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

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Math Expert
Joined: 02 Sep 2009
Posts: 43335

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

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

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24 Dec 2017, 00:20
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Difficulty:

35% (medium)

Question Stats:

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

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

(1) a/c = b/c
(2) b = c
[Reveal] Spoiler: OA

_________________

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

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 817

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

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

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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

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

Manager
Joined: 24 Nov 2016
Posts: 151

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

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

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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.

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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