="color: #222222;"> </span></b></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">          </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">4         </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">3</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">                                                                       </span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">  +     </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">7          </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">5</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">     </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">_____________       </span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">             </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">3225</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">     </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">_____________</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">          3 x 5 = 15</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">          carry = </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">1</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">          4 x 5 = 20</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">         7 x 3 = 21</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">   + </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">_________</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">           </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">42</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">        Carry = </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">4</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">      4 x 7 = 28</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">  + __________</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">        </span></b><b><span style="color: #222222;"> </span></b><b><span style="color: #222222;">32</span></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><b><span style="color: #222222;"><span style="font-size: large;"><br /></span></span></b></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><u><span style="color: purple;">    For the three-digit number:- </span></u></b><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><b><span style="color: #222222;">  </span></b><span style="color: #222222;"> </span><b><span style="color: #222222;">               </span></b><b><span style="color: #222222;"> </span></b><span style="color: #222222;">A         </span><span style="color: #222222;"> </span><span style="color: #222222;">B         </span><span style="color: #222222;"> </span><span style="color: #222222;">C</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="color: #222222;"><span style="font-size: large;">  </span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">        X </span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">       </span><span style="color: #222222;">  </span><span style="color: #222222;">          </span><span style="color: #222222;"> </span><span style="color: #222222;">D        </span><span style="color: #222222;"> </span><span style="color: #222222;">E          </span><span style="color: #222222;"> </span><span style="color: #222222;">F</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">________________________________</span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">  AD/AE+BD/BE+AF+CD/BF+CE/CF                                                                                                                </span><span style="color: #222222;"><o:p></o:p></span></span></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><br /></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"><span style="font-size: large;"><span style="color: #222222;">      earlier</span><span style="color: #222222; text-indent: -0.25in;"> you feel that it is something difficult than our regular method of </span><span style="color: #222222; text-indent: -0.25in;"> </span><span style="color: #222222; text-indent: -0.25in;">multiplying because we are not familiar with this method , But when</span><span style="color: #222222; text-indent: -0.25in;"> </span><span style="color: #222222; text-indent: -0.25in;"> we regularly calculate with this method you find it is more easy and quick from that of our regular multiplying method.</span></span></div><span style="font-size: large;"><span style="color: #222222; font-family: 'Times New Roman', serif;">So take example questions of your books and try solving by this method , you will find that this is the most</span><span style="color: #222222; font-family: 'Times New Roman', serif;"> </span><b><span style="color: #222222; font-family: 'Times New Roman', serif;">easiest method to multiplication</span></b><span style="color: #222222; font-family: 'Times New Roman', serif;">.