# CAT 2017 Question Paper | Quants Slot 2

###### CAT Previous Year Paper | CAT Number Theory Questions | Question 21

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Question 21 : If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

1. 1777
2. 1785
3. 1875
4. 1877

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##### Method of solving this CAT Question from Number Theory

Given that the product of three consecutive positive integers is 15600 and we have to find the sum of the squares of the integers
As we have two zeroes in 15600 we should have some number ending in zero or in five
156 = 12 × 13
15600 = 12 × 13 × 100 = 12 × 13 × 25 × 4
15600 = 24 × 25 × 26
The product of n (n+1)(n+2) should have a multiple of 52
The sum of the squares of these integers 24 , 25 , 26 is
242 + 262 + 252 = 576 + 625 + 676
242 + 262 + 252 = 1877

The question is "If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is"

##### Hence, the answer is 1877

Choice D is the correct answer

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