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# 0 < a < b

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0 < a < b [#permalink]  19 May 2017, 01:54
Expert's post
00:00

Question Stats:

82% (00:52) correct 17% (01:05) wrong based on 51 sessions

$$0 < a < b$$

 Quantity A Quantity B a% of $$\frac{1}{b}$$ b% of $$\frac{1}{a}$$

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]  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

[Reveal] Spoiler:
B

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Brent Hanneson – Creator of greenlighttestprep.com

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Re: 0 < a < b [#permalink]  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]  29 May 2017, 07:58
1
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Expert's post
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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Brent Hanneson – Creator of greenlighttestprep.com

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