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

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

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New post 05 Aug 2014, 04:14
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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
[Reveal] Spoiler: OA
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Re: If a≠b and a·b≠0, which of the following may be true? [#permalink]

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New post 05 Aug 2014, 05:35
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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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New post 05 Aug 2014, 05:44
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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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Re: If a≠b and a·b≠0, which of the following may be true? [#permalink]

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New post 06 Aug 2014, 00:37
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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If a≠b and a·b≠0, which of the following may be true? [#permalink]

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New post 13 Aug 2014, 07:25
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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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New post 19 Dec 2015, 19:09
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. :oops:
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Re: If a≠b and a·b≠0, which of the following may be true? [#permalink]

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New post 20 Dec 2015, 03:07
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. :oops:[/quote]

If =1/2 and b=-1/2, then (a^2 = 1/4) ≠ (-b^2 = -1/4).
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 20 Dec 2015, 03:59
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. :oops:


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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Re: If a≠b and a·b≠0, which of the following may be true?   [#permalink] 03 Feb 2018, 20:11
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