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C
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Difficulty:
95%
(hard)
Question Stats:
29% (01:38) correct
71%
(01:30)
wrong
based on 410
sessions
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What is the value of xy?
(1) \(3^x*5^y=75\)
(2) \(3^{(x-1)(y-2)}=1\)
M27-22
(1) \(3^x*5^y=75\)
(2) \(3^{(x-1)(y-2)}=1\)
M27-22
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06 Mar 2014, 00:05
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swati007
What is the value of \(xy\)?
Notice that we are not told that the \(x\) and \(y\) are integers.
(1) \(3^x*5^y=75\) --> if \(x\) and \(y\) are integers then as \(75=3^1*5^2\) then \(x=1\) and \(y=2\) BUT if they are not, then for any value of \(x\) there will exist some non-integer \(y\) to satisfy given expression and vise-versa (for example if \(y=1\) then \(3^x*5^y=3^x*5=75\) --> \(3^x=25\) --> \(x=some \ irrational \ #\approx{2.9}\)). Not sufficient.
(2) \(3^{(x-1)(y-2)}=1\) --> \((x-1)(y-2)=0\) --> either \(x=1\) and \(y\) is ANY number (including 2) or \(y=2\) and \(x\) is ANY number (including 1). Not sufficient.
(1)+(2) If from (2) \(x=1\) then from (1) \(3^x*5^y=3*5^y=75\) --> \(y=2\) and if from (2) \(y=2\) then from (1) \(3^x*5^y=3^x*25=75\) --> \(x=1\). Thus \(x=1\) and \(y=2\). Sufficient.
Answer: C.
P.S. Please read carefully and follow: https://gmatclub.com/forum/rules-for-pos ... 33935.html Pay attention to rule 3. Thank youl.
General Discussion
06 Mar 2014, 00:49
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swati007
Since we do not know that x and y are integers hence statement I and II will be insufficient as we can have multiple answers. Combining will be sufficient here as we will have two equations and two answers.
