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XAT 2016 — QA & DI Question 17

FactorsMedium

For two positive integers a and b, if (a + b)(a+b) is divisible by 500, then the least possible value of a × b is:

Answer & solution

  • A

    ​​​​​​​8

  • 9

  • C

    10

  • D

    12

  • E

    None of the above

Solution

500 = 22 × 53

For (a + b)(a+b) to be divisible by 500, it should have power of 2 as well as 5 in it.

∴ a + b should have power of both 2 as well as 5.

The least such number is 1010.

∴ a + b = 10.

∴ a × b is minimum when a = 9 and b = 1 (or vice-versa)

Hence, the least possible value is 9.

Hence, option (b).

XAT 2016 QA & DI Q17: For two positive integers a and b, if (a + b) (a+b) is divisible by 500, then the least possible value of a &t — Solution | TheCATExam