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CAT 2017 Slot 2 — QA Question 21

Number TheoryEasy

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

Answer & solution

  • A

    1777

  • B

    1785

  • C

    1875

  • 1877

Solution

Since 15600 is product of 3 consecutive we can start by taking the cube of an integer closest to 15600, which is actually 15625

Now 156253=25

Dividing 15600 by 25 we get 624
624 can be expressed as a product of 24 and 26. So the 3 consecutive positive integers are 24, 25 and 26

242 + 252 + 252 = 576 + 625 + 676 = 1877

Hence, option (d).

CAT 2017 Slot 2 QA Q21: If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers i — Solution | TheCATExam