Sum of Squares of Consecutive Integers

CAT 2017 Slot 2 · Quantitative Ability · Hard · Number Theory

This is a hard Quantitative Ability question from the CAT 2017 Slot 2 paper. It tests Number Theory. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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

A.
1777
B.
1785
C.
1875
D.
1877

Answer

Explanation

Let the three consecutive integers be $n-1, n, n+1$ .

Product $(n-1)n(n+1) = n^3 - n = 15600$ .

Since $n^3 \approx 15600$ , $n \approx \sqrt[3]{15600} \approx 25$ .

Let's test $n = 25$ : $24 \times 25 \times 26 = 15600$ .

Sum of squares = $(n-1)^2 + n^2 + (n+1)^2 = 24^2 + 25^2 + 26^2 = 576 + 625 + 676 = 1877$ .

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Sum of Squares of Consecutive Integers

Explanation

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