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# Quantitative Aptitude Tricks & Shortcuts for CAT 2018

Oct 17, 2018 15:53 IST

CAT Toppers have termed Quantitative Aptitude section as the most scoring section in the CAT exam. However, at the same time, they also claim that Quant questions can be very tricky and time-consuming, if you don’t know the right way around them. Therefore, in order to crack Quantitative Aptitude section, CAT aspirants have to learn and adopt several Quant tricks and Quant shortcuts. Let’s find out the most common Quant shortcuts and tricks that can help you in solving the Quantitative Aptitude questions quickly.

## 1. Squares of Two Digit Numbers

This Quant Shortcut helps aspirants find squares of two digit numbers easily. In order to do so, aspirants can follow the below-given steps:

• Step 1: Find the difference for the number of which you need the square from 25àThis will be the first two digits of the Answer
• Step 2: Find the square of the difference for the number of which you need the square from 50àthis will the last two digits of the Answer. In case of carry over, please add the carry over to the answer derived through the first step.

Example:

1. If you want to find square of 51 or 512

• Step 1: Difference from 25 à 51-25 = 26
• Step 2: Difference from 50 à51-50= 01
• Now we need to find the square of 01 that would be 01

2. Let us try with 63

• Step 1: Difference from 25 is 38
• Step 2: Difference from 50 is 13
• Step 3: Square of 13 is 169
• Answer of Step 1 (first two digits): = 38+1 = 39
• Answer of Step 2 (last two digits): And last 2 digits of 169= 69

3. Now let us try with a smaller number 28

• Step 1: Difference with 25 is 3
• Step 2: Difference with 50 is 22
• Step 3: Square of 22 is 484
• Answer of Step 1 (first two digits): 3 plus 4= 7
• Answer of Step 2 (last two digits): of 484 i. e. 84

## 2. Squares of Three Digit Numbers

To find square of a three digit number using traditional mathematical process is a time consuming process, which is not ideally suited for CAT exam. Therefore, candidates can use to below given short-cut method to find squares of 3 digit numbers.

Find Square of XYZ

• Step 1: Last digit = Square of Last Digit (Z)
• Step 2: Second last digit = 2*Y*Z + any carryover from STEP 1
• Step 3: Third last digit 2*X*Z+ Square(Y) + any carryover from STEP 2
• Step 4: Fourth last digit is 2*X*Y + any carryover from STEP 3
• Step 5: Beginning of result will be Square(X) + any carryover from Step 4

Example:

Find the square of 221

• Step 1: Last digit àSquare of Last Digit (1) = 1
• Step 2: Second last digit à 2*2*1 + any carryover from STEP 1=4+0=4
• Step 3: Third last digit =2*2*1+ Square of 2 + any carryover from STEP 2 à 8
• Step 4: Fourth last digit is 2*2*2 + any carryover from STEP 3 à8
• Step 5: Beginning of result will be Square(2) + any carryover from Step 4 à4

Example: Find the square of 771

• Step 1: Last digit = Square of Last Digit 1 =1
• Step 2: Second Last digit= 2*7*1+ 0= 14
• Step 3:  2*7*1+49+1 = 64
• Step 4:  2*7*7+6=104
• Step 5: Square of 7 +10=59

Example: Find the square of 111

• Step 1:  Last digit= Square of Last Digit i.e. 1= 1
Step 2: Second Last digit:  2*1*1+0=2
• Step 3: Third digit: 2*1*1+ square of 1+ 0=3
• Step 4: Fourth digit: 2*1*1+0=2
• Step 5:  Beginning of the result= square of 1= 1

## 3. Finding Average or Change in Average

Here’s how you can find averages or change in average questions quickly using a shortcut technique.

• Step 1: Calculate difference between old average and new number
• Step 2: Divide the difference by the sample size for average à it will give you average increase
• Step 3: Multiply the average increase by the sample size

Example: The average of a batsman in 16 innings is 30. In the next innings, he is scoring 70 runs. What will be his new average?

Answer throughRegular Method: Total runs scored by the batsman in 17 innings: 480+70=550

Total innings played= 17

Hence, the new average = 550/17=32.35

Answer using the Short Cut technique:

• Step 1: Take the difference between the new score and the old average = 70 – 30= 40
• Step 2:40 extra runs are spread over 17 innings. So, the innings average will increase by 40/17 = 2.35
• Step 3: Hence, the average increases by => 30+2.35 = 32.35.

Example 2: The average marks of 20girls in a particular school are 50. When a new girl with marks 80 joins the class, what will be the new average of the class?

• Step 1: Take the difference between the new marks and the old average marks = 80 – 50= 30
• Step 2: 30 extra marks are spread over 21 girls. So, the average marks will be increased by: 30/21= 1.43
• Step 3: Hence the new average = 50+1.43= 51.43

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