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# If a≠b and a·b≠0, which of the following may be true?

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Senior Manager
Joined: 21 Oct 2013
Posts: 409
If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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05 Aug 2014, 05:14
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58% (01:57) correct 42% (01:49) wrong based on 177 sessions

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If a≠b and a·b≠0, which of the following may be true?

A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0
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Joined: 09 Feb 2014
Posts: 4
Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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05 Aug 2014, 06:35
1
goodyear2013 wrote:
If a≠b and a·b≠0, which of the following may be true?

A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0

A and B are effectively the same
C square can't be less than 0
D give a = b refuted is question stem

leaves only E
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Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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05 Aug 2014, 06:44
1
goodyear2013 wrote:
If a≠b and a·b≠0, which of the following may be true?

A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0

A and B are the same, but how are they wrong? Those equations still makes sense because we're not told whether a and b are integers only.
Consider a = \sqrt{-5} and b= \sqrt{5}

So, a^2 = -5
and b^2 = 5

Therefore, a^2 = - b^2
Math Expert
Joined: 02 Sep 2009
Posts: 59020
If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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13 Aug 2014, 08:25
1
1
PareshGmat wrote:
mehulsayani wrote:
goodyear2013 wrote:
If a≠b and a·b≠0, which of the following may be true?

A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0

A and B are the same, but how are they wrong? Those equations still makes sense because we're not told whether a and b are integers only.
Consider a = \sqrt{-5} and b= \sqrt{5}

So, a^2 = -5
and b^2 = 5

Therefore, a^2 = - b^2

Agreed to this.. unless otherwise, 5 & -5 fit best for option E

a^2 (nonnegative number) could equal to -b^2 (nonpositive number) if and only a=b=0 but we are told that a≠b, so neither A nor B could be true.

Your example is not valid because the square roots from negative numbers are not defined for the GMAT (all numbers on the GMAT are real numbers).

Hope it's clear.
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Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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06 Aug 2014, 01:37
mehulsayani wrote:
goodyear2013 wrote:
If a≠b and a·b≠0, which of the following may be true?

A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0

A and B are the same, but how are they wrong? Those equations still makes sense because we're not told whether a and b are integers only.
Consider a = \sqrt{-5} and b= \sqrt{5}

So, a^2 = -5
and b^2 = 5

Therefore, a^2 = - b^2

Agreed to this.. unless otherwise, 5 & -5 fit best for option E
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Joined: 05 Mar 2015
Posts: 986
Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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19 Dec 2015, 20:09
A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0

a^2 (nonnegative number) could equal to -b^2 (nonpositive number) if and only a=b=0 but we are told that a≠b, so neither A nor B could be true.

Your example is not valid because the square roots from negative numbers are not defined for the GMAT (all numbers on the GMAT are real numbers).

Hope it's clear.[/quote]

Can we assume a=1/2 and b=-1/2.
then also option B is correct.
Math Expert
Joined: 02 Sep 2009
Posts: 59020
Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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20 Dec 2015, 04:07
rohit8865 wrote:
If a≠b and a·b≠0, which of the following may be true?

A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0

a^2 (nonnegative number) could equal to -b^2 (nonpositive number) if and only a=b=0 but we are told that a≠b, so neither A nor B could be true.

Your example is not valid because the square roots from negative numbers are not defined for the GMAT (all numbers on the GMAT are real numbers).

Hope it's clear.

Can we assume a=1/2 and b=-1/2.
then also option B is correct. [/quote]

If =1/2 and b=-1/2, then (a^2 = 1/4) ≠ (-b^2 = -1/4).
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Concentration: Strategy, General Management
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Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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20 Dec 2015, 04:59
Bunuel wrote:
rohit8865 wrote:
If a≠b and a·b≠0, which of the following may be true?

A. a/b=−b/a
B. a^2=−b^2
C. (a−b)^2<0
D. a−b=b−a
E. (a+b)(a−b)=0

a^2 (nonnegative number) could equal to -b^2 (nonpositive number) if and only a=b=0 but we are told that a≠b, so neither A nor B could be true.

Your example is not valid because the square roots from negative numbers are not defined for the GMAT (all numbers on the GMAT are real numbers).

Hope it's clear.

Can we assume a=1/2 and b=-1/2.
then also option B is correct.

If =1/2 and b=-1/2, then (a^2 = 1/4) ≠ (-b^2 = -1/4).[/quote]

Hi,

For option B,

If a = 1/2, and b = -1/2
a^2 = 1/4 and b^2 = 1/4, => -b^2 = -1/4.

But the condition is a^2=-b^2. On Substituting we get, 1/4 ≠ -1/4. Hence B is not the correct option.

On the other hand,
Consider E, (a+b)(a-b)=0
gives, a+b=0 or a-b=0 ,
a=-b or a=b. Since a ≠ b, a=-b.
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Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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03 Feb 2018, 21:11
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Re: If a≠b and a·b≠0, which of the following may be true?   [#permalink] 03 Feb 2018, 21:11
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