Bunuel wrote:
The Official Guide For GMAT® Quantitative Review, 2ND EditionIf Q is an integer between 10 and 100, what is the value of Q?
(1) One of Q's digits is 3 more than the other, and the sum of its digits is 9.
(2) Q < 50
We are given that Q is an integer between 10 and 100, and we must determine the value of Q.
Statement One Alone:One of Q's digits is 3 more than the other, and the sum of its digits is 9.
Statement one alone is not sufficient to answer the question. If we let A = the tens digit and B = the units digit, then we can create the following equations:
A + B = 9
A = B + 3 (keep in mind that this can be reversed)
B + 3 + B = 9
2B = 6
B = 3
Thus, A = 6
So Q could be 36 or 63. Statement one is not sufficient to answer the question.
Statement Two Alone:Q < 50
Only knowing that Q is less than 50 is not enough information to answer the question. Thus, statement two alone is not sufficient to answer the question.
Statements One and Two Together:
From statement one, we see that Q is either 36 or 63. From statement two, Q < 50. So Q must be 36 to satisfy both statements. The two statements together are sufficient to answer the question.
Answer: C
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