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Given that a>1 and b>1. Is (a^x)(b^y)<1? (1)

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Given that a>1 and b>1. Is (a^x)(b^y)<1? (1) [#permalink] New post 15 Aug 2009, 13:52
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Question Stats:

25% (03:22) correct 75% (01:01) wrong based on 10 sessions
Given that a>1 and b>1. Is (a^x)(b^y)<1?
(1) a^(x+y) < 1
(2) b^(x+y) < 1
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Re: Is (a^x)(b^y)<1 [#permalink] New post 15 Aug 2009, 22:58
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yezz wrote:
Given that a>1 and b>1. Is (a^x)(b^y)<1?
(1) a^(x+y) < 1
(2) b^(x+y) < 1



St1:
Given: a^(x+y) < 1 => a^x * a^y < 1
St1 could be true in the following 3 cases:
a) x<=0 & y<=0 .............. (They cannot be both zero at the same time)
-> (a^x)(b^y)<1 is TRUE
b) x<0, y>=0 & y < Abs(x), where Abs(x) means absolute value of x
-> Whether (a^x)(b^y)<1 is true or not depends on the relation between a & b.
c) y<0, x>=0 & x < Abs(y), where Abs(y) means absolute value of y
-> Whether (a^x)(b^y)<1 is true or not depends on the relation between a & b.
=> NOT SUFFICIENT

St2:
By same reasoning,
=> NOT SUFFICIENT

St1 & St2 Together:
Since we still donot know and cannot deduce any relation between a & b, we cannot conclude anything.
=> NOT SUFFICIENT


ANS: E
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Re: Is (a^x)(b^y)<1 [#permalink] New post 10 Sep 2009, 08:40
Go for E too. What's the OA?
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Re: Given that a>1 and b>1. Is (a^x)(b^y)<1? (1) [#permalink] New post 31 Jan 2012, 07:43
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+1 E

I solved it by picking numbers and using a table. Is there a faster method to solve it?
It took me more than 2 min :s.
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Re: Given that a>1 and b>1. Is (a^x)(b^y)<1? (1)   [#permalink] 31 Jan 2012, 07:43
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