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

[steph]

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!

[Raj]

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.

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!

[steph]

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.

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!

[RonPurewal]

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.

[AbhilashM94]

Ron,

Can you explain how St2 works?
you get

b^2 = c^2
b^2 - C^2 = 0
b+c)(b-c) = 0

b+c = 0 or b-c = 0

so its not certain - can you explain why I'm wrong, Ron?

[tim]

Please read Ron's post. The setup clearly states that all numbers are positive, so b+c=0 can't work and we have to throw out that possibility.

[RonPurewal]

Ron,

Can you explain how St2 works?
you get

b^2 = c^2
b^2 - C^2 = 0
b+c)(b-c) = 0

b+c = 0 or b-c = 0

so its not certain - can you explain why I'm wrong, Ron?

The way to fix this problem is to WRITE DOWN ALL CONDITIONS. If you commit this sort of oversight often, then write them down multiple times.

[RonPurewal]

By the way, if you see this^2 = that^2, you should know right away that this = ±that. (If both are positive, as they are here, then this = that.) You shouldn't have to go through a factoring process to figure this out.