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:
Explanation:
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).
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