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0 < a < b

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0 < a < b [#permalink] New post 19 May 2017, 01:54
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Question Stats:

84% (00:49) correct 15% (01:48) wrong based on 32 sessions

0 < a < b

Quantity A
Quantity B
a% of 1/b
b% of 1/a


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

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Re: 0 < a < b [#permalink] New post 26 May 2017, 12:25
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Expert's post
Carcass wrote:

0 < a < b

Quantity A
Quantity B
a% of 1/b
b% of 1/a


A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.


a% of 1/b = (a/100)(1/b)
= a/(100b)

b% of 1/a = (b/100)(1/a)
= b/(100a)

So, we have:
Quantity A: a/(100b)
Quantity B: b/(100a)

Multiply both quantities by 100b to get:
Quantity A: a
Quantity B: b²/a

Multiply both quantities by a to get:
Quantity A: a²
Quantity B: b²

We're told that 0 < a < b, which means 0 < a² < b²

Answer:
[Reveal] Spoiler:
B

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Re: 0 < a < b [#permalink] New post 29 May 2017, 07:17
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But it is not given that the numbers are integers.If the a & b are fraction then the result would be opposite.
hence, the answer should be D
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Re: 0 < a < b [#permalink] New post 29 May 2017, 07:58
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malimah wrote:
But it is not given that the numbers are integers.If the a & b are fraction then the result would be opposite.
hence, the answer should be D


If 0 < a < b, then 0 < a² < b², regardless of whether a and b are fractions

If you want to choose D as the correct answer, then you need to find values of a and b that show either quantity can be greater.

Cheers,
Brent
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Re: 0 < a < b [#permalink] New post 29 Sep 2018, 11:19
I picked B
Re: 0 < a < b   [#permalink] 29 Sep 2018, 11:19
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