</span><span style="color: #222222; font-family: 'Times New Roman', serif;"> </span><span style="color: #222222; font-family: 'Times New Roman', serif;">And you can solve maths paper</span><span style="color: #222222; font-family: 'Times New Roman', serif;"> </span><b><span style="color: #222222; font-family: 'Times New Roman', serif;">quickly</span></b><span style="color: #222222; font-family: 'Times New Roman', serif;"> </span><span style="color: #222222; font-family: 'Times New Roman', serif;">in any of the competitive exams</span></span><div><span style="color: #222222; font-family: Times New Roman, serif;"><span style="font-size: 15px;"><br /></span></span></div><div><span style="color: #222222; font-family: Times New Roman, serif;"><span style="font-size: 15px;"><br /></span></span></div><div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: inherit;"><span class="apple-style-span"><span style="font-size: 16pt;">For multiplication by 5, you should multiply the figure given by 10 and then divide it by 2.</span></span><o:p></o:p></span></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: inherit;"><span class="apple-style-span"><span style="font-size: 16pt;">e.g. 12986 × 5 = 129860/2 = 64930.</span></span><o:p></o:p></span></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><br /></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: inherit;"><span class="apple-style-span"><span style="font-size: 16pt;">For multiplication by 25, you should multiply the figure given by 100 and then divide it by 4.</span></span><o:p></o:p></span></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span style="font-family: inherit;"><span class="apple-style-span"><span style="font-size: 16pt;">e.g. 12986 × 25 = 1298600/4 = 324650.</span></span><o:p></o:p></span></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><br /></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span class="apple-style-span"><span style="font-size: 16pt;"><span style="font-family: inherit;">For multiplication by 125, you should multiply the figure given by 1000 and then divide it by 8.</span></span></span><o:p></o:p></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><span class="apple-style-span"><span style="font-size: 16pt;"><span style="font-family: inherit;"><br /></span></span></span></div><div class="MsoNormal" style="background: rgb(252, 254, 255); 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Maths : How To Calculate/Multiply Fast in Competitive Exams - Tricks

MATHEMATICSWhenever we are going to solve any competitive exam`s  questions  paper we have four subjects to solve: -1. Computer  2. English  3. General knowledge   4. Reasoning5. Mathematics          …

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10 rules to Use of 'A' 'An' & 'The' English Grammar Short Tricks with examples

<div dir="ltr" style="text-align: left;" trbidi="on"><h2 style="background-color: white; margin: 9pt 0in 0.0001pt; text-align: left;"><span style="color: #222222; font-family: Cambria, serif; font-size: large;"><b>10 rules to Use of 'A' 'An' & 'The'  English Grammar Short Tricks with examples </b></span></h2><div class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; margin: 9pt 0in 0.0001pt;"><span style="color: #222222; font-family: Cambria, serif; font-size: large;"><b><br /></b></span></div><div class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; margin-bottom: 0.0001pt;"><span style="font-size: large;"><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"> Here  we are going to learn about</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">Articles.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />Let's see how to use articles :<br /></span><b><span style="color: purple; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">Before using articles first we have to learn their rules :</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br /><br /></span><a href="https://www.blogger.com/null" name="more"></a><b><span style="color: purple; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />1. <u>Use of 'A'</u></span></b><b><span style="color: purple; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"> : 'A'</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">is used in case of a countable giving out a</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">consonant sound.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br /><b>Examples  :</b><br />I. He has</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">a book</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">in his hand.<br />II. He is</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">a one</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">eyed man.<br />III. She is</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">a</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">B. A.<br /><b> </b><br /></span><b><span style="color: purple; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">2. <u>Use of 'An'</u></span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"> : 'An' </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">is used in case of a countable giving out a <b>vowel sound.</b><br /><b>Examples  :</b><br />I. She bought</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">an umbrella.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II. She is</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">an honest</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">lady.<br /><br /></span><b><span style="color: purple; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">3. <u>'A(n)'</u></span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">should be placed between</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">'Half'</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">and a noun and after</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">'many' 'what' and 'opportunity'.