Is ab positive?

Question

Is ab positive?

1.  (a + b)^{2} < (a - b)^{2} 
2. a = b

Bunuel · Answer

Is ab positive?

(1)  (a + b)^{2}  <  (a - b)^{2}

a^2 + 2ab + b^2 < a^2 - 2ab + b^2

4ab < 0

ab<0

Sufficient.

(2) a = b. If a = b = 0, then ab = 0 but if a = b = 1, then ab = 1 > 0. Not sufficient.

Answer: A.

Bunuel · Answer

Just noticed - statements contradict here. ab<0 and a=b cannot simultaneously be true. So, the question is flawed: On the GMAT, two data sufficiency statements always provide TRUE information and these statements NEVER contradict each other or the stem.

Are you sure you copied the question correctly?

Mo2men · Answer

Can you please specify from which test you copied the question above? I have searched in all 9 GMAC paper tests and did not find this question. Maybe I missed something.

Thanks

jedit · Answer

Am I correct in my assertion that you cannot assume 0 as positive and hence second statement becomes insufficient?

ashwink · Answer

Looks like I copied the question from a wrong source. Apologies. Please remove the thread if this is a poor quality question.

Could you please however explain how the contradiction happened? We do have a clear YES in statement 1 & and multiple choice(YES and a NO) in statement 2 making it insufficient. 
As per the source(practice question from another material), the OA is A as per this explanation. Why are we trying to combine statement 1 & 2 when we have a definite YES in 1?

Bunuel · Answer

(1) says that ab < 0, so a and b have different signs, which in tiurn means that a does not equal to b.
(2) says that a = b

The statements clearly contradict each other.

mvictor · Answer

A for me too. Arrived at the solution the same way as Bunuel did.
what is the difficulty level of this question?

ScottTargetTestPrep · Answer

We need to determine whether ab > 0.

Statement One Alone:

(a + b)^2 < (a - b)^2

We can simplify the information in statement one:

(a + b)^2 < (a - b)^2

a^2 + 2ab + b^2 < a^2 - 2ab + b^2

2ab < -2ab

4ab < 0

ab < 0

Since ab is less than zero, ab is not positive. Statement one is sufficient to answer the question.

Statement Two Alone:

a = b

The information in statement two is not sufficient to answer the question. If a and b are both 1, then ab is positive; however, if a and b are both 0, then ab is NOT positive.

Answer: A

Is ab positive?

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GMAT Data Sufficiency (DS) Questions

Is ab positive?

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