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Is ab positive?

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ashwink
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Is ab positive? [#permalink] New post   08 Mar 2017, 06:04
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Is ab positive?

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

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Bunuel
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Re: Is ab positive? [#permalink] New post   08 Mar 2017, 06:15
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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.
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Bunuel
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Re: Is ab positive? [#permalink] New post   08 Mar 2017, 06:29
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Bunuel wrote:
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.


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?
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Re: Is ab positive? [#permalink] New post   09 Mar 2017, 03:21
ashwink wrote:
Is ab positive?

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



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
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Re: Is ab positive? [#permalink] New post   09 Mar 2017, 04:17
Bunuel wrote:
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.


Am I correct in my assertion that you cannot assume 0 as positive and hence second statement becomes insufficient?
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Re: Is ab positive? [#permalink] New post   09 Mar 2017, 06:32
Bunuel wrote:
Bunuel wrote:
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.


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?


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?
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Bunuel
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Re: Is ab positive? [#permalink] New post   09 Mar 2017, 06:54
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ashwink wrote:
Bunuel wrote:
Bunuel wrote:
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.


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?


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?


(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.
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Re: Is ab positive? [#permalink] New post   09 Mar 2017, 08:52
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A for me too. Arrived at the solution the same way as Bunuel did.
what is the difficulty level of this question?
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Re: Is ab positive? [#permalink] New post   15 Mar 2017, 16:24
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ashwink wrote:
Is ab positive?

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


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

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Re: Is ab positive? [#permalink]
15 Mar 2017, 16:24
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Bunuel
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