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Senior Manager  Joined: 21 Oct 2013
Posts: 411
If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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5 00:00

Difficulty:   55% (hard)

Question Stats: 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
Intern  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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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
Manager  Joined: 03 Jul 2012
Posts: 89
GMAT 1: 710 Q50 V36 GPA: 3.9
WE: Programming (Computer Software)
Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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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
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Joined: 27 Dec 2012
Posts: 1749
Location: India
Concentration: General Management, Technology
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Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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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: 02 Sep 2009
Posts: 58445
If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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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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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 V
Joined: 02 Sep 2009
Posts: 58445
Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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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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Posts: 25
Location: United States
Concentration: Strategy, General Management
WE: General Management (Pharmaceuticals and Biotech)
Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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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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Posts: 13275
Re: If a≠b and a·b≠0, which of the following may be true?  [#permalink]

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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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