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br /><b>Examples  :</b><br />I. We came</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">after half an hour.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II. She gave me</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">half a dozen</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">pencil.<br />III.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">Many a man</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">is born in object poverty.<br />IV.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">What an opportunity</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">you have missed!<br /><br /><b>4.</b></span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">When two subjects or articles naturally go together and are thought of as a unit it is not necessary to repeat the indefinite article with the second noun .<br /><b>Examples  :</b><br />I. A cigarette is made of</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">a paper and tobacco.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II. He was ready with</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">a cup and saucer.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br /><br /><b>5.</b></span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The indefinite article is used distributively and also with a person's name to indicate that the person is perhaps unknown to the person addressed.<br /><b>Examples  :</b><br />I. He visit the town</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">once in a blue moon.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II. He can walk</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">six miles an hour .</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />III.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">A Mr. John</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">is at the door.<br /><b><br />6.</b></span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">Article 'the' should be used with the name of the following :<br />rivers, mountains, monuments, great books, ocean, island, descriptive names of countries, newspaper, directions, unique things etc.<br /><b>Examples  :</b><br />I. A flying saucer was seen encircling<b> </b>over</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the Atlantic.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The Thames</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">discharged several crores of cusecs of water into the sea every year.<br />III.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The Indian express</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">has the largest circulation in Nepal.<br />IV.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The sun</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">risen in the east.<br />V.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The moon</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">is the nearest planet to</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the earth.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />VI. They went to Agra to see the</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">Taj Mahal.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />VII.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The U.S.A.</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">and</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The U.S.S.R.</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">are the most powerful countries of the world.<br /><br /><b>7.</b></span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The definite article</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">'the'</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">should be used with the</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">superlative degrees</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">and</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">comparative degrees (when two),</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">and with</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">two noun (proper and common noun)</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">naturally going together and spoken of as a unit.<br /><b>Examples  :</b><br />I. She is</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the best</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">student of the class.<br />II.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The more</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">you eat,</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the more</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">hungry you feel.<br />III.</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The Agra University</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">was founded in 1927.<br /><br /><b>8. 'The'</b></span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">is used as a weak form of 'this' , 'these' , 'that' , 'those' , applied to person(s), thing(s), event(s), etc. already referred to or being discussed.