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

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Retired Moderator
Joined: 05 Jul 2006
Posts: 1748

Kudos [?]: 448 [1], given: 49

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

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15 Aug 2009, 13:52
1
KUDOS
00:00

Difficulty:

55% (hard)

Question Stats:

73% (01:36) correct 27% (01:59) wrong based on 15 sessions

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

(1) a^(x+y) < 1
(2) b^(x+y) < 1
[Reveal] Spoiler: OA

Kudos [?]: 448 [1], given: 49

Manager
Joined: 25 Jul 2009
Posts: 114

Kudos [?]: 267 [1], given: 17

Schools: NYU, NUS, ISB, DUKE, ROSS, DARDEN
Re: Given that a>1 and b>1. Is (a^x)(b^y)<1? (1) [#permalink]

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15 Aug 2009, 22:58
1
KUDOS
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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Kudos [?]: 267 [1], given: 17

Re: Given that a>1 and b>1. Is (a^x)(b^y)<1? (1)   [#permalink] 15 Aug 2009, 22:58
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