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# Is ab positive?

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Manager
Joined: 15 Mar 2014
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Is ab positive?  [#permalink]

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08 Mar 2017, 05:04
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Difficulty:

45% (medium)

Question Stats:

58% (00:57) correct 42% (01:08) wrong based on 41 sessions

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Is ab positive?

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

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Re: Is ab positive?  [#permalink]

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08 Mar 2017, 05:15
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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Re: Is ab positive?  [#permalink]

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08 Mar 2017, 05:29
1
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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Is ab positive?  [#permalink]

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09 Mar 2017, 02:21
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]

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09 Mar 2017, 03:17
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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Is ab positive?  [#permalink]

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09 Mar 2017, 05:32
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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Re: Is ab positive?  [#permalink]

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09 Mar 2017, 05:54
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]

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09 Mar 2017, 07:52
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]

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15 Mar 2017, 15:24
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? &nbs [#permalink] 15 Mar 2017, 15:24
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# Is ab positive?

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