<br /><b>Examples  :</b><br />I. Please close</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the doors.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II. Will you have a walk by</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the river.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br /><br /><b>9.</b></span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">It is also used to indicate vague time and part of the day.<br /><b>Example  : </b><br />I. He came in</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the evening.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II. They always play in</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the morning.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />III. He will have lunch in</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">the afternoon.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br /><b><br />10.</b></span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">The definite article</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">'the'</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">should not be used with the names of the following :</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">games, disease, colours, days, months</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">etc.<br /><b>Examples  :</b><br />I.<b> </b>I am suffering from</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">typhoid.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />II. His shirt is dyed in</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">green.</span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><br />III. They came on</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">Monday</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">last.<br />IV. They meet us in</span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";">January</span></b><b><span style="color: #222222; font-family: "Times New Roman","serif"; mso-bidi-font-size: 11.0pt; mso-fareast-font-family: "Times New Roman";"> </span></b></span><span style="color: #222222; font-family: "Times New Roman","serif"; mso-fareast-font-family: "Times New Roman";"><span style="font-size: large;">last.<br /><br /><b>These are very important rules by using them you can easily solve questions related to articles. but this can possible only when you practice more and more. So to become strong in English grammar just practice the questions.</b></span><o:p style="font-size: 11.5pt;"></o:p></span></div><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8o4BeZhgLWr6i5F-w8A7y2FjfYIk2zi-c1KaNBkp-UwzvMDH9Eihu7AcUvz0LbGrdpkpPCEYx4hEPlkSNklOnbMdlipEafPBxiMgcTd_Lbh_MeuEuZBU-ZGY_VMw758Ybigw4fTvADGI/s1600/english-tricks.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="209" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi8o4BeZhgLWr6i5F-w8A7y2FjfYIk2zi-c1KaNBkp-UwzvMDH9Eihu7AcUvz0LbGrdpkpPCEYx4hEPlkSNklOnbMdlipEafPBxiMgcTd_Lbh_MeuEuZBU-ZGY_VMw758Ybigw4fTvADGI/s1600/english-tricks.png" width="320" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgByUnrKTnr14mLLkZjGM-JXymM1WMaNJ0hqBzM_wbp6dbBdOGl_UM5nss1jw-oDS2-sCms47yAT_xwZUcNkvESnRUamcKbDDBL5Gd3-JOEBUXF3BJGyhC6Tvd3vaOAY4UP8X9lHZGe07s/s1600/how+to+debug+a+batch+job+in+AS400+steps.png" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgByUnrKTnr14mLLkZjGM-JXymM1WMaNJ0hqBzM_wbp6dbBdOGl_UM5nss1jw-oDS2-sCms47yAT_xwZUcNkvESnRUamcKbDDBL5Gd3-JOEBUXF3BJGyhC6Tvd3vaOAY4UP8X9lHZGe07s/s1600/how+to+debug+a+batch+job+in+AS400+steps.png" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFp9ErZkTKx4QMl96tACna1C416o8qDbCgLnHsHqKSyKzrKlI6U8mJhKxomBTY5omDkC-HhZGf0S9un_70h7ZoMJQGr34-CRWVKZz9fBr8Ns9_yvBFnkDBfjOru_rHDVL0pcsj2OM7qEg/s1600/top+tips+and+tricks.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgFp9ErZkTKx4QMl96tACna1C416o8qDbCgLnHsHqKSyKzrKlI6U8mJhKxomBTY5omDkC-HhZGf0S9un_70h7ZoMJQGr34-CRWVKZz9fBr8Ns9_yvBFnkDBfjOru_rHDVL0pcsj2OM7qEg/s1600/top+tips+and+tricks.jpg" /></a></div><div class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; margin-bottom: 0.0001pt;"><span style="color: #222222; font-family: "Times New Roman","serif"; font-size: 11.5pt; mso-fareast-font-family: "Times New Roman";"><b><br /></b></span></div><div class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; margin-bottom: 0.0001pt;"><span style="color: #222222; font-family: "Times New Roman","serif"; font-size: 11.5pt; mso-fareast-font-family: "Times New Roman";"><b><br /></b></span></div></div>

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16 Easy Quantitative Aptitude short tricks for all competitive exams with practice set Quiz test

