What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
OA IS B
length
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- Anurag@Gurome
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To maximize the length of an integer less then 1,000, we should minimize its prime bases.grandh01 wrote:What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
OA IS B
Minimum prime base = 2
So, 2^x < 1,000
or x < 10
Maximum length = 9 for 2^9 = 512
Also, note that 2^9 is not the only integer whose length is 9, for example 2^8 * 3 = 768 < 100 also has the length of 8 + 1 = 9
The correct answer is B.
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- Brent@GMATPrepNow
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I think I should mention that we're missing a pretty important part of this question. The GMAT does not expect people to know the term "length of an integer"grandh01 wrote:What is the greatest possible length of
a positive integer less than 1,000?
(A) 10
(B) 9
(C) 8
(D) 7
(E) 6
OA IS B
Excerpt from another question: For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k.
For example, if k = 24, the length of k is equal to 4, since 24 = (2)(2)(2)(3)
If k = 30, the length of k is equal to 3, since 30 = (2)(3)(5)
Cheers,
Brent
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Brent: If such a question appears in the exam, will it contain this information - 'For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k.' ?
Anil Gandham
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The GMAT would never assume that you know what "length of an integer" means. In fact, I don't believe there's an existing mathematical definition of this term that matches the GMAT's definition.neelgandham wrote:Brent: If such a question appears in the exam, will it contain this information - 'For any integer k > 1, the term "length of an integer" refers to the number of positive prime factors, not necessarily distinct, whose product is equal to k.' ?
As such, the GMAT would supply have sort of definition accompanying this term (and any other unfamiliar/made-up terms).
Cheers,
Brent