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20 Jun 2015, 11:36
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A
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:
62% (01:16) correct
38%
(01:21)
wrong
based on 150
sessions
History
Date
Time
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Not Attempted Yet
20 Jun 2015, 11:36
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Official Solution:
Is \(x^3 < 3^y\)?
Note that \(x^3\) can be positive (if \(x\) is positive), negative (if \(x\) is negative), or 0 (if \(x = 0\)), while \(3^y\) can only be positive (a positive number raised to any power is positive).
(1) \(5^x = \frac{1}{25}\)
\(5^x = 25^{-1}\);
\(5^x = 5^{-2}\);
\(x = -2\).
Thus, \(x^3 = (-2)^3 = -8\), which is negative.
Therefore, \((x^3 = negative) < (3^y = positive)\). Sufficient.
(2) \(y^5 = -32\).
From above, we can deduce that \(y^5 = (-2)^5\), which implies that \(y = -2\). Thus, \(3^y = \frac{1}{9}\). However, we don't know the value of \(x\) to evaluate \(x^3\) and compare it to \(3^y = \frac{1}{9}\). Not sufficient.
Answer: A
Is \(x^3 < 3^y\)?
Note that \(x^3\) can be positive (if \(x\) is positive), negative (if \(x\) is negative), or 0 (if \(x = 0\)), while \(3^y\) can only be positive (a positive number raised to any power is positive).
(1) \(5^x = \frac{1}{25}\)
\(5^x = 25^{-1}\);
\(5^x = 5^{-2}\);
\(x = -2\).
Thus, \(x^3 = (-2)^3 = -8\), which is negative.
Therefore, \((x^3 = negative) < (3^y = positive)\). Sufficient.
(2) \(y^5 = -32\).
From above, we can deduce that \(y^5 = (-2)^5\), which implies that \(y = -2\). Thus, \(3^y = \frac{1}{9}\). However, we don't know the value of \(x\) to evaluate \(x^3\) and compare it to \(3^y = \frac{1}{9}\). Not sufficient.
Answer: A
05 Jun 2016, 00:36
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Good Question
Learning :- don't hurry to mark your answer, direct answers could be a GMAT Trap
Learning :- don't hurry to mark your answer, direct answers could be a GMAT Trap
