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If a, b, and c are positive, is a =b^2/c ?

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V
Joined: 02 Sep 2009
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Kudos [?]: 139568 [0], given: 12794

If a, b, and c are positive, is a =b^2/c ? [#permalink]

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New post 24 Dec 2017, 00:20
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A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

74% (00:41) correct 26% (02:43) wrong based on 19 sessions

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Kudos [?]: 139568 [0], given: 12794

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P
Joined: 25 Feb 2013
Posts: 817

Kudos [?]: 381 [0], given: 42

Location: India
GPA: 3.82
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Re: If a, b, and c are positive, is a =b^2/c ? [#permalink]

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New post 24 Dec 2017, 01:44
Bunuel wrote:
If a, b, and c are positive, is a =b^2/c ?

(1) a/c = b/c
(2) b = c


Statement 1: \(\frac{a}{c}=\frac{b}{c} => a=b\) (as \(c\) is positive so \(c≠0\))

Now if \(b=c\), then we have a Yes but if \(b≠c\) then we have a NO. Hence Insufficient

Statement 2: \(b=c\). Nothing mentioned about \(a\). if \(a=b\) then we have a Yes and if \(a≠b\) then we have a No. Hence Insufficient

Combining 1 & 2, we have \(a=b=c\). Hence we have a Yes. Sufficient

Option C

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Joined: 24 Nov 2016
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Kudos [?]: 31 [0], given: 40

Re: If a, b, and c are positive, is a =b^2/c ? [#permalink]

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New post 24 Dec 2017, 12:42
Bunuel wrote:
If a, b, and c are positive, is a =b^2/c ?

(1) a/c = b/c
(2) b = c


(1) a/c = b/c, then \(a=bc/c\) -> \(a=b\); but we don't know what is \(c\), insufficient.

If a = b = 3 and c = 4, then \(a=b^2/c\) becomes: \(3=9/4\), answer to the question is no.
If a = b = 3 and c = 3, then \(a=b^2/c\) becomes: \(3=9/3=3\), answer to the question is yes.

(2) b = c. There is no info on what \(a\) could be, insufficient.

If a = 3 and b = c = 4, then \(a=b^2/c\) becomes: \(3=16/4\), answer to the question is no.
If a = 3 and b = c = 3, then \(a=b^2/c\) becomes: \(3=9/3=3\), answer to the question is yes.

(1)&(2): If \(a=b\) and \(c=b\); then, \(a=b^2/c\) becomes \(b=b^2/b\) which is \(b=b\), sufficient.

(C) is the answer.

Kudos [?]: 31 [0], given: 40

Re: If a, b, and c are positive, is a =b^2/c ?   [#permalink] 24 Dec 2017, 12:42
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