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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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Updated on: 18 Aug 2012, 00:40
1
1
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:18) correct 20% (01:56) wrong based on 122 sessions

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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

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Originally posted by metallicafan on 17 Aug 2012, 14:01.
Last edited by Bunuel on 18 Aug 2012, 00:40, edited 1 time in total.
Edited the question.
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Re: If a, b, and c are nonzero integers and c is equal  [#permalink]

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18 Aug 2012, 14:23
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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21 Aug 2012, 00:02
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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.

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

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26 Oct 2017, 14:41
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.

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Re: If a, b, and c are nonzero integers and c is equal &nbs [#permalink] 26 Oct 2017, 14:41
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