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What is x?

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Intern
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Joined: 26 Jul 2016
Posts: 28
Location: India
Concentration: Operations, Entrepreneurship
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GPA: 3.69
WE: Analyst (Manufacturing)
What is x? [#permalink]

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New post Updated on: 16 Oct 2016, 12:58
2
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:03) correct 35% (00:45) wrong based on 233 sessions

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What is x?

(1) x = 4y − 4
(2) xy = 8

Originally posted by yashrakhiani on 14 Oct 2016, 13:20.
Last edited by Bunuel on 16 Oct 2016, 12:58, edited 2 times in total.
Renamed the topic and added the OA.
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Re: What is x? [#permalink]

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New post 14 Oct 2016, 16:12
Answer is E

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..
answer option C

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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Re: What is x? [#permalink]

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New post 14 Oct 2016, 16:13
Consider giving me kudos if you got clarity on how to approach the question.

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Re: What is x? [#permalink]

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New post 16 Oct 2016, 08:41
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

Answer:

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Re: What is x? [#permalink]

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New post 07 Dec 2016, 15:13
Can we not do this: x=4y-4

x=4(y-1) ie x = 4?
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What is x? [#permalink]

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New post 07 Dec 2016, 16:52
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 .
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Re: What is x? [#permalink]

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New post 08 Sep 2017, 21:34
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
Re: What is x?   [#permalink] 08 Sep 2017, 21:34
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