CAT Quantitative Aptitude questions can be solved easily with the help of some shortcut methods and tricks. However, these tricks can be applied to every question but you can save your time and effort by applying these tricks on questions where you need squares, averages of the numbers, etc. Download CAT Question Paper

CAT Quantitative Aptitude section is heavily reliant on the candidate's speed of calculation and accuracy. In order to clear the CAT Cut-Offs, candidates have to make sure that they are thorough with the shortcuts for the Quant section, as it can help in shaving off time, improving confidence, and scoring well. Check CAT 2021 Syllabus. 

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CAT QA Shortcut Method to Calculate Square 

CAT QA ShortCut for Multiplication

Method 1: Base

• One number is used as a base
• For eg. 10 - number closer must be taken

105 x 107

• 100 is taken as base as it is closer to both 105 and 107
• Right: Product of Surplus. Since base = 100, and surplus is 5 and 7. 
• Left: Either number plus surplus of either number i.e either 105+7 or 107+5
• Left would be equivalent to number x 100 ie 112 x 100 = 11,200
• Add right and left - 11200 + 35 = 11,235

Method 2: Units Digit Method

• Sum of units digit is used provided that LHS of unit degree is the same. 
• E.g: 75 x 75

The sum of the units digit = 10, so we add 1.0 in one of the digits on the left-hand side.

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CAT QA Shortcut for Squaring: Base 10 Method

Square of 9 using this method: 

• Since 9 is 1 less than 10, decrease it still further to 8. This is the left side of our answer.
• On the right-hand side, put the square of the deficiency that is 12. Hence, the answer is 81. Similarly, 82 = 64, 72 = 49
• For numbers above 10, look at the surplus instead of the deficit. For example,

112 = (11 + 1); 10 + 12 = 121

122 = (12 + 2); 10 + 22 = 144

142 = (14 + 4); 10 + 42 = 18; 10 + 16 = 196 and so on

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CAT QA ShortCut for Finding Average/Change in Average

• Find difference between old average and new average. 
• Divide difference by the sample size
• Multiply average increase you found in step 2 by sample size

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CAT QA Algebra Shortcuts

1. If one is in ratio, the other one is zero

• This is used to solve simple simultaneous equations with big numbers.
• EG: 

6x + 7y = 8

19x + 14y = 16

Here, the ratio of coefficients of y is the same as that of the constant terms. Therefore, the ‘other’ is zero, i.e., x = 0. Hence, the solution of the equations is x = 0 and y = 8/7.

Alternatively,

19x + 14y = 16 is equivalent to (19/2)x + 7y = 8. 

Therefore, x has to be zero and no ratio is needed; divide by 2.

Note that it would not work if both had been ‘in ratio’:

6x + 7y = 8

12x + 14y = 16

2. When samuccaya is the same, then that samuccaya is zero.

• This formula is useful for solving equations that can be solved visually. 
• ‘Samuccaya’ has various meanings
• It may mean a term which occurs as a common factor in all the terms concerned.

For example, an equation ‘12x + 3x = 4x + 5x’. Since ‘x’ occurs as a common factor in all the terms, therefore, x = 0 is the solution. 

• Samuccaya can also be the product of independent terms. 

For instance, in (x + 7) (x + 9) = (x + 3) (x + 21), the samuccaya is 7 × 9 = 3 × 21; therefore, x = 0 is the solution. 

• It can be also the sum of the denominators of two fractions having the same numerical numerator, 

for example: 1/(2x − 1) + 1/(3x − 1) = 0 means 5x − 2 = 0

• The more commonly used meaning of the word is total. 

For instance, if the sum of the numerators and the sum of denominators are the same, then that sum is zero.

• This meaning (‘total’) can also be applied in solving quadratic equations. The total meaning not only implies sum but also subtraction.
• Mental cross multiplication reveals that the resulting equation is quadratic 
• This yields the other root of a quadratic equation.
• The interpretation of ‘total’ is also applied in multi-term RHS and LHS. For instance, consider 
• There are several other cases where samuccaya can be applied with great versatility.

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CAT Sample Questions for Preparation

Ques: What will be the sum of the roots if f(5 + x) = f(5 - x) for every real x and f(x) = 0 and has 4 different real roots?

1. 0
2. 40
3. 10
4. 20

Solution: 4

Ques: If a>0 then what will be the mean of a four-digit even and natural number which can be represented as aabb?

1. 5544
2. 4466
3. 4864
4. 5050

Solution: 1

Ques: If x, y and z are positive integers such that xy = 432, yz = 96, and z < 9, then what will be the smallest possible value of x+y+z?

1. 56
2. 49
3. 46
4. 59

Solution: 3

TITA Type Questions in CAT 

Ques: The area of the region satisfying the inequalities |x| - y ≤ 1, y ≥ 0, and y ≤ 1 is

Solution: 3

Ques: What will be the value of y if log4 5 = (log4 y) (log6 √5)?

Solution: 36

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