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M23-33

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M23-33 [#permalink]

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New post 16 Sep 2014, 00:20
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D
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Question Stats:

51% (01:11) correct 49% (01:31) wrong based on 41 sessions

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Kudos [?]: 139428 [0], given: 12790

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Re M23-33 [#permalink]

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New post 16 Sep 2014, 00:20
Official Solution:

For any numbers \(x\) and \(y\), \(x@y=xy-x-y\). If \(x@y=1\), which of the following cannot be the value of \(y\) ?

A. -2
B. -1
C. 0
D. 1
E. 2

Given \(xy-x-y=1\), which is the same as \((1-x)(1-y)-1=1\) or \((1-x)(1-y)=2\). Now, if \(y=1\) then \((1-x)(1-1)=0 \ne 2\), so in order the given equation to hold true \(y\) cannot equal to 1.

Answer: D
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Re: M23-33 [#permalink]

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New post 02 Dec 2014, 13:32
(1-x)(1-y)-1=1 or (1-x)(1-y)=2

I understand above equation. But in exam time this logic will not come automatically. Is there any other way to find answer?

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Re: M23-33 [#permalink]

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New post 20 Jun 2015, 04:24
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How is this for a solution?

Expressing x in terms of y:

x = (1+y)/(y-1)

Therefore y cannot equal 1 - answer D.

I think it's more intuitive than the official answer.

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Re: M23-33 [#permalink]

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New post 10 Sep 2016, 13:50
We can also solve this question by substituting.
only y=1 gives final result as -1=1 which is contradictory.

else option leaves x = some value which is feasible.

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Re: M23-33 [#permalink]

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New post 16 Jan 2017, 01:25
nealz wrote:
We can also solve this question by substituting.
only y=1 gives final result as -1=1 which is contradictory.

else option leaves x = some value which is feasible.


i second you x=1+y/y-1....
now substitute x and make the equation in terms of y and then substitute from the option
its long but better than official sol

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Re: M23-33 [#permalink]

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New post 16 Sep 2017, 21:31
Bunuel, can you explain how you got from the original equation to (1−x)(1−y)−1=1?

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Re: M23-33 [#permalink]

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New post 17 Sep 2017, 01:46
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Re: M23-33   [#permalink] 17 Sep 2017, 01:46
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