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M23-33

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M23-33  [#permalink]

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New post 16 Sep 2014, 01:20
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

58% (01:32) correct 42% (01:31) wrong based on 123 sessions

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Re M23-33  [#permalink]

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New post 16 Sep 2014, 01:20
1
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, 14:32
(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, 05:24
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2
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, 14:50
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, 02:25
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, 22:31
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, 02:46
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Re: M23-33  [#permalink]

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New post 30 Mar 2018, 05:56
X= 1+Y/Y-1
substitute the value of y one by one
when y = 1 than 1-1 =0 ,any no divided by 0 is not defined
therefore ans is D
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Re: M23-33  [#permalink]

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New post 30 Mar 2018, 06:34
Express x in terms of y. x=(1+y)/(1-y). y can't be 1. Hence option D
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Re: M23-33  [#permalink]

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New post 30 Mar 2018, 09:27
I solved this by plugging in each answer for Y.

For (D): you get X-X-1=1 Which is 0-1=1 or 0=2, which doesn't work
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Re M23-33  [#permalink]

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New post 28 Jul 2018, 08:00
Given xy-x-y=1
Since we want to know the value of y, we can isolate y to one side i.e.
y=xy-x-1
y+1=xy-x
y+1=x(y-1)
now browse through the options, if you pick y's value as 1, then right hand side will become 0, whereas left hand side cannot be zero, since we have a "+1" there. This would make both sides unequal
therefore, value of y cannot be 1
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Re M23-33 &nbs [#permalink] 28 Jul 2018, 08:00
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