Applyo - College Application Platform

CAT 2017 Slot 2 QA Question & Solution

AlgebraMedium

Question

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

Options

1777
1785
1875
1877

Solution

$(x -1)x(x+1) = 15600$
=> $x^3 - x= 15600$
The nearest cube to 15600 is 15625 = $25^3$
We can verify that x = 25 satisfies the equation above.
Hence the three numbers are 24, 25, 26. Sum of their squares = 1877