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16 Sep 2014, 01:49
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
60% (01:26) correct
40%
(01:18)
wrong
based on 80
sessions
History
Date
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Result
Not Attempted Yet
16 Sep 2014, 01:49
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Official Solution:
We must determine if \(x\) is greater than \(y\).
Statement 1 tells us that \(6x \gt 5y\). To isolate \(x\), we divide both sides by 6, leaving \(x \gt \frac{5}{6} y\). From this inequality, there is no way to tell if \(x \gt y\) or if \(\frac{5}{6}y \lt x \lt y\). For example, if \(x = 13\) and \(y = 12\), then statement 1 becomes \(13 \gt \frac{5}{6}(12)\), or \(13 \gt 10\), which is true, and \(x \gt y\). If, however, \(x = 11\) and \(y = 12\), then statement 1 becomes \(11 \gt \frac{5}{6}(12)\), or \(11 \gt 10\), which is also true, only now \(y \gt x\). In other words, \(x\) can be greater than or less than \(y\). Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice is B, C, or E.
Statement 2 tells us that the product of \(x\) and \(y\) is less than 0. This can only be the case if one, but not both, of \(x\) and \(y\) is negative, and one, but not both, of \(x\) and \(y\) is positive. Yet without further information, there is no way to tell which one is negative and which one is positive, and thus no way to tell if \(x \gt y\). Statement 2 is NOT sufficient. Eliminate answer choice B. The correct answer must be either C or E.
Considering the statements together, we know that one of \(x\) and \(y\) is positive and one is negative, and that \(x \gt \frac{5}{6}y\). Since no negative number can be greater than the product of a positive fraction and a positive number, we know that \(x\) must be positive and that \(y\) must be negative. Thus, \(x \gt y\). The statements together are sufficient to answer the question.
Answer: C
We must determine if \(x\) is greater than \(y\).
Statement 1 tells us that \(6x \gt 5y\). To isolate \(x\), we divide both sides by 6, leaving \(x \gt \frac{5}{6} y\). From this inequality, there is no way to tell if \(x \gt y\) or if \(\frac{5}{6}y \lt x \lt y\). For example, if \(x = 13\) and \(y = 12\), then statement 1 becomes \(13 \gt \frac{5}{6}(12)\), or \(13 \gt 10\), which is true, and \(x \gt y\). If, however, \(x = 11\) and \(y = 12\), then statement 1 becomes \(11 \gt \frac{5}{6}(12)\), or \(11 \gt 10\), which is also true, only now \(y \gt x\). In other words, \(x\) can be greater than or less than \(y\). Statement 1 is NOT sufficient to answer the question. Eliminate answer choices A and D. The correct answer choice is B, C, or E.
Statement 2 tells us that the product of \(x\) and \(y\) is less than 0. This can only be the case if one, but not both, of \(x\) and \(y\) is negative, and one, but not both, of \(x\) and \(y\) is positive. Yet without further information, there is no way to tell which one is negative and which one is positive, and thus no way to tell if \(x \gt y\). Statement 2 is NOT sufficient. Eliminate answer choice B. The correct answer must be either C or E.
Considering the statements together, we know that one of \(x\) and \(y\) is positive and one is negative, and that \(x \gt \frac{5}{6}y\). Since no negative number can be greater than the product of a positive fraction and a positive number, we know that \(x\) must be positive and that \(y\) must be negative. Thus, \(x \gt y\). The statements together are sufficient to answer the question.
Answer: C
20 Jun 2015, 08:16
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hi
just wondering , it doesn't say than x and y are integers, so if x were to be .3 and y .31 then the answer would be E?
just wondering , it doesn't say than x and y are integers, so if x were to be .3 and y .31 then the answer would be E?
