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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If k is an integer
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= (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.
(0.0025)(0.025)(0.00025) × 10^kshahfahad 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
= (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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Another approach is to convert everything to fractions.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 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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(0.0025)(0.025)(0.00025) is already a very small positive number. That is it equals 0.00000somethingshahfahad 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.
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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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.
