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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: 52296
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:

25% (medium)

Question Stats:

76% (01:10) correct 24% (01:43) wrong based on 81 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

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

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24 Dec 2017, 01:44
1
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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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.

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

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25 Jan 2018, 09:43
from st 1, we know a = b -> insufficient
from st 2, we know b = b^2 / b = b^2 / c -> insufficient
combine both of them, a =b^2/c
Re: If a, b, and c are positive, is a =b^2/c ? &nbs [#permalink] 25 Jan 2018, 09:43
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