<h2 style="text-align: left;"><span style="font-size: large;">16 Easy Quantitative Aptitude short tricks for all competitive exams with practice set Quiz test</span></h2><div dir="ltr" style="text-align: left;" trbidi="on"><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho7ouFlywNBb3wqwpJyK7NP3Sl-yv_teOSTKSaj1nktibYoiDnfW8SF6ShnsckMOE46MV-hQvX7fyJWis_MGw61aqqWk6BgeWlzWEe37dlWIQ70odvOx7aihVrWvwedgLC5cou5swzwLs/s1600/exam-tips.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEho7ouFlywNBb3wqwpJyK7NP3Sl-yv_teOSTKSaj1nktibYoiDnfW8SF6ShnsckMOE46MV-hQvX7fyJWis_MGw61aqqWk6BgeWlzWEe37dlWIQ70odvOx7aihVrWvwedgLC5cou5swzwLs/s1600/exam-tips.jpg" /></a></div><div class="separator" style="clear: both; text-align: center;"><br /></div><span style="font-size: large;"><b><span face=""Verdana","sans-serif"" style="color: maroon;">(1) Multiplication by 5<br /></span></b><span face=""Verdana","sans-serif"">It's often more convenient instead of multiplying by 5 to multiply first by 10 and then divide by 2. For example, 137·5=1370/2=685. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(2) Division by 5<br /></span></b><span face=""Verdana","sans-serif"">Similarly, it's often more convenient instead to multiply first by 2 and then divide by 10. For example, 1375/5=2750/10=275.</span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(3) Division/multiplication by 4<br /></span></b><span face=""Verdana","sans-serif"">Replace either with a repeated operation by 2. For example 124/4=62/2=31. Also, 124·4=248·2=496. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(4) Division/multiplication by 25<br /></span></b><span face=""Verdana","sans-serif"">Use operations with 4 instead. For example, 37·25=3700/4=1850/2=925. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(5) Division/multiplication by 8<br /></span></b><span face=""Verdana","sans-serif"">Replace either with a repeated operation by 2. For example 124·8=248·4=496·2=992. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(6) Division/multiplication by 125<br /></span></b><span face=""Verdana","sans-serif"">Use operations with 8 instead. For example, 37·125=37000/8=18500/4=9250/2=4625. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(7) Squaring two digit numbers. </span></b><br /><b><span face=""Verdana","sans-serif"">You should memorize the first 25 squares:</span></b> <br /><!--[if !supportMisalignedColumns]--><!--[endif]--></span><table border="1" cellpadding="0" class="MsoNormalTable" style="mso-cellspacing: 1.5pt; mso-padding-alt: 1.5pt 1.5pt 1.5pt 1.5pt; width: 100%px;"> <tbody><tr> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">1</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">2</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">3</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">4</span></b><br /> </span></td> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">5</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">6</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">7</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">8</span></b><br /> </span></td> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">9</span></b><br /> </span></td> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">10</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">11</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">12</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 8%;" width="8%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">13</span></b><br /> </span></td> <td style="padding: 1.5pt; width: 8%;" width="8%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">14</span></b><br /> </span></td> </tr><tr> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">1</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">2</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">9</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">16</span><br /> </span></td> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">25</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">36</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">49</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">64</span><br /> </span></td> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">81</span><br /> </span></td> <td style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">100</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">121</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">144</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 8%;" width="8%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">169</span><br /> </span></td> <td style="padding: 1.5pt; width: 8%;" width="8%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">196</span><br /> </span></td> </tr><tr> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">15</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">16</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">17</span></b><br /> </span></td> <td colspan="3" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">18</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">19</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">20</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">21</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">22</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">23</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">24</span></b><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 10%;" width="10%"> <span style="font-size: large;"><b><span face=""Verdana","sans-serif"">25</span></b><br /> </span></td> </tr><tr> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">225</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">256</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">289</span><br /> </span></td> <td