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CAT 2017 [slot 2] Question with solution 21

Question 55:
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
Option: 4
Explanation:

$(x -1)x(x+1) = 15600$
=> $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


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