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# M23-33

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Math Expert
Joined: 02 Sep 2009
Posts: 47015

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16 Sep 2014, 01:20
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:32) correct 42% (01:30) wrong based on 116 sessions

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 47015

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16 Sep 2014, 01:20
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.

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Manager
Joined: 11 Sep 2013
Posts: 149
Concentration: Finance, Finance

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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?
Intern
Joined: 04 Sep 2014
Posts: 49
Schools: CBS '18 (D)

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20 Jun 2015, 05:24
5
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.
Current Student
Joined: 18 Jun 2015
Posts: 41

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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.
Intern
Joined: 22 Nov 2014
Posts: 29

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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
Intern
Joined: 31 Aug 2017
Posts: 1

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16 Sep 2017, 22:31
Bunuel, can you explain how you got from the original equation to (1−x)(1−y)−1=1?
Math Expert
Joined: 02 Sep 2009
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17 Sep 2017, 02:46
1
rochmarcbenoit wrote:
Bunuel, can you explain how you got from the original equation to (1−x)(1−y)−1=1?

$$xy-x-y=1$$

$$xy-x-y + 1 - 1=1$$

$$(xy-y) + (1-x) - 1=1$$

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

$$(1-x)(1-y)- 1=1$$
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Joined: 07 Jun 2017
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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
Director
Joined: 08 Jun 2015
Posts: 519
Location: India
GMAT 1: 640 Q48 V29
GMAT 2: 700 Q48 V38

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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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Intern
Joined: 02 Jun 2014
Posts: 19
GMAT 1: 740 Q49 V41

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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
Re: M23-33   [#permalink] 30 Mar 2018, 09:27
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# M23-33

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