If \(k\) is an integer and \((0.0025)(0.025)(0.00025)10^k\) is an integer, what is the least possible value of \(k?\)

[VJesus12]

If \(k\) is an integer and \((0.0025)(0.025)(0.00025)10^k\) is an integer, what is the least possible value of \(k?\)

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12

[spoiler]OA=E[/spoiler]

Source: Official Guide

[Brent@GMATPrepNow]

If \(k\) is an integer and \((0.0025)(0.025)(0.00025)10^k\) is an integer, what is the least possible value of \(k?\)

(A) -12
(B) -6
(C) 0
(D) 6
(E) 12

[spoiler]OA=E[/spoiler]

Source: Official Guide

One approach is to convert everything to fractions.

(0.0025)(0.025)(0.00025) × 10^k is an integer
So, (25/10,000)(25/1,000)(25/100,000) × 10^k is an integer
Simplify to get: (25³/1,000,000,000,000) × 10^k is an integer
To create an integer, we need 1,000,000,000,000 to EQUAL 10^k
So, k = 12

Answer: E

Cheers,
Brent