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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### GMAT/MBA Expert

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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.**

Anurag Mairal, Ph.D., MBA

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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 "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

**length of an integer**"

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

- neelgandham
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**Posts:**1060**Joined:**13 May 2011**Location:**Utrecht, The Netherlands**Thanked**: 318 times**Followed by:**52 members

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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Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

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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