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 Post subject: GMAT Number Theory
PostPosted: Tue Dec 21, 2010 6:19 pm 
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Let x be a two-digit number whose tens digit is t and whose units digit is u. What is the value of x?
(1) x is a multiple of 15.
(2) The sum of the digits t and u is 9.

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.

(E) (To understand units and tens, in 75 7 is tens and 5 is units.) Two-digit numbers are the integers from 10 to 99. Statement (1) alone is not sufficient since there are six possible multiples of 15: 15, 30, 45, 60, 75, 90.

Statement (2) alone is not sufficient either, since all multiples of 9 between 18 and 99 will have digits that add up to 9.

Taken together, the two statements are still insufficient. Both the numbers 45 and 90 will satisfy the conditions of the two statements. Because there are two possible answers, we do not have sufficient information to determine the two-digit number.

Since both statements are insufficient, even combined, the correct answer is choice (E).
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I feel that C is the correct answer. Because 90 is the number which is a multiple of 15 and the sum of two digits (9 + 0) is equal to 9.


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 Post subject: Re: GMAT Number Theory
PostPosted: Tue Dec 21, 2010 6:23 pm 
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Joined: Sun May 30, 2010 2:23 am
Posts: 498
90 fits the both criteria. However it is NOT the only number which fits.
E.g. 45 fits the both criteria as well: 45 is a multiple of 15, 4 + 5 = 9.

Therefore we CANNOT give a definite answer in this case. The both statements taken together are insufficient.


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