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If a, b, and c are nonzero integers and c is equal

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If a, b, and c are nonzero integers and c is equal [#permalink]

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If a, b, and c are nonzero integers and c is equal to the difference of a and b, all of the following could be true EXCEPT

(A) \(a = b + c\)
(B) \(a = b - c\)
(C) \(b = a + c\)
(D) \(b = a - c\)
(E) \(c = a + b\)

Source: http://www.gmathacks.com
[Reveal] Spoiler: OA

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Last edited by Bunuel on 18 Aug 2012, 01:40, edited 1 time in total.
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Re: If a, b, and c are nonzero integers and c is equal [#permalink]

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New post 18 Aug 2012, 15:23
c= |a-b|
From the info given it follows that either
i> c = a - b or
ii> c = b - a

from i, we get a = b+c and b = a-c
from ii we get b= a+c and a = b-c

the one left out is E.

Alternatively, c is the difference of a and b, not their sum.
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Re: If a, b, and c are nonzero integers and c is equal [#permalink]

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New post 21 Aug 2012, 01:02
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metallicafan wrote:
If a, b, and c are nonzero integers and c is equal to the difference of a and b, all of the following could be true EXCEPT

(A) \(a = b + c\)
(B) \(a = b - c\)
(C) \(b = a + c\)
(D) \(b = a - c\)
(E) \(c = a + b\)

Source: http://www.gmathacks.com


That's an interesting question because it can be answered without even reading the stem. Remember we cannot have more than one correct answer in PS.

Now, since options A and D are the same (b=a-c --> a=b+c), then neither of them can be correct. Similarly, since options B and C are the same (b=a+c --> a=b-c), then neither of them can be correct. Only option left is E.

Answer: E.
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Re: If a, b, and c are nonzero integers and c is equal [#permalink]

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New post 26 Oct 2017, 15:41
metallicafan wrote:
If a, b, and c are nonzero integers and c is equal to the difference of a and b, all of the following could be true EXCEPT

(A) \(a = b + c\)
(B) \(a = b - c\)
(C) \(b = a + c\)
(D) \(b = a - c\)
(E) \(c = a + b\)


c = a - b, or c = b - a

With the first equation, we have:

c + b = a

and

b = a - c

With the second equation, we have:

c + a = b

and

a = b - c

Thus, we see that E cannot be true.

Answer: E
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Re: If a, b, and c are nonzero integers and c is equal   [#permalink] 26 Oct 2017, 15:41
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