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# (x−2)(2+y)=? (1) x·y=6 (2) x+y=5

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Senior Manager
Joined: 12 Apr 2010
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(x−2)(2+y)=? (1) x·y=6 (2) x+y=5 [#permalink]  20 Jun 2011, 23:58
00:00

Difficulty:

35% (medium)

Question Stats:

54% (02:19) correct 46% (00:25) wrong based on 39 sessions
(x−2)(2+y)=?

(1) x·y=6

(2) x+y=5

Source Master Gmat sample Test Q 20
[Reveal] Spoiler: OA

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Manager
Joined: 16 Mar 2011
Posts: 177
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Kudos [?]: 31 [0], given: 13

Re: x,y and the rest of the band [#permalink]  21 Jun 2011, 00:15
Statement 1: if you substitute for 6/x for y you get 2 values for x which means there is no certain answer
Statement 2: ditto. if you substitute 5-y for x you get (3-y)(2+y), which gives you, y = 3 of y = -2.

I had some trouble working it out and the whole post got messed up (I think I did something wrong using some math signs or something:S), I'll try to do it later.
SVP
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Kudos [?]: 363 [0], given: 36

Re: x,y and the rest of the band [#permalink]  21 Jun 2011, 00:15
The answer is E. (1) and (2) don't give single specific values for x and y. Combination of (1) and (2) gives a quadratic equation, which can give 2 values of x (or y), which in turn can result in two values of the expression that we're supposed to evaluate. Hence there is no single specific answer for the expression based on data given.
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Intern
Joined: 14 Mar 2010
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Kudos [?]: 7 [0], given: 1

Re: x,y and the rest of the band [#permalink]  21 Jun 2011, 06:59
shouldnt it b C?

From 1 and 2 we can get values of X and y ( 2 equations and 2 variables )

from 1 & 2 -> x = 7/2 , y=3/2

from this we can calculate the value of x−2)(2+y)=?
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Current Student
Joined: 26 May 2005
Posts: 565
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Kudos [?]: 146 [0], given: 13

Re: x,y and the rest of the band [#permalink]  21 Jun 2011, 07:12
msbinu wrote:
shouldnt it b C?

From 1 and 2 we can get values of X and y ( 2 equations and 2 variables )

from 1 & 2 -> x = 7/2 , y=3/2

from this we can calculate the value of x−2)(2+y)=?

from 1 & 2 -> x = 7/2 , y=3/2..............??????

this is wrong.. x*y = 6
Intern
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Re: x,y and the rest of the band [#permalink]  21 Jun 2011, 07:16
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Manager
Joined: 03 Jun 2010
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Concentration: Marketing, General Management
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Kudos [?]: 31 [0], given: 40

Re: x,y and the rest of the band [#permalink]  21 Jun 2011, 07:17
msbinu wrote:
shouldnt it b C?

From 1 and 2 we can get values of X and y ( 2 equations and 2 variables )

from 1 & 2 -> x = 7/2 , y=3/2

from this we can calculate the value of x−2)(2+y)=?

From 1) and 2) we have answer pairs:
$$(2;3) and (3;2)$$
substitute it and get:
$$1*4=4$$
or
$$0*5=0$$
(E)
Director
Joined: 01 Feb 2011
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Kudos [?]: 74 [0], given: 42

Re: x,y and the rest of the band [#permalink]  25 Jun 2011, 18:28
1. Not sufficient
different combinations of x , y yields different values.

2 3
6 1
2. Not sufficient
different combinations of x , y yields different values.
1 4
2 3

Together .. Not sufficient

we know that x can be 2 or 3
then y can be 3 or 2.
these two combinations yields different values..

Director
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Re: x,y and the rest of the band [#permalink]  20 Jul 2011, 02:36
Normally, the 2 equation system has 2 set of solution
Manager
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Kudos [?]: 46 [0], given: 15

Re: x,y and the rest of the band [#permalink]  05 Sep 2011, 08:22
Quote:
(x−2)(2+y)=?

(1) x·y=6

(2) x+y=5

Source Master Gmat sample Test Q 20

(x-2)(2+y) = xy - 2y + 2x -4 ...............[eq 1]

From Statement 1
Insert x.y=6 into [eq 1], 6 - 12/x + 2x - 4 = 2x-10
insufficient

From Statement 2
x+y=5
y=5-x

Insert into [eq 1], x(5-x)-2(5-x)+2x-4 = 5x-x^2-10+2x+2x-4 = -x^2+9x-14
insufficient

Statement 1 + 2
x(5-x)=6
5x-x^2-6=0
(-x-2)(x-3)=0
x=3 or x =2
Insufficient

Quote:
The answer is E. (1) and (2) don't give single specific values for x and y. Combination of (1) and (2) gives a quadratic equation, which can give 2 values of x (or y), which in turn can result in two values of the expression that we're supposed to evaluate. Hence there is no single specific answer for the expression based on data given.

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Re: x,y and the rest of the band   [#permalink] 05 Sep 2011, 08:22
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