# CAT 2018 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Number Theory Questions | Question 10

This question from CAT 2018 Question paper tests your knowledge on numbers. Number Theory is another zone to which the CAT Exam gives importance. So, make sure you study this topic really well during your CAT Course Online and solve loads of such questions from CAT Previous Year Paper. Solve this question without looking at the solution to ace your CAT Online Preparation.

Question 10: While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is:
[TITA]

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##### Method of solving this CAT Question from Coordinate Geometry: A clear understanding of graphs and equations will help to solve.

Let the three real numbers be a, b, c. c is taken as 73 instead of 37
So, 73ab = 37ab + 720
36 ab = 720
ab = $$frac{720}{36}$ = 20 We know, AM ≥ GM $\frac{$a^2 + b^2$}{2}) ≥ ab
(a2 + b2) ≥ 2ab
(a2 + b2) ≥ 40
(Or)
ab = 20
(a,b) = (√20, √20)
(a2 + b2) = 20 + 20 = 40

The question is " While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is: The minimum possible value is 40 "

##### Hence, the answer is 40.

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