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

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

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New post 09 Oct 2017, 23:44
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65% (00:52) correct 35% (00:34) wrong based on 56 sessions

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Kudos [?]: 135613 [0], given: 12705

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

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New post 10 Oct 2017, 03:43
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


Answer: Option A
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Last edited by GMATinsight on 10 Oct 2017, 05:18, edited 2 times in total.

Kudos [?]: 2401 [0], given: 51

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Kudos [?]: 135613 [0], given: 12705

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

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New post 10 Oct 2017, 03:46
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

Answer: Option E


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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New post 10 Oct 2017, 04:00
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

Answer: A

Kudos [?]: 108 [0], given: 66

Re: If a, b, and c are positive integers, is b = ac^(-1/2)   [#permalink] 10 Oct 2017, 04:00
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