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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> <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> <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;"> </div><div class="MsoNormal" style="background: white; margin-top: 9pt; mso-outline-level: 3;"> </div><div class="MsoNormal" style="background: white; margin-top: 9pt; mso-outline-level: 3;"> </div><div align="center" class="MsoNormal" style="background: white; text-align: center;">MATHEMATICS<o:p></o:p></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"> </div><div class="MsoNormal" style="background: white;">Whenever we are going to solve any competitive exam`s  questions  paper we have four subjects to solve: -<o:p></o:p></div><div class="MsoNormal" style="background: white;">1. Computer  <o:p></o:p></div><div class="MsoNormal" style="background: white;">2. English  <o:p></o:p></div><div class="MsoNormal" style="background: white;">3. General knowledge   <o:p></o:p></div><div class="MsoNormal" style="background: white;">4. Reasoning<o:p></o:p></div><div class="MsoNormal" style="background: white;">5. Mathematics  <o:p></o:p></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"> </div><div class="MsoNormal" style="background: white;">            Dear friends, when we are fighting any competitive exam, whether it is <a href="http://www.ibps.in/">IBPS</a>, <a href="http://www.ssc.nic.in/">SSC</a> 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.<o:p></o:p></div><div class="MsoNormal" style="background: white;">  Now you will ask how, Here I am telling you how to calculate fast in second.<o:p></o:p></div><div class="MsoNormal" style="background: white;"> </div><div class="MsoNormal" style="background: white;">                         <o:p></o:p></div><div class="MsoNormal" style="background: white;">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…………<o:p></o:p></div><div class="MsoNormal" style="background: white;">Multiplication: -<o:p></o:p></div><div class="MsoNormal" style="background: white;">Multiply the Two Digit numbers:-<o:p></o:p></div><div align="center" class="MsoNormal" style="background: white; text-align: center;"> </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;"><img border="0" height="240" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjsK5CzTk5n1LKvMX7b005Xe3SbSMdmuHYqcP17ihYT4dyMFb0LRtrs8LeF4majZAzEFX3sWr_2S7WuPBCenhaC8Wow4O4FQ6NNXvW3N863QGuOcRpmNgRB9OZUWMr6zIU310EbbrdPYs0/s1600/www.topnaukrialert.com.png" width="320" /></a></div><div align="center" class="MsoNormal" style="background: white; text-align: center;">  <o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">      1. First we are taking two two-digit numbers AB and CD. <o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">      2. Now, the digit of unit of the first number multiplied by the digit of unit of the second number.<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">      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.<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">      4. Again, the ten-digit of the first number multiplied by the ten-digit of the second number.<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">     Example:-   </div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">           4          3<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">                                                                       <o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">  +      7           5<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">      _____________       <o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">              3225<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">      _____________<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">          3 x 5 = 15<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">          carry =  1<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">          4 x 5 = 20<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">         7 x 3 = 21<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">   +  _________<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">            42<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">        Carry =  4<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">        4 x 7 = 28<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">  + __________<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">           32<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"> </div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">    For the three-digit number:- <o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">                   A          B          C<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">  </div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">        X <o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">                    D         E           F<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">________________________________<o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">  AD/AE+BD/BE+AF+CD/BF+CE/CF                                                                                                                <o:p></o:p></div><div class="MsoNormal" style="background: white; text-indent: -0.25in;"> </div><div class="MsoNormal" style="background: white; text-indent: -0.25in;">      earlier you feel that it is something difficult than our regular method of  multiplying because we are not familiar with this method , But when  we regularly calculate with this method you find it is more easy and quick from that of our regular multiplying method.</div>So take example questions of your books and try solving by this method , you will find that this is the most easiest method to multiplication. And you can solve maths paper quickly in any of the competitive exams<div> </div><div> </div><div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">For multiplication by 5, you should multiply the figure given by 10 and then divide it by 2.<o:p></o:p></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">e.g. 12986 × 5 = 129860/2 = 64930.<o:p></o:p></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"> </div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">For multiplication by 25, you should multiply the figure given by 100 and then divide it by 4.<o:p></o:p></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">e.g. 12986 × 25 = 1298600/4 = 324650.<o:p></o:p></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"> </div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;">For multiplication by 125, you should multiply the figure given by 1000 and then divide it by 8.<o:p></o:p></div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"> </div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"> </div><div class="MsoNormal" style="background: rgb(252, 254, 255); mso-margin-bottom-alt: auto; mso-margin-top-alt: auto;"><div dir="ltr" style="font-family: Helvetica, Arial, sans-serif; font-size: 14px;" trbidi="on">Jobklix provides you recruitment notifications only you should refer official website of related department. 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Maths : How To Calculate/Multiply Fast in Competitive Exams - Tricks

