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

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Intern
Joined: 18 Jul 2011
Posts: 32
GMAT 1: 610 Q44 V31
WE: Consulting (Telecommunications)
What is "x"? 1) x² + y = 17 2) y = 2x + 2  [#permalink]

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30 Jul 2011, 04:35
00:00

Difficulty:

(N/A)

Question Stats:

78% (01:13) correct 22% (00:43) wrong based on 68 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?
Retired Moderator
Joined: 20 Dec 2010
Posts: 1784
Re: DS: What is "x"  [#permalink]

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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"
*******************************************

algebra-101576.html#p787276
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Intern
Joined: 11 Sep 2010
Posts: 10
Location: India
GMAT 1: 620 Q49 V25
Re: DS: What is "x"  [#permalink]

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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.
Manager
Joined: 12 Dec 2010
Posts: 225
Concentration: Strategy, General Management
GMAT 1: 680 Q49 V34
GMAT 2: 730 Q49 V41
GPA: 4
WE: Consulting (Other)
Re: DS: What is "x"  [#permalink]

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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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Manager
Joined: 25 Jun 2008
Posts: 121
Concentration: General Management, Technology
Re: DS: What is "x"  [#permalink]

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31 Jul 2011, 22:12
Fluke provided a great explanation. You should be able to solve this type of problem within 60 seconds.
Intern
Joined: 18 Jul 2011
Posts: 32
GMAT 1: 610 Q44 V31
WE: Consulting (Telecommunications)
Re: DS: What is "x"  [#permalink]

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01 Aug 2011, 00:38
Thank you very much for the nice explanation!
Just recognized my fault and wont do it again
Director
Joined: 01 Feb 2011
Posts: 646
Re: DS: What is "x"  [#permalink]

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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.

Director
Joined: 12 Nov 2016
Posts: 725
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
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Re: What is "x"? 1) x² + y = 17 2) y = 2x + 2  [#permalink]

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