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 Post subject: GMAT Number Theory (Data Sufficiency)Posted: Wed Nov 16, 2011 12:16 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
What is the value of integer n if the inequality 30 > n > 9 holds?
(1) When n is divided by 9, the remainder is 0.
(2) When n is divided by 2, the remainder is 1.

A. Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
B. Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
C. Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
D. Either statement BY ITSELF is sufficient to answer the question.
E. Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, meaning that further information would be needed to answer the question.

(C) Statement (1) alone is not sufficient since both 18 and 27 are divisible by 9 with a zero remainder.

Statement (2) is also not sufficient. Integers between 9 and 30 that may be divided by 2 with a remainder of 1 are: 11, 13, 15, 17, 19, 21, 23, 25, 27, 29.

Taken together, you are able to find the only number that fills both statements: 27.

Remember that, in Data Sufficiency questions, you do not need to actually solve for an answer; you simply need to establish whether you have enough information to solve for one.
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The question asked here is "what is the value of n" and not the question about whether a value of n can be found or not.

If the question is "what is n" then the answer will be option E as we can't find the value of n. If the question asked is "Does the value of n exist in the above inequality" then the option will be C.

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 Post subject: Re: GMAT Number Theory (Data Sufficiency)Posted: Wed Nov 16, 2011 12:25 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
questioner wrote:
If the question is "what is n" then the answer will be option E as we can't find the value of n.
Using statements (1) and (2) together we've found one definite value of n. It is 27.

30 > 27 > 9
(1) When 27 is divided by 9, the remainder is 0.
(2) When 27 is divided by 2, the remainder is 1.

There is NO other number that fits all the three statements.

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