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# What is x?

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Intern
Joined: 26 Jul 2016
Posts: 28
Location: India
Concentration: Operations, Entrepreneurship
Schools: Tepper '19
GPA: 3.69
WE: Analyst (Manufacturing)

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Updated on: 16 Oct 2016, 11:58
4
00:00

Difficulty:

35% (medium)

Question Stats:

67% (01:30) correct 33% (01:02) wrong based on 315 sessions

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What is x?

(1) x = 4y − 4
(2) xy = 8

Originally posted by yashrakhiani on 14 Oct 2016, 12:20.
Last edited by Bunuel on 16 Oct 2016, 11:58, edited 2 times in total.
Renamed the topic and added the OA.
Intern
Joined: 24 Jun 2016
Posts: 30

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14 Oct 2016, 15:12

EXPLANATION
Statement I & II individually will not be able to answer as both have 2 variable and 1equation.

Hence option A,B,&D are ELIMINATED

now checking for..

Solving together
From i) x=4y-4
ii) y=8/x using this
We get x^2 + 4x - 32 = 0
(x+8)(x-4)=0
I.E x= -8, +4
Hence 2 solution
We do not have a definite value of x

Hence answer option E is correct

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Intern
Joined: 24 Jun 2016
Posts: 30

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14 Oct 2016, 15:13
Consider giving me kudos if you got clarity on how to approach the question.

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GMAT Club Legend
Joined: 11 Sep 2015
Posts: 4360

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16 Oct 2016, 07:41
2
Top Contributor
yashrakhiani wrote:
What is x?

(1) x = 4y − 4
(2) xy = 8

Target question: What is the value of x?

Statement 1: x = 4y − 4
1 equation with 2 variables means there are infinitely many possible values for x.
If we're uncertain, we can TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 0 and y = 1. in this case x = 0
Case b: x = 4 and y = 2. in this case x = 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: xy = 8
1 equation with 2 variables means there are infinitely many possible values for x.
If we're uncertain, we can TEST some values.
There are several values of x and y that satisfy statement 2. Here are two:
Case a: x = 1 and y = 8. in this case x = 1
Case b: x = 4 and y = 2. in this case x = 4
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that x = 4y − 4
Statement 2 tells us that xy = 8

Take x = 4y − 4, and solve for y.
So, add 4 to both sides to get: x + 4 = 4y
Divide both sides by 4 to get: (x + 4)/4 = y

Now take xy = 8 and replace y with (x + 4)/4 to get...
(x)(x + 4)/4 = 8
Multiply both sides by 4 to get: (x)(x + 4) = 32
Expand: x² + 4x = 32
Set equal to zero to get: x² + 4x - 32 = 0
Factor: (x + 8)(x - 4) = 0
So, EITHER x = -8 OR x = 4
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

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Intern
Joined: 30 Sep 2016
Posts: 7

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07 Dec 2016, 14:13
Can we not do this: x=4y-4

x=4(y-1) ie x = 4?
Manager
Joined: 13 Jun 2012
Posts: 195
Location: United States
WE: Supply Chain Management (Computer Hardware)

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07 Dec 2016, 15:52
Nasahtahir wrote:
Can we not do this: x=4y-4

x=4(y-1) ie x = 4?

No Sir, we cant. you mentioned correctly x=4(y-1), so to find X we have to know y. If you see some of the previous posts you will find the way .
Director
Joined: 12 Nov 2016
Posts: 678
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66

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08 Sep 2017, 20:34
yashrakhiani wrote:
What is x?

(1) x = 4y − 4
(2) xy = 8

So this question is actually a "C" trap

St 1

Clearly too many options

Insuff

St 2

Clearly too many options insuff

St 1 & 2

If x + 4 =4y and xy= 8 then

x + 4 (x) =32

X= 4 or -8

Insuff

E
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Joined: 09 Sep 2013
Posts: 14156

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18 Jan 2020, 07:17
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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Re: What is x?   [#permalink] 18 Jan 2020, 07:17
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