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

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01 Aug 2008, 04:40

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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.

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?

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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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

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.

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.

Please let me know what are the sources of these questions which u post ?

a^m < a^k if m<k if a>1 if 0<a<1 then a^m > a^k if m<k

(1) does not indicate whether a<1 or not since either k <0 or a <1 if k<0 then a^m < a^k if k>0 and a<1 then a^m > a^k => insufficient

(2) does not indicate whether a<1 or not since either m <0 or a <1 if m<0 then a^m < a^k if m>0 and a<1 then a^m > a^k => insufficient

(1) and (2) taken together : says that a^k<1 and a^m<1

this is possible when a <1 and k,m are positive or a> 1 and k,m both are < 0 in both the cases => opposite results hence A,B,C,D eliminated IMO E
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