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If a>0, b>0 and c>0, is a(b-c)=0?

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steph
 Post subject: If a>0, b>0 and c>0, is a(b-c)=0?
 Post Posted: Fri Aug 29, 2008 8:38 pm 
Data Sufficiency:

If a>0, b>0 and c>0, is a(b-c)=0?
(1) b-c = c-d
(2) b/c = c/b

ans D.

So i rephrased the original statement as "Is b=c?" Statement 1 is exactly the same as my rephrase, so it's good! :-) BUT, I do not understand how the second statement is sufficient. If I were to rephrase statement 2 as b^2 = c^2 then either b or c could be a negative number and the relationship will still hold. What am I missing? Please help!
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Raj
 Post subject: Re: If a>0, b>0 and c>0, is a(b-c)=0?
 Post Posted: Sat Aug 30, 2008 3:22 pm 
I dont know what you mean by " Statement 1 is exactly the same as my rephrase, so it's good!". How does b-c = c-d answer b=c? I am assuming the "d" in statement was a typo. Please confirm.

Anyways, for statement 2, the only way I think b/c = c/b is when b = c or b = -c but since a, b, c are positive, b = c.

Hope that helps,
-Raj.

steph wrote:
Data Sufficiency:

If a>0, b>0 and c>0, is a(b-c)=0?
(1) b-c = c-d
(2) b/c = c/b

ans D.

So i rephrased the original statement as "Is b=c?" Statement 1 is exactly the same as my rephrase, so it's good! :-) BUT, I do not understand how the second statement is sufficient. If I were to rephrase statement 2 as b^2 = c^2 then either b or c could be a negative number and the relationship will still hold. What am I missing? Please help!
Top 
steph
 Post subject: Re: If a>0, b>0 and c>0, is a(b-c)=0?
 Post Posted: Sat Sep 06, 2008 5:48 pm 
Raj wrote:
I dont know what you mean by " Statement 1 is exactly the same as my rephrase, so it's good!". How does b-c = c-d answer b=c? I am assuming the "d" in statement was a typo. Please confirm.

Anyways, for statement 2, the only way I think b/c = c/b is when b = c or b = -c but since a, b, c are positive, b = c.

Hope that helps,
-Raj.

steph wrote:
Data Sufficiency:

If a>0, b>0 and c>0, is a(b-c)=0?
(1) b-c = c-d
(2) b/c = c/b

ans D.

So i rephrased the original statement as "Is b=c?" Statement 1 is exactly the same as my rephrase, so it's good! :-) BUT, I do not understand how the second statement is sufficient. If I were to rephrase statement 2 as b^2 = c^2 then either b or c could be a negative number and the relationship will still hold. What am I missing? Please help!


My bad!! Raj, you are right! statement 1 reads, b-c = c-b :-) sorry!
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RonPurewal
 Post subject: Re: If a>0, b>0 and c>0, is a(b-c)=0?
 Post Posted: Mon Sep 29, 2008 5:32 am 
Offline
ManhattanGMAT Staff


Posts: 6765
steph wrote:
If I were to rephrase statement 2 as b^2 = c^2 then either b or c could be a negative number and the relationship will still hold. What am I missing? Please help!


what you're missing is the condition that's explicitly imposed on a, b, and c at the beginning of the problem: all of them are declared to be positive.
you typed it yourself!

moral of this particular story: ALWAYS pay attention to the conditions. if the conditions are nontrivial*, then they'll usually affect the problem in some tangible way.

--

* by "trivial" i mean conditions that HAVE to be true. for instance, denominators must be nonzero; therefore, if you have a problem containing the expression x/y, then the problem will specify that y != 0 out of necessity. that's not much of a condition - it HAS to be true - but the problem will still mention it.
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