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# a, b, c are integers. Is their product abc equal to 0? 1.

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a, b, c are integers. Is their product abc equal to 0? 1. [#permalink]  25 Sep 2007, 07:17
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a, b, c are integers. Is their product abc equal to 0?

1. a^2 = 2a

2. b/c = [(a+b)^2/(a^2 + 2ab + b^2)] - 1

A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: DS [#permalink]  25 Sep 2007, 07:26
Parbe wrote:
a, b, c are integers. Is their product abc equal to 0?

1. a^2 = 2a

2. b/c = [(a+b)^2/(a^2 + 2ab + b^2)] - 1

A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

Hi,

Statement 1 alone is not sufficient because (a) could be equal to zero or not. We also do not know about (b) and (c).

In statement 2 note that (a^2 + 2ab + b^2) = (a+b)^2
which makes [(a+b)^2/(a^2 + 2ab + b^2)] - 1 = 1 - 1 = 0
so we know now that b/c = 0. Since a,b,c are integers we conclude that b=0.

Thus Statement 2 alone is sufficient.
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I would say answer is B.

Since to hold true B/C = 0 ; B =0
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Re: DS [#permalink]  25 Sep 2007, 14:06
Parbe wrote:
a, b, c are integers. Is their product abc equal to 0?

1. a^2 = 2a

2. b/c = [(a+b)^2/(a^2 + 2ab + b^2)] - 1

A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

I could not figure out anything to make the answer E. it is B.
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Re: DS [#permalink]  25 Sep 2007, 14:23
Parbe wrote:
a, b, c are integers. Is their product abc equal to 0?

1. a^2 = 2a

2. b/c = [(a+b)^2/(a^2 + 2ab + b^2)] - 1

A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

E.

(1) a can be 0 or 2
INSUFFICIENT

(2) b/c = [(a+b)^2/(a^2 + 2ab + b^2)] - 1
=> b = c*[(a+b)^2/(a^2 + 2ab + b^2)] - c
=> b+c = c*[(a+b)^2/(a+b)^2]
=> (a+b)^2 * (b+c) = c*(a+b)^2
=> (a+b)^2 * (b+c) - c*(a+b)^2 = 0
=> ((a+b)^2) * (b) = 0
This gives b=0 or a=-b
INSUFFICIENT

Together, if a=0, then b=0
if a=2, then b=-2
INSUFFICIENT since we don't know c.
CEO
Joined: 29 Mar 2007
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This has to be E.

S1: a could be 2 or 0 insuff.

S2: b/c (when worked out) = 0 (not -1 as I originally posted)

anyway its still insuff.

Last edited by GMATBLACKBELT on 25 Sep 2007, 17:53, edited 1 time in total.
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St1:
Could be a = 0, a = 2. Insufficient.

St2:
b/c = [(a+b)^2/(a+b)^2] - 1
b/c = 0

So b = 0. a*b*c = 0.
Sufficient.

Ans B
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Re: DS [#permalink]  26 Sep 2007, 05:42
Parbe wrote:
a, b, c are integers. Is their product abc equal to 0?

1. a^2 = 2a

2. b/c = [(a+b)^2/(a^2 + 2ab + b^2)] - 1

A. Statement (1) ALONE is sufficient, but Statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but Statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

It's E
1) a=0 or a=2 => insufficient
2) b/c=0 (or b=0) only if (a+b) does not equal to 0 (a does not equal to -b), since we know nothing about a => insufficient
1&2) if a=0 and b=0 we forbid the statement that a should not equal to -b
so insufficient
Director
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this was tricky one.. i fell for the trap and had B at first. thanks for the good explanation
Manager
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I don't know how anyone could think the answer is e.

statement 1: a = 0, 2. insufficient

statement 2: b = 0. if be = 0, the answer is yes a * b * c = 0

The answer is B very obviously.
SVP
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I say B.

St. 1 just tells us that a=2 or -2. Nothing bout b or c, so insufficient

St. 2 tells us that b/c = 1-1 =0 . Therefore, b must equal 0. And any product where one of the terms is 0 makes the overall product 0 .

So , statement 2 seems to be enough, and thats what got me to B
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