# CAT 2019 Question Paper | Quants Slot 1

###### CAT Previous Year Paper | CAT Quants Questions | Question 12

This is a very time consuming question from CAT 2019 when done in an algebraic manner. It involves a lot of formulas and manipulation of variables. However if you observe the CAT previous year paper, you will observe there are usually questions that can be solved using a mix of your math intuition and option choices. This is one such question. Try both the conventional method & see if you are able to spot the quicker method as well.

Question 12 : The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

1. 50
2. 85
3. 95
4. 58

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Let the two numbers be a and b
From the question, we know
a x b = 616
and =
=
=
=
= - 1 =
=
=
= 3 x 3 x 4 = 36
a - b = 6, ab = 616
616 can be rewritten as 22 x 28, where 28 - 22= 6 using trial and error
So, a + b = 28 + 22 = 50

The question is "The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is "

##### Hence, the answer is 50

Choice A is the correct answer.

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