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CAT 2000 — QA Question 39

Number TheoryEasy

Let N = 553 + 173 – 723. N is divisible by

 

Answer & solution

Correct answer: both 3 and 17

  • A

    both 7 and 13

  • B

    both 3 and 13

  • C

    both 17 and 7

  • both 3 and 17

Solution

N = 553 + 173 − 723 = 553 + 173 +(−723)

It is known that if a + b + c = 0 then a3 + b3 + c3 = 3abc.

In the given expression, 55 + 17 + (−72) = 0

∴ N = 3 × 55 × 17 × (−72)

∴ N is divisible by both 3 and 17.

Hence, option (d)

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CAT 2000 QA Q39: Let N = 55 3 + 17 3 – 72 3 . N is divisible by — Solution | TheCATExam