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

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Bunuel
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If a b and ab 0, which of the following may be true? [#permalink] New post   26 May 2022, 07:00
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E

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Question Stats:

59% (01:55) correct 41% (01:44) wrong based on 41 sessions
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If \(a≠b\) and \(ab≠0\), which of the following may be true?


A. \(\frac{a}{b}=−\frac{b}{a}\)

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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E
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ThatDudeKnows
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Re: If a b and ab 0, which of the following may be true? [#permalink] New post   26 May 2022, 07:38
Expert Reply
Bunuel wrote:
If \(a≠b\) and \(ab≠0\), which of the following may be true?


A. \(\frac{a}{b}=−\frac{b}{a}\)

B. \(a^2=−b^2\)

C. \((a−b)^2<0\)

D. \(a−b=b−a\)

E. \((a+b)(a−b)=0\)


(A) If a and b both have the same sign, the left side will be positive and the right will be negative. If a and b have opposite signs, the left side will be negative and the right side will be positive. Wrong.
(B) Positive = negative. Wrong.
(C) Anything squared is greater than or equal to zero. Wrong.
(D) Only works if a and b are equal, but that's not allowed. Wrong.
(E) Can we get either (a+b) or (a-b) to be equal to 0? We aren't allowed to do (a-b)=0 because that would make a=b. What about (a+b)? a=1 and b=-1.

Answer choice E.
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Re: If a b and ab 0, which of the following may be true? [#permalink] New post   10 Jun 2022, 02:31
ThatDudeKnows wrote:
Bunuel wrote:
If \(a≠b\) and \(ab≠0\), which of the following may be true?


A. \(\frac{a}{b}=−\frac{b}{a}\)

B. \(a^2=−b^2\)

C. \((a−b)^2<0\)

D. \(a−b=b−a\)

E. \((a+b)(a−b)=0\)


(A) If a and b both have the same sign, the left side will be positive and the right will be negative. If a and b have opposite signs, the left side will be negative and the right side will be positive. Wrong.
(B) Positive = negative. Wrong.
(C) Anything squared is greater than or equal to zero. Wrong.
(D) Only works if a and b are equal, but that's not allowed. Wrong.
(E) Can we get either (a+b) or (a-b) to be equal to 0? We aren't allowed to do (a-b)=0 because that would make a=b. What about (a+b)? a=1 and b=-1.

Answer choice E.



but,
(a+b)(a−b)=0
(a^2 - b^2)=0
a^2=b^2
a=b
i.e. not possible so how come E?
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Re: If a b and ab 0, which of the following may be true? [#permalink] New post   10 Jun 2022, 03:03
Expert Reply
WilliamKane wrote:
ThatDudeKnows wrote:
Bunuel wrote:
If \(a≠b\) and \(ab≠0\), which of the following may be true?


A. \(\frac{a}{b}=−\frac{b}{a}\)

B. \(a^2=−b^2\)

C. \((a−b)^2<0\)

D. \(a−b=b−a\)

E. \((a+b)(a−b)=0\)


(A) If a and b both have the same sign, the left side will be positive and the right will be negative. If a and b have opposite signs, the left side will be negative and the right side will be positive. Wrong.
(B) Positive = negative. Wrong.
(C) Anything squared is greater than or equal to zero. Wrong.
(D) Only works if a and b are equal, but that's not allowed. Wrong.
(E) Can we get either (a+b) or (a-b) to be equal to 0? We aren't allowed to do (a-b)=0 because that would make a=b. What about (a+b)? a=1 and b=-1.

Answer choice E.



but,
(a+b)(a−b)=0
(a^2 - b^2)=0
a^2=b^2
a=b
i.e. not possible so how come E?


We are told in the question stem that a does not equal b.

Also worth noting that a^2=b^2 does not necessarily mean that a=b, as you have in your last step. 1^2=(-1)^2.

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Re: If a b and ab 0, which of the following may be true? [#permalink]
10 Jun 2022, 03:03
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