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# a is a positive integer, k and m are integers. If k>m, is

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Current Student
Joined: 11 May 2008
Posts: 551
a is a positive integer, k and m are integers. If k>m, is [#permalink]

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01 Aug 2008, 04:40
a is a positive integer, k and m are integers. If k>m, is a^k>a^m?
(1) a^k<1
(2) a^m<1
A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

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Senior Manager
Joined: 16 Jul 2008
Posts: 279

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01 Aug 2008, 04:56
I think E, because a can be equal to 1.
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Current Student
Joined: 11 May 2008
Posts: 551

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01 Aug 2008, 05:04
but, if a=1....., then how does it help ??a^m,and a^k is what important... hmm i feel.
we want to know a^m and a^k relation. so even if a=1. since from given conditions, m and k are both -ve... that is what we should consider right?
Senior Manager
Joined: 16 Jul 2008
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01 Aug 2008, 05:17
"a is a positive integer, k and m are integers. If k>m, is a^k>a^m?"

If a = 1, then a^k = a^m.
If a > 1, then a^k > a^m.

So, unless we have more info on a, we cannot anwer the question.
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VP
Joined: 28 Dec 2005
Posts: 1484

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01 Aug 2008, 05:28
id pick D for this one
Intern
Joined: 24 Jul 2008
Posts: 3

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01 Aug 2008, 05:56
there could be 3 options

1. m>0
then k>0
and a^k > a^m allways

2. m<0
which goes into 2 options
2.1. k>0. a^k > a^m allways
2.2 k<0 a^k < a^m allways

now lets see what else we know

1) a^k<1
means k<0 for all a>0
thus a^k < a^m
sufficient

2)a^m<1
means m<0 for all a>0
it stays unclear for k; k >0 or k e <0
insufficient

1) and 2)
k<0
m<0
k>m
then
a^k < a^m allways

my bet is C
SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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01 Aug 2008, 08:32
Nerdboy wrote:
I think E, because a can be equal to 1.

a is a positive integer, k and m are integers. If k>m, is a^k>a^m?
(1) a^k<1
(2) a^m<1

State 1:
a^k<1 -- a can't be equal to 1..
if a=1 for any value of K( -ve or +ve) a^k<1 == 1<1 (so "a" not equal to 1" ) a>1
a must be >1 from statement (1)
a^k<1 --> a>1 and k --> -ve integer
k>m must be -ve integer
( k=-2 m=-3)
a^k>a^m --> 1/a^2 > 1/a^3

sufficient

State 2:
also sufficient use the above logic.

D for me.

what is OA
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Current Student
Joined: 11 May 2008
Posts: 551

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01 Aug 2008, 09:05
hmmm..... the ans is D.
so i think we can uncork a champagne bottle huh!!!
or if someone feels otherwise , they are most welcome to stop the party...
cos suggestions and rectifications are part of the learning process..
so for guys who said D hmmmmm welll
i'd got it as D too
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Joined: 30 Apr 2008
Posts: 1841
Location: Oklahoma City
Schools: Hard Knocks

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01 Aug 2008, 09:14
BUT SURESH, IF a=1 and k=-2 and m=-3,
a^k<1 and also a^m<1.
so why cant a be 1?

This isn't true.

If you have a negative exponent, such as $$2^{-2}$$ that is the same as $$\frac{1}{2^2}$$ or $$\frac{1}{4}$$.

If a = 1 and k = -2, then you have $$\frac{1}{1^k} = \frac{1}{1}$$ so this cannot be < 1. same applies for a^m.
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Current Student
Joined: 11 May 2008
Posts: 551

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01 Aug 2008, 09:17
hmmm... allen ... thanks..
sorry suresh.. guess u were right abt that one..
cheers!!!
Director
Joined: 20 Sep 2006
Posts: 631

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01 Aug 2008, 11:19
arjtryarjtry wrote:
a is a positive integer, k and m are integers. If k>m, is a^k>a^m?

to answer this we wanna make sure if:

a=0
a=1
k=m=0 (not possible since k>m)

(1) a^k<1 and a is a positive integer

either k is -ve or a =0
if K is -ve and k>m then Is a^k>a^m True
if a =0 then Is a^k>a^m False

INSUFF

(2) a^m<1 and a is a positive integer

either m is -ve or a=0 INSUFF
if M is -ve and k>m then Is a^k>a^m True
if a =0 then Is a^k>a^m False

INSUFF

Together

either a=0 or M and K are -ve

if K and M are -ve and k>m then Is a^k>a^m True
if a =0 then Is a^k>a^m False

INSUFF

A. Statement (1) ALONE is sufficient but Statement (2) ALONE is not sufficient.
B. Statement (2) ALONE is sufficient but Statement (1) ALONE is not sufficient.
C. BOTH Statements TOGETHER are sufficient, but NEITHER Statement alone is sufficient.
D. Each Statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

IMO E

BTW what is OA?
VP
Joined: 17 Jun 2008
Posts: 1288

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02 Aug 2008, 23:44
[quote="arjtryarjtry"]a is a positive integer, k and m are integers. If k>m, is a^k>a^m?
(1) a^k1
if 0 a^k if m0 and a a^k => insufficient

(2) does not indicate whether a0 and a a^k => insufficient

(1) and (2) taken together :
says that [color=#FF0000]a^k 1 and k,m both are opposite results
hence A,B,C,D eliminated
IMO E

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Re: exponents....   [#permalink] 02 Aug 2008, 23:44
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# a is a positive integer, k and m are integers. If k>m, is

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