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

To maximize the length of an integer less then 1,000, we should minimize its prime bases.
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.

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

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"

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 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.' ?

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.
As such, the GMAT would supply have sort of definition accompanying this term (and any other unfamiliar/made-up terms).

Cheers,
Brent