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What is "x"? 1) x² + y = 17 2) y = 2x + 2

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Intern
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Joined: 18 Jul 2011
Posts: 32

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GMAT 1: 610 Q44 V31
WE: Consulting (Telecommunications)
What is "x"? 1) x² + y = 17 2) y = 2x + 2 [#permalink]

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New post 30 Jul 2011, 04:35
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

80% (00:49) correct 20% (00:43) wrong based on 51 sessions

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Hi,

actually I keep wondering about the following problem from the 3rd MGMAT Guide:


What is "x"?

1) x² + y = 17
2) y = 2x + 2

Could you please just explain the solution to me?
[Reveal] Spoiler: OA

Kudos [?]: 6 [0], given: 6

Math Forum Moderator
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Joined: 20 Dec 2010
Posts: 1964

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Re: DS: What is "x" [#permalink]

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New post 30 Jul 2011, 05:48
jbelli wrote:
Hi,

actually I keep wondering about the following problem from the 3rd MGMAT Guide:


What is "x"?

1) x² + y = 17
2) y = 2x + 2

Could you please just explain the solution to me?


1)
x=0; y=17
x=1; y=16
In fact, there are infinite solutions for x.
Not Sufficient.

2)
x=0; y=2
x=5; y=12
Infinite solutions for x.
Not Sufficient.

Together:
x² + y = 17 ------------------1
y = 2x + 2 -------------------2

Substituting value of y from 2 in 1:

\(x^2+2x+2=17\)
\(x^2+2x-15=0\)
\(x^2+5x-3x-15=0\)
\(x(x+5)-3(x+5)=0\)
\((x-3)(x+5)=0\)

x can be +3 OR -5.
Not Sufficient.

Ans:"E"
*******************************************

For more on quadratic:
algebra-101576.html#p787276
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Intern
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Re: DS: What is "x" [#permalink]

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New post 30 Jul 2011, 06:31
jbelli wrote:
Hi,

actually I keep wondering about the following problem from the 3rd MGMAT Guide:


What is "x"?

1) x² + y = 17
2) y = 2x + 2

Could you please just explain the solution to me?


Its E.

1 not sufficient. Two variable one equation not possible
2 not sufficient. Two variable one equation not possible

Combining,

x = -5 or 3. No one solution hence not possible

So its E.

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Re: DS: What is "x" [#permalink]

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New post 31 Jul 2011, 22:03
jbelli wrote:
Hi,

actually I keep wondering about the following problem from the 3rd MGMAT Guide:


What is "x"?

1) x² + y = 17
2) y = 2x + 2

Could you please just explain the solution to me?


I would do this way-

1) 2 variables one equation - no definite (at least here) so not sufficient!

2) Again this equation also does not provide a definite solution so insufficient!

now lets consider both together-
by plugging value of y from 2nd equation into 1st equation we get x= -5, 3 (which is again not a single value)

so here also we see that we are not sure to get a single answer so we are done- E it is!

had it been that X is +ve, natural number, -ve then C could have been an answer :!:
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Re: DS: What is "x" [#permalink]

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New post 31 Jul 2011, 22:12
Fluke provided a great explanation. You should be able to solve this type of problem within 60 seconds.

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Re: DS: What is "x" [#permalink]

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New post 01 Aug 2011, 00:38
Thank you very much for the nice explanation!
Just recognized my fault and wont do it again ;-)

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Re: DS: What is "x" [#permalink]

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New post 01 Aug 2011, 09:57
1. Not sufficient

For different y values we will get different x.

2. Not sufficient.

For different y values we will get different x.

together,

we can solve the two equations . But its still not sufficient as we have two values for x. x = 3 or -5.

Answer is E.

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Re: What is "x"? 1) x² + y = 17 2) y = 2x + 2 [#permalink]

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New post 08 Sep 2017, 22:56
jbelli wrote:
Hi,

actually I keep wondering about the following problem from the 3rd MGMAT Guide:


What is "x"?

1) x² + y = 17
2) y = 2x + 2

Could you please just explain the solution to me?


Usually when you see the form x(x +something) = something - on the GMAT then this means there are more than 1 solutions. In this situation

x(x +2) =15

x = 3, -5

Also consider

x(x-5) = 0

X could be 0 or 5

E

Kudos [?]: 35 [0], given: 164

Re: What is "x"? 1) x² + y = 17 2) y = 2x + 2   [#permalink] 08 Sep 2017, 22:56
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