colspan="3" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">324</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">361</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">400</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">441</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">484</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">529</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">576</span><br /> </span></td> <td colspan="2" style="padding: 1.5pt; width: 10%;" width="10%"> <span style="font-size: large;"><span face=""Verdana","sans-serif"">625</span><br /> </span></td> </tr><tr height="0"> <td style="border: none;" width="52"></td> <td style="border: none;" width="16"></td> <td style="border: none;" width="37"></td> <td style="border: none;" width="30"></td> <td style="border: none;" width="23"></td> <td style="border: none;" width="44"></td> <td style="border: none;" width="9"></td> <td style="border: none;" width="51"></td> <td style="border: none;" width="9"></td> <td style="border: none;" width="44"></td> <td style="border: none;" width="23"></td> <td style="border: none;" width="30"></td> <td style="border: none;" width="37"></td> <td style="border: none;" width="16"></td> <td style="border: none;" width="51"></td> <td style="border: none;" width="51"></td> <td style="border: none;" width="16"></td> <td style="border: none;" width="37"></td> <td style="border: none;" width="30"></td> <td style="border: none;" width="23"></td> <td style="border: none;" width="44"></td> <td style="border: none;" width="16"></td> <td style="border: none;" width="59"></td> </tr></tbody></table><div class="MsoNormal"><span style="font-size: large;"><br /></span></div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;"><span style="font-size: large;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman';">         </span></span><!--[endif]--><b><span face=""Verdana","sans-serif"">Squares of numbers from 26 through 50.<br /></span></b><span face=""Verdana","sans-serif"">Let A be such a number. Subtract 25 from A to get x. Subtract x from 25 to get, say, a. Then A²=a²+100x. For example, if A=26, then x=1 and a=24. Hence 26²=24²+100=676. Similarly, if A=37, then x=37-25=12, and a=25-12=13. Therefore, 37²=13²+100·12=1200+169=1369. Why does this work? (25+x)²-(25-x)²=[(25+x)+(25-x)]·[(25+x)-(25-x)]=50·2x=100x. </span></span></div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;"><span style="font-size: large;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman';">         </span></span><!--[endif]--><b><span face=""Verdana","sans-serif"">Squares of numbers from 51 through 99.<br /></span></b><span face=""Verdana","sans-serif"">The idea is the same as above. (50+x)²-(50-x)²=100·2x=200x. For example, 63²=37²+200·13= 1369+2600=3969. </span></span></div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;"><span style="font-size: large;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman';">         </span></span><!--[endif]--><b><span face=""Verdana","sans-serif"">Squares of numbers from 51 through 99, second approach (this one was communicated to me by my father Moisey Bogomolny).<br /></span></b><span face=""Verdana","sans-serif"">We are looking to compute A², where A=50+a. Instead compute 100·(25+a) and add a². Example: 57². a=57-50=7. 25+7=32. Append 49=7². <b>Answer:</b> 57²=3249. </span></span></div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;"><span style="font-size: large;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman';">         </span></span><!--[endif]--><span face=""Verdana","sans-serif"">In general, a² = (a + b)(a - b) + b². Let a be 57 and, again, we wish to compute 57². Let b = 3. Then 57² = (57 + 3)(57 - 3) + 3², or 57² = 60·54 + 9 = 3240 + 9 = 3249. </span></span></div><span style="font-size: large;"><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(8) Squares of numbers that end with 5.<br /></span></b><span face=""Verdana","sans-serif"">Let A=10a+5. Then A²=(10a+5)²=100a²+2·10a·5+25=100a(a+1)+25. For example, to compute 115², where a=11, first compute 11·(11+1)=11·12=132 (since 3=1+2). Next, append 25 to the right of 132 to get 13225! Another example, to compute 245², let a=24. Then 24·(24+1)=24²+24=576+24=600. Therefore 245²=60025. Here is another way to compute 24·25: 24·25=2400/4=1200/2=600. The rule naturally applies to 2-digit numbers as well. 75²=5625 (since 7·8=56). </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(9) Product of two one-digit numbers greater than 5.<br /></span></b><span face=""Verdana","sans-serif"">This is a rule that helps remember a big part of the multiplication table. Assume you forgot the product 7·9. Do this. First find the access of each of the multiples over 5: it's 2 for 7 (7 - 5 = 2) and 4 for 9 (9 - 5 = 4). Add them up to get 6 = 2 + 4. Now find the complements of these two numbers to 5: it's 3 for 2 (5 - 2 = 3) and 1 for 4 (5 - 4 = 1). Remember their product 3 = 3·1. Lastly, combine thus obtained two numbers (6 and 3) as 63 = 6·10 + 3. </span><br /><b><span face=""Verdana","sans-serif"">The explanation comes from the following formula: </span></b><br /></span><div class="MsoNormal"><span face=""Verdana","sans-serif"" style="font-size: large;">(5 + a)(5 + b) = 10(a + b) + (5 - a)(5 - b) </span></div><span style="font-size: large;"><span face=""Verdana","sans-serif"">In our example, a = 2 and b = 4. