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If K=m*n^5, where n is an integer and m=4^n. Is K>0? (1)

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If K=m*n^5, where n is an integer and m=4^n. Is K>0? (1) [#permalink] New post 31 Jul 2008, 19:35
16. If K=m*n^5, where n is an integer and m=4^n. Is K>0?
(1) m>m^2
(2) n is an even number.
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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Re: IS k>0? [#permalink] New post 31 Jul 2008, 19:44
A

statement 1: m > m^2, this says that 0 < m < 1
that m=4^n, n must be a negative

neg^5 is a negative, and m is positive, so (+)(-) = (-)
so K is negative
suff

statement 2: n is an even number, n can be -2 or 2 or 0
k can be negative or positive or zero
insuff

Last edited by gmatnub on 31 Jul 2008, 19:50, edited 1 time in total.
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Re: IS k>0? [#permalink] New post 31 Jul 2008, 19:47
arjtryarjtry wrote:
16. If K=m*n^5, where n is an integer and m=4^n. Is K>0?
(1) m>m^2
(2) n is an even number.
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.


Since m=4^n, m is always going to be greater than 0.
The question asks you is k>0. If you already know m>0, the question is really asking you whether n is positive or negative.
Statement 2, by itself is not sufficient as an even number can be both positive or negative
Statement 1, however is sufficient. If m>m^2 and m=4^n, this tell you that m has to be a fraction, only in a situation of fraction, you will find m>m^2. If m is a faction, which means n has to be a negative number. Thus k will be less than 0.

Answer A
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Re: IS k>0? [#permalink] New post 01 Aug 2008, 03:40
i get A

from stat 1, m(1-m)>0, so either m>0 and 1-m>0 or m<0 and 1-m<0. The second condition doesnt work, so we have 0<m<1.

This means that n must be negative, and if n is negative, since is it raised to an odd power (5, in this case), that term will always be negative, thus making the entire expression negative.

from stat 2, we dont know if n is positive or negative; the answers are different in each case. insuff.
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Re: IS k>0? [#permalink] New post 01 Aug 2008, 07:06
arjtryarjtry wrote:
16. If K=m*n^5, where n is an integer and m=4^n. Is K>0?
(1) m>m^2
(2) n is an even number.
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.


1) m>m^2 --> 0>m>1

m=4^n --> "n" must be negative for integer
So K=m*n^5=4^n * n^5 always <0 (because n^5 -- always negative and m is +)

stat 1 is sufficient

2)

K =4^n * n^5 ( assume n=2)
K >0
assume N=-2
K<0

state 2 is Not sufficient.


A is the answer
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Re: IS k>0? [#permalink] New post 02 Aug 2008, 23:06
arjtryarjtry wrote:
16. If K=m*n^5, where n is an integer and m=4^n. Is K>0?
(1) m>m^2
(2) n is an even number.
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.


(1) is sufficient since sign of K depends on whether n is +ve or -ve since m is always +ve => m> m^2 implie n <0 => K<0 => sufficient
(2) this is insufficient since sign of n is not known

A is IMO answer
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Re: IS k>0?   [#permalink] 02 Aug 2008, 23:06
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