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

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

by VJesus12 » Fri Jul 24, 2020 6:50 am

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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
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Re: 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?\

by Brent@GMATPrepNow » Fri Jul 24, 2020 8:33 am
VJesus12 wrote: ↑
Fri Jul 24, 2020 6:50 am
 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
Brent Hanneson - Creator of GMATPrepNow.com
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