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If k is an integer

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by shahfahad » Thu Nov 26, 2015 1:39 am
Q: 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


Answer is E.

Why couldn't the answer be -12 as it is asking for the LEAST possible value.
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by GMATGuruNY » Thu Nov 26, 2015 4:00 am
When posting problems, please use the spoiler function to hide the OA.
shahfahad wrote:Q: 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
(0.0025)(0.025)(0.00025) × 10^k

= (25)(10ˉ�)(25)(10ˉ³)(25)(10ˉ�)(10^k)

= 25³(10ˉ¹²)(10^k).

We can PLUG IN THE ANSWERS, which represent the least possible value of k.

A: 25³(10ˉ¹²)(10ˉ¹²) = 25³(10ˉ²�).
B: 25³(10ˉ¹²)(10ˉ�) = 25³(10ˉ¹�).
C: 25³(10ˉ¹²)(10�) = 25³(10ˉ¹²).
D: 25³(10ˉ¹²)(10�) = 25³(10ˉ�).
E: 25³(10ˉ¹²)(10¹²) = 25³(10�) = 25³.

Only E yields an integer value

The correct answer is E.
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by Brent@GMATPrepNow » Thu Nov 26, 2015 11:54 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
Another 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

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Brent
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by Brent@GMATPrepNow » Thu Nov 26, 2015 11:58 am
shahfahad wrote:Q: 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


Answer is E.

Why couldn't the answer be -12 as it is asking for the LEAST possible value.
(0.0025)(0.025)(0.00025) is already a very small positive number. That is it equals 0.00000something
10^(-12) = 0.000000000001
So, multiplying an already small number by 0.000000000001 will not result in an integer.

Here's a free video on negative exponents - https://www.gmatprepnow.com/module/gmat- ... video/1028
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by shahfahad » Thu Nov 26, 2015 11:58 am
Got it. We need a value of offset the 10^-12 value so the answer is 12. Otherwise, the other options would not yield an integer.
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by Matt@VeritasPrep » Fri Nov 27, 2015 12:00 am
You could also think of what you'd need to do to make the expression an integer. Since (.0025)*(.025)*(.00025) is already less than 1, multiplying it by some very small fraction (such as 10�¹²) wouldn't make it an integer, it'd actually make it a smaller fraction than it already is.
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