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# If a > 0 and b > 0, is a/b > b/a ?

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Math Expert
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If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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21 Aug 2016, 03:13
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If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2
(2) a/(4b) =1/5

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Re: If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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21 Aug 2016, 04:48
Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2
(2) a/(4b) =1/5

a and b can be 0.5,1,2,3....

1) a = b - 2

when 3 = 5 - 2...here a = 3 and b = 5 , then 3/5 < 5/3...Sufficient.

if a = 8 and b = 10
8 = 10 -2... then 8/10 < 10/8...Sufficient..

2 ) a/b = 4/5 and b/a = 5/4.
a/b < b/a.. Sufficient..

OA please...will correct if I missed anything..
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Re: If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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21 Aug 2016, 20:01
If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2

Which means b=a+2.
Substituting values, we have to find if if a/(a+2) > (a+2)/a
Given that a>0.
Hence, Sufficient

(2) a/(4b) =1/5

This means, a/b = 4/5
We have to find, if 4/5 > 5/4
Hence, sufficient.

I believe correct answer is D
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Re: If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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22 Aug 2016, 04:13
Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2
(2) a/(4b) =1/5

I concur.My take is D.

statement 1: Since a and b are positive, min value of b > 2.

Statement 2: Rearrangement makes the equation (a/b) = 4/5 so (b/a) = 5/4.
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Re: If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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22 Aug 2016, 05:01
1
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1
Bunuel wrote:
If a > 0 and b > 0, is a/b > b/a ?

(1) a = b - 2
(2) a/(4b) =1/5

Target question: Is a/b > b/a ?

Given: a > 0 and b > 0

This is a great candidate for REPHRASING the target question: Is a/b > b/a ?
Since a and b are both POSITIVE, we can multiply both sides of the inequality by ab to get: Is a² > b²?

Nice Rules: If 0 < b < a, then and b² < a²
Conversely, if a and b are positive AND b² < a², then we can be certain that b < a

This allows us to REPHRASE our target question once more to get...
REPHRASED target question: Is b < a?

Once we're rephrased the target question like this, the statements are pretty easy to analyze.

Statement 1: a = b - 2
In other words, a is 2 less than b
So, we can be certain that a < b
In other words, it is definitely NOT the case that b < a
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: a/(4b) =1/5
Multiply both sides by 4b to get: a = (4/5)b
In other words, a is equal to 4/5 of b
Since it's given that a and b are positive, we can be certain that a < b
In other words, it is definitely NOT the case that b < a
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

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If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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02 Sep 2016, 17:24
Think Stmt 1 and Stmt 2 are contradicting each other a/b >1 in Stmt 1 and a/b < 1 in Stmt 2.
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Re: If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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04 Sep 2016, 03:44
AbhiJ wrote:
Think Stmt 1 and Stmt 2 are contradicting each other a/b >1 in Stmt 1 and a/b < 1 in Stmt 2.

For both a < b. How did you get that a > b for (1)? It says a = b - 2, so a < b.
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Re: If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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15 Sep 2018, 06:24
I tried with fractions and integers-- the question doesn't expressly say its not an integer.
1) St 1; if with integers, a = 8, b = 10 - 2 --> 8/10 < 5/4 A is suff, with a = 1/4 , b = 9/4 A suff
2) a = 4/5 b, which is suff for both integers and fractions

Ans D
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Re: If a > 0 and b > 0, is a/b > b/a ?  [#permalink]

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23 Sep 2019, 04:48
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Re: If a > 0 and b > 0, is a/b > b/a ?   [#permalink] 23 Sep 2019, 04:48
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