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# If a>0, b>0, c>0, Is a(b-c)=0 1) b-c=c-b 2) b/c=c/b

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Manager
Joined: 21 Jun 2007
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If a>0, b>0, c>0, Is a(b-c)=0 1) b-c=c-b 2) b/c=c/b [#permalink]  06 Jun 2008, 10:19
If a>0, b>0, c>0, Is a(b-c)=0

1) b-c=c-b
2) b/c=c/b

I don't have an OA, but want to verify my answer. Thanks.
Soomodh
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Re: Is a(b-c)=0 [#permalink]  06 Jun 2008, 10:39
I think each one is suff. (D)

(1) gives b=c. So suff. for any a.
(2) gives b=c or b=-c, but, taken together with the condition b>0, c>0, it gives b=c. Suff.
Manager
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Re: Is a(b-c)=0 [#permalink]  06 Jun 2008, 10:42
Greenoak, thanks thats what I got (I initially got wrong coz I didn't realize greater than zero condition).
S
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Re: Is a(b-c)=0 [#permalink]  06 Jun 2008, 11:52
Hi guys,
I got D.

1) b - c = c - b

or 2B = 2C, B = C. any value of a * (b - c) will be 0 .suff

2) b/c = c/b
= c^2 = b^2
or c = b , again same analysis. suff.

if my logic is incorrect, please let me know.
Manager
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Re: Is a(b-c)=0 [#permalink]  06 Jun 2008, 14:28
ca_gold careful with c2= b2 , so c= b statement, this is only true if c and b are positive, if -ve then not.
Soomodh
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Re: Is a(b-c)=0 [#permalink]  06 Jun 2008, 15:32
It's D.

Statement (1) is straight forward.

Lets look at statement (2)
$$\frac {b} {c} = \frac {c} {b}$$

or $$b^2=c^2$$
or $$b^2-c^2=0$$
or $$(b+c)(b-c)=0$$

which gives us either$$b=c$$, or $$b=-c$$
Since we know from the question stem that $$b>0, c>0$$, we can ignore $$b=-c$$
Therefore, statement (2) is also sufficient.
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Re: Is a(b-c)=0 [#permalink]  06 Jun 2008, 17:51
soomodh wrote:
ca_gold careful with c2= b2 , so c= b statement, this is only true if c and b are positive, if -ve then not.
Soomodh

hi soomodh,
good call, thanks for the that!
Re: Is a(b-c)=0   [#permalink] 06 Jun 2008, 17:51
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