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# If a, b, and c are positive integers, is b = ac^(-1/2)

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Math Expert
Joined: 02 Sep 2009
Posts: 44351
If a, b, and c are positive integers, is b = ac^(-1/2) [#permalink]

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10 Oct 2017, 00:44
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Question Stats:

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If a, b, and c are positive integers, is $$b = \frac{a}{\sqrt{c}}$$?

(1) $$c = \frac{a^2}{b^2}$$

(2) $$\sqrt{c} = \frac{b}{a}$$
[Reveal] Spoiler: OA

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If a, b, and c are positive integers, is b = ac^(-1/2) [#permalink]

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10 Oct 2017, 04:43
Bunuel wrote:
If a, b, and c are positive integers, is $$b = \frac{a}{\sqrt{c}}$$?

(1) $$c = \frac{a^2}{b^2}$$

(2) $$\sqrt{c} = \frac{b}{a}$$

Question: is $$b = \frac{a}{\sqrt{c}}$$?

Statement 1: $$c = \frac{a^2}{b^2}$$
Taking square root both sides
√c = a/b
SUFFICIENT

Statement 2: $$\sqrt{c} = \frac{b}{a}$$
@a = b = c = 1 Answer to the question is YES
@a = 1, b=2, c = 4 Answer to the question is NO
NOT SUFFICIENT

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Last edited by GMATinsight on 10 Oct 2017, 06:18, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 44351
Re: If a, b, and c are positive integers, is b = ac^(-1/2) [#permalink]

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10 Oct 2017, 04:46
GMATinsight wrote:
Bunuel wrote:
If a, b, and c are positive integers, is $$b = \frac{a}{c}$$?

(1) $$c = \frac{a^2}{b^2}$$

(2) $$\sqrt{c} = \frac{b}{a}$$

Question: is $$b = \frac{a}{c}$$?

Statement 1: $$c = \frac{a^2}{b^2}$$
If a = b = c = 1 then answer to the question is YES
if a = b = 2 then c = 1 then answer to the question is NO

NOT SUFFICIENT

Statement 2: $$\sqrt{c} = \frac{b}{a}$$

If a = b = c = 1 then answer to the question is YES
if a = b = 2 then c = 1 then answer to the question is NO

NOT SUFFICIENT

After combining the two statements

If a = b = c = 1 then answer to the question is YES
if a = b = 2 then c = 1 then answer to the question is NO

NOT SUFFICIENT

Sorry GMATinsight, the question is "If a, b, and c are positive integers, is $$b = \frac{a}{\sqrt{c}}$$?" NOT "If a, b, and c are positive integers, is $$b = \frac{a}{c}$$?". Edited.
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Re: If a, b, and c are positive integers, is b = ac^(-1/2) [#permalink]

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10 Oct 2017, 05:00
Bunuel wrote:
If a, b, and c are positive integers, is $$b = \frac{a}{\sqrt{c}}$$?

(1) $$c = \frac{a^2}{b^2}$$

(2) $$\sqrt{c} = \frac{b}{a}$$

(1) $$c = \frac{a^2}{b^2}$$
=> taking square root
=> $$\sqrt{c} = \frac{a}{b}$$
=> $$b = \frac{a}{\sqrt{c}}$$
Sufficient

(2) $$\sqrt{c} = \frac{b}{a}$$
=> $$b =a\sqrt{c}$$
In this case :
if c = 1 => $$b =a\sqrt{c}$$ => $$b = \frac{a}{\sqrt{c}}$$
if c = 4 => $$b =a\sqrt{c}$$ is not same as $$b = \frac{a}{\sqrt{c}}$$
Insufficient

Re: If a, b, and c are positive integers, is b = ac^(-1/2)   [#permalink] 10 Oct 2017, 05:00
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