MATHEMATICS Whenever we are going to solve any competitive exam`s questions paper we have four subjects to solve: - 1. Computer 2. Eng...

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;">10 rules to Use of 'A' 'An' & 'The'  English Grammar Short Tricks with examples </h2><div class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; margin: 9pt 0in 0.0001pt;"> </div><div class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; margin-bottom: 0.0001pt;"> Here  we are going to learn about Articles. Let's see how to use articles : Before using articles first we have to learn their rules : <a href="https://www.blogger.com/null" name="more"></a> 1. Use of 'A'  : 'A' is used in case of a countable giving out a consonant sound. Examples  : I. He has a book in his hand. II. He is a one eyed man. III. She is a B. A.   2. Use of 'An'  : 'An' is used in case of a countable giving out a vowel sound. Examples  : I. She bought an umbrella. II. She is an honest lady. 3. 'A(n)' should be placed between 'Half' and a noun and after 'many' 'what' and 'opportunity'. Examples  : I. We came after half an hour. II. She gave me half a dozen pencil. III. Many a man is born in object poverty. IV. What an opportunity you have missed! 4. 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 . Examples  : I. A cigarette is made of a paper and tobacco. II. He was ready with a cup and saucer. 5. 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. Examples  : I. He visit the town once in a blue moon. II. He can walk six miles an hour . III. A Mr. John is at the door. 6. Article 'the' should be used with the name of the following : rivers, mountains, monuments, great books, ocean, island, descriptive names of countries, newspaper, directions, unique things etc. Examples  : I. A flying saucer was seen encircling over the Atlantic. II. The Thames discharged several crores of cusecs of water into the sea every year. III. The Indian express has the largest circulation in Nepal. IV. The sun risen in the east. V. The moon is the nearest planet to the earth. VI. They went to Agra to see the Taj Mahal. VII. The U.S.A. and The U.S.S.R. are the most powerful countries of the world. 7. The definite article 'the' should be used with the superlative degrees and comparative degrees (when two), and with two noun (proper and common noun) naturally going together and spoken of as a unit. Examples  : I. She is the best student of the class. II. The more you eat, the more hungry you feel. III. The Agra University was founded in 1927. 8. 'The' 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. Examples  : I. Please close the doors. II. Will you have a walk by the river. 9. It is also used to indicate vague time and part of the day. Example  :  I. He came in the evening. II. They always play in the morning. III. He will have lunch in the afternoon. 10. The definite article 'the' should not be used with the names of the following : games, disease, colours, days, months etc. Examples  : I. I am suffering from typhoid. II. His shirt is dyed in green. III. They came on Monday last. IV. They meet us in January last. 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.<o:p style="font-size: 11.5pt;"></o:p></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> <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> <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;"> </div><div class="MsoNormal" style="background-color: white; background-position: initial initial; background-repeat: initial initial; margin-bottom: 0.0001pt;"> </div></div>

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

10 rules to Use of 'A' 'An' & 'The' English Grammar Short Tricks with examples Here we are going to learn ab...

