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# If a, b, x, and y are positive integers, is a^(-x) > b(-y)?

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Intern
Joined: 27 Oct 2013
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If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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30 Oct 2013, 18:58
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If a, b, x, and y are positive integers, is a^(-x) > b^(-y)?

(1) a < b
(2) x < y

[Reveal] Spoiler:
I chose E because if a=1/4, b=1/2, x=1, y=2, wouldn't a^(-x)=b^(-y)?
[Reveal] Spoiler: OA

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Last edited by Bunuel on 16 Feb 2015, 03:23, edited 2 times in total.
Edited the question.
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Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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30 Oct 2013, 21:33
zbvl wrote:
If a, b, x, and y are positive integers, is a^(-x)>b(-y)?

(1) a<b

(2) x<y

I chose E because if a=1/4, b=1/2, x=1, y=2, wouldn't a^(-x)=b^(-y)?

The question stem mentions specifically that a,b,x and y are positive INTEGERS. Your choice of a,b doesn't subscribe to that.

From F.S 1, we know that b>a . Thus, for a=2,b=3 and x=y=1, we have $$b^y>a^x$$and thus a YES for the question stem.Again, for a=2,b=3 and x=10,y=1, we have $$b^y<a^x$$, and a NO.Insufficient.

Similarly for F.S 2, Insufficient.

Taking both together, we know that b>a and y>x.Thus:
1.$$b^y>a^y$$
2.$$a^y>a^x$$

Thus, $$b^y>a^x.$$ Sufficient.

C.
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Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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10 Dec 2013, 12:15
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Question: a^-x > b^-y? --> 1/a^x > 1/b^y?

We need to find a definit YES or NO.

(1) a < b If a=2 and b = 8 and x = 1 and y = 1 then YES. But if a = 2 and b = 8 and x = 100 and y = 1 then NO. IS
(2) x < y If a = 2 and b = 8 and x = 1 and y = 2 then YES. But if a = 100 and b = 1 then NO. IS

TOGETHER a < b and x < y ==> plug in numbers Suff. Hence C.
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Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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14 Feb 2015, 06:49
1
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zbvl wrote:
If a, b, x, and y are positive integers, is a^(-x) > b(-y)?

(1) a < b
(2) x < y

[Reveal] Spoiler:
I chose E because if a=1/4, b=1/2, x=1, y=2, wouldn't a^(-x)=b^(-y)?

Hi,

You need to correct the typo "b(-y)". I think it should read b^(-y)

TO
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Joined: 02 Sep 2009
Posts: 43901
Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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16 Feb 2015, 03:24
thorinoakenshield wrote:
zbvl wrote:
If a, b, x, and y are positive integers, is a^(-x) > b(-y)?

(1) a < b
(2) x < y

[Reveal] Spoiler:
I chose E because if a=1/4, b=1/2, x=1, y=2, wouldn't a^(-x)=b^(-y)?

Hi,

You need to correct the typo "b(-y)". I think it should read b^(-y)

TO

_____________
Edited. Thank you.
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Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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18 Feb 2016, 20:09
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Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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08 Mar 2016, 21:24
Here is my approach
W need to prove that x1/a^x >1/b^x
now we can flip the inequality if they are of same sign while doing the reciprocal..
hence we need to prove => a^x<b^y
statement 1 => no clue of x and y => not sufficient
statement 2 => no clue of a and b => not sufficient
combing them we can say that the bae an exponent of rhs are always greater hence rhs would be greater
thus C
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Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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08 Sep 2016, 03:35
Bunuel Please if you can help by doing it your way. I understand the question by taking the examples. But that is time consuming. Is there any other way to solve this question?
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Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]

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17 Mar 2017, 22:04
We can redefine the question as (1/a)^x > (1/b)^y

S1 a < b We know nothing about x and y here. So if a=3 and b = 4 and x = 1 and y = 1 then YES. But if a = 3 and b = 4 and x = 10 and y = 1 then NO. This statement is insufficient.

S2 x < y We know nothing about a and b here.So if a = 3 and b = 4 and x = 1 and y = 2 then YES. But if a = 10 and b = 1 and x=1 and y=2 then NO. This statement is insufficient.

Taking S1 and S2 together is sufficient to get the answer.

Hence C.
Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)?   [#permalink] 17 Mar 2017, 22:04
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