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spaceland prep
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- Joined: Thu Feb 24, 2011 10:05 am
- Location: USA
Q. Is x > sqrt(3)?
(1) 3^(-x) = sqrt(27)
(2) log (3^x) - cos (x*pi) = x^(-1/3)
NOTE: Logarithms and trigonometry are not concepts tested on the GMAT.
NOTE: Data sufficiency statements will not contradict one another as they do in this example.
The point of the second statement is to acknowledge that no matter how great one is at math, there will always be something one can't handle. How can this question be confidently answered?
[spoiler]The strategy here is to recognize what needs to be done to answer the question. The questions can be sufficiently answered in two way, 1) yes, x is greater than the square root of three, or 2) no, x is not greater than the square root of three.
Never does the exact value of x come into play. One might be tempted to solve the first statement for x, which deals with concepts tested on the GMAT. But, only a human calculator (or a human with a calculator) could attempt to solve the second statement.
But one needn't be a math person to know that an equation containing a single variable that is not being absolute valued or raised to an even exponent will have a unique solution on the GMAT.
So, applied here, this means Statement (1) is SUFFICIENT and Statement (2) is SUFFICIENT, since each will yield one value for x. It is irrelevant whether x is greater than the square root of three. The answer is EACH statement ALONE is sufficient.
[/spoiler]
The point here is twofold. First, one shouldn't do unnecessary work to answer a question that is solvable by simply understanding the self-imposed restrictions of the GMAT. Second, everyone gets stumped by a math problem sometimes. But if one knows lateral ways of attacking questions, then any mathematical blind spots are less damaging.
(1) 3^(-x) = sqrt(27)
(2) log (3^x) - cos (x*pi) = x^(-1/3)
NOTE: Logarithms and trigonometry are not concepts tested on the GMAT.
NOTE: Data sufficiency statements will not contradict one another as they do in this example.
The point of the second statement is to acknowledge that no matter how great one is at math, there will always be something one can't handle. How can this question be confidently answered?
[spoiler]The strategy here is to recognize what needs to be done to answer the question. The questions can be sufficiently answered in two way, 1) yes, x is greater than the square root of three, or 2) no, x is not greater than the square root of three.
Never does the exact value of x come into play. One might be tempted to solve the first statement for x, which deals with concepts tested on the GMAT. But, only a human calculator (or a human with a calculator) could attempt to solve the second statement.
But one needn't be a math person to know that an equation containing a single variable that is not being absolute valued or raised to an even exponent will have a unique solution on the GMAT.
So, applied here, this means Statement (1) is SUFFICIENT and Statement (2) is SUFFICIENT, since each will yield one value for x. It is irrelevant whether x is greater than the square root of three. The answer is EACH statement ALONE is sufficient.
[/spoiler]
The point here is twofold. First, one shouldn't do unnecessary work to answer a question that is solvable by simply understanding the self-imposed restrictions of the GMAT. Second, everyone gets stumped by a math problem sometimes. But if one knows lateral ways of attacking questions, then any mathematical blind spots are less damaging.