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

<h2 style="text-align: left;">16 Easy Quantitative Aptitude short tricks for all competitive exams with practice set Quiz test</h2><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/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;"> </div>(1) Multiplication by 5 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. (2) Division by 5 Similarly, it's often more convenient instead to multiply first by 2 and then divide by 10. For example, 1375/5=2750/10=275. (3) Division/multiplication by 4 Replace either with a repeated operation by 2. For example 124/4=62/2=31. Also, 124·4=248·2=496. (4) Division/multiplication by 25 Use operations with 4 instead. For example, 37·25=3700/4=1850/2=925. (5) Division/multiplication by 8 Replace either with a repeated operation by 2. For example 124·8=248·4=496·2=992. (6) Division/multiplication by 125 Use operations with 8 instead. For example, 37·125=37000/8=18500/4=9250/2=4625. (7) Squaring two digit numbers. You should memorize the first 25 squares: <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%"> 1 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 2 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 3 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 4 </td> <td style="padding: 1.5pt; width: 7%;" width="7%"> 5 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 6 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 7 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 8 </td> <td style="padding: 1.5pt; width: 7%;" width="7%"> 9 </td> <td style="padding: 1.5pt; width: 7%;" width="7%"> 10 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 11 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 12 </td> <td colspan="2" style="padding: 1.5pt; width: 8%;" width="8%"> 13 </td> <td style="padding: 1.5pt; width: 8%;" width="8%"> 14 </td> </tr><tr> <td style="padding: 1.5pt; width: 7%;" width="7%"> 1 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 2 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 9 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 16 </td> <td style="padding: 1.5pt; width: 7%;" width="7%"> 25 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 36 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 49 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 64 </td> <td style="padding: 1.5pt; width: 7%;" width="7%"> 81 </td> <td style="padding: 1.5pt; width: 7%;" width="7%"> 100 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 121 </td> <td colspan="2" style="padding: 1.5pt; width: 7%;" width="7%"> 144 </td> <td colspan="2" style="padding: 1.5pt; width: 8%;" width="8%"> 169 </td> <td style="padding: 1.5pt; width: 8%;" width="8%"> 196 </td> </tr><tr> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 15 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 16 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 17 </td> <td colspan="3" style="padding: 1.5pt; width: 9%;" width="9%"> 18 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 19 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 20 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 21 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 22 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 23 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 24 </td> <td colspan="2" style="padding: 1.5pt; width: 10%;" width="10%"> 25 </td> </tr><tr> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 225 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 256 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 289 </td> <td colspan="3" style="padding: 1.5pt; width: 9%;" width="9%"> 324 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 361 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 400 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 441 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 484 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 529 </td> <td colspan="2" style="padding: 1.5pt; width: 9%;" width="9%"> 576 </td> <td colspan="2" style="padding: 1.5pt; width: 10%;" width="10%"> 625 </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"> </div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;">·         Squares of numbers from 26 through 50. 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. </div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;">·         Squares of numbers from 51 through 99. 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. </div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;">·         Squares of numbers from 51 through 99, second approach (this one was communicated to me by my father Moisey Bogomolny). 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. Answer: 572=3249. </div><div style="margin-left: 0.5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -0.25in;">·         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. </div> (8) Squares of numbers that end with 5. 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). (9) Product of two one-digit numbers greater than 5. 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. The explanation comes from the following formula: <div class="MsoNormal">(5 + a)(5 + b) = 10(a + b) + (5 - a)(5 - b) </div>In our example, a = 2 and b = 4. (10) Product of two 2-digit numbers. <div style="margin-left: 0.5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -0.25in;">·         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. </div><div style="margin-left: 0.5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -0.25in;">·         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. </div> <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;"><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" /></a></div> (11) Product of numbers that only differ in units. 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. (12) Multiplying by 11. 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. (13) Faster subtraction. 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. (14) Faster addition. 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. (15) Faster addition, #2. 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. <div class="separator" style="clear: both; text-align: center;"> </div>(16) Multipliply, then subtract. 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.  <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> </div>

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

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