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(10) Product of two 2-digit numbers. </span></b><br /></span><div style="margin-left: 0.5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -0.25in;"><span style="font-size: large;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman';">         </span></span><!--[endif]--><span face=""Verdana","sans-serif"">If the numbers are not too far apart, and their difference is even, one might use the well known formula (a+n)(a-n)=a²-n². a here is the average of the two numbers. For example, 28·24=26²-2²=676-4=672 since 26=(24+28)/2. Also, 19·31=25²-6²=625-36=589 since 25=(19+31)/2. </span></span></div><div style="margin-left: 0.5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -0.25in;"><span style="font-size: large;"><!--[if !supportLists]--><span style="font-family: Symbol; mso-bidi-font-family: Symbol; mso-bidi-font-size: 12.0pt; mso-fareast-font-family: Symbol;">·<span style="font-family: 'Times New Roman';">         </span></span><!--[endif]--><span face=""Verdana","sans-serif"">If the difference is odd use either n(m+1)=nm+n or n(m-1)=nm-n. Example 37·34=37·35-37=36²-1²-37=1296-1-37=1258. On the other hand, 37·34=37·33+37=35²-2²+37=1225-4+37=1258. </span></span></div><span style="font-size: large;"><br /><br /></span><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWUKzqpxCL8SjEMzUZN70_9fWNZ8vJDSAFlFCSrEzwozkK0hOHGXOUAMajuMEQUVrTrIdkHaD3Ix3KKAgXDGSIJiNSBpc1QSpkjwfLd7AAERsm2RGbKLS5aje5gVGX0yGaqHdNnZEcEZI/s1600/16+Easy+Quantitative+Aptitude+shortcut+tricks+for+all+competitive+exams.jpg" style="margin-left: 1em; margin-right: 1em;"><span style="font-size: large;"><img border="0" height="226" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiWUKzqpxCL8SjEMzUZN70_9fWNZ8vJDSAFlFCSrEzwozkK0hOHGXOUAMajuMEQUVrTrIdkHaD3Ix3KKAgXDGSIJiNSBpc1QSpkjwfLd7AAERsm2RGbKLS5aje5gVGX0yGaqHdNnZEcEZI/s1600/16+Easy+Quantitative+Aptitude+shortcut+tricks+for+all+competitive+exams.jpg" width="320" /></span></a></div><span style="font-size: large;"><br /><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(11) Product of numbers that only differ in units.<br /></span></b><span face=""Verdana","sans-serif"">If the numbers only differ in units and the sum of the units is 10, like with 53 and 57 or 122 and 128, then think of them as, say 10a+b and 10a+c, where b+c=10. The product (10a+b)(10a+c) is given by 100a²+10a(b+c)+bc =&nbs;100a(a+1)+bc. Thus to compute 53 times 57 (a=5, b=3, c=7), multiply 5 times (5+1) to get 30. Append to the result (30) theproduct of the units (3·7=21) to obtain 3021. Similarly 122·128 = 12·13·100+2·8=15616. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(12) Multiplying by 11.<br /></span></b><span face=""Verdana","sans-serif"">To multiply a 2-digit number by 11, take the sum of its digits. If it's a single digit number, just write it between the two digits. If the sum is 10 or more, do not forget to carry 1 over. For example, 34·11=374 since 3+4=7. 47·11=517 since 4+7=11. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(13) Faster subtraction.<br /></span></b><span face=""Verdana","sans-serif"">Subtraction is often faster in two steps instead of one. Example: 427-38=(427-27)-(38-27)=400-11=389. A generic advice might be given as "First remove what's easy, next whatever remains". Another example: 1049-187=1000-(187-49)=900-38=862. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(14) Faster addition.<br /></span></b><span face=""Verdana","sans-serif"">Addition is often faster in two steps instead of one. Example: 487+38=(487+13)+(38-13)=500+25=525. A generic advice might be given as "First add what's easy, next whatever remains". Another example: 1049+187=1100+(187-51)=1200+36=1236. </span><br /><br /><b><span face=""Verdana","sans-serif"" style="color: maroon;">(15) Faster addition, #2.<br /></span></b><span face=""Verdana","sans-serif"">It's often faster to add a digit at a time starting with higher digits. For example, 583+645=583+600+40+5=1183+40+5=1223+5=1228. </span><br /><br /></span><div class="separator" style="clear: both; text-align: center;"> </div><span style="font-size: large;"><b><span face=""Verdana","sans-serif"" style="color: maroon;">(16) Multipliply, then subtract.<br /></span></b><span face=""Verdana","sans-serif"">When multiplying by 9, multiply by 10 instead, and then subtract the other number. For example, 23·9=230-23=207. The same applies to other numbers near those for which multiplication is simplified. 23·51=23·50+23=2300/2+23=1150+23=1173. 87·48=87·50-87·2=8700/2-160-14=4350-160-14=4190-14=4176. </span></span><br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibCH76oNoalphygw3KykSk03MGBJuaEgMHRunFSoMfl4iTRxvkW4fQQNGLK-_tsY-hnsae2EjR5T9H1sBi5bV5YYOHqOA_D3kgfhBuzNS7sqwGtwx0nZx-pI_frpGzc47LCBRJauaFEyY/s1600/top-tips-tricks.jpg" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="205" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEibCH76oNoalphygw3KykSk03MGBJuaEgMHRunFSoMfl4iTRxvkW4fQQNGLK-_tsY-hnsae2EjR5T9H1sBi5bV5YYOHqOA_D3kgfhBuzNS7sqwGtwx0nZx-pI_frpGzc47LCBRJauaFEyY/s1600/top-tips-tricks.jpg" width="320" /></a></div><br /><br /><br /></div>

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16 Easy Quantitative Aptitude short tricks for all competitive exams with practice set Quiz test

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