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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, 22:33
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.\(a^y>a^x\)
Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]
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10 Dec 2013, 13:15
1
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.
Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]
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08 Mar 2016, 22:24
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
_________________
Concentration: General Management, General Management
Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]
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17 Mar 2017, 23:04
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.
Re: If a, b, x, and y are positive integers, is a^(-x) > b(-y)? [#permalink]
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08 May 2018, 07:00
Top Contributor
zbvl wrote:
If a, b, x, and y are positive integers, is \(a^{(-x)} > b^{(-y)}\)?
(1) a < b (2) x < y
Target question:Is a^(-x) > b^(-y)? This is a great candidate for rephrasing the target question. Aside: At the bottom of this post, you can find a video with tips on rephrasing the target question
First recognize the following: a^(-x) = 1/(a^x) and b^(-y) = 1/(b^y) So, we can ask Is 1/(a^x) > 1/(b^y)? Also, since a and b are POSITIVE, we can be certain that (a^x) is POSITIVE and (b^y) is POSITIVE So, we can safely take the inequality 1/(a^x) > 1/(b^y) and multiply both sides by (a^x) to get: 1 > (a^x)/(b^y) Next, we can multiply both sides by (b^y) to get: (b^y) > (a^x) So, we can now ask... REPHRASED target question:Is (b^y) > (a^x)?
Statement 1: a < b No information about x or y. So, statement 1 is NOT SUFFICIENT
Statement 2: x < y No information about a or b. So, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined The key here is that all 4 variables are positive. If b is greater than a AND y is greater than x, we can be certain that (b^y) > (a^x) Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT