GMATPrep Problem

[adi]

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

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

Each statement alone is sufficient - answer. Anyone care to share the reasoning behind this?

[simplyjat]

for a(b-c) to be 0, either of the factors should be zero, and we know that a is non-zero. So we have to look for a statement that tells b - c = 0 or b = c.

1) Zero is the only subtractive identity; that means -0 = 0. so this statement means that b-c = 0 or b-c = -0.

2) One is the only multiplicative identity; that means 1 = (1)^(-1). so this statement tells that b/c = 1 or (1)^(-1). implying that b = c....

[Bharat]

Answer must be A
Condition 1 is sufficient & condition 2 is insufficient
Condn: 1. b - c= c - b
=> 2b = 2c
=> b = c
SUFFICIENT
Condn: 2. b/c = c/b
=> b*b = C*C
=> b = c or b = -c
INSUFFICIENT

Regarding the multiplicative identity, please note that -1 will also yield the same results: - 1 = (-1)^(-1)

Let me know in case of doubts/queries, if any.

Regards,
Bharat.

[Stuart@KaplanGMAT]

Answer must be A
Condition 1 is sufficient & condition 2 is insufficient
Condn: 1. b - c= c - b
=> 2b = 2c
=> b = c
SUFFICIENT
Condn: 2. b/c = c/b
=> b*b = C*C
=> b = c or b = -c
INSUFFICIENT

Regarding the multiplicative identity, please note that -1 will also yield the same results: - 1 = (-1)^(-1)

Let me know in case of doubts/queries, if any.

Regards,
Bharat.

From the original question:

If a>0, b>0 and c>0

So, for statement (2), since we know that b and c are both positive, it's also sufficient on its own.