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What is the value of x − 3z?

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Director
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What is the value of x − 3z?  [#permalink]

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New post Updated on: 11 Jul 2018, 10:11
1
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A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (01:15) correct 26% (01:28) wrong based on 35 sessions

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What is the value of \(x − 3z?\)

(1) \(x + 4y = 3\)
(2) \(x^2 + 4xy − 3xz − 12yz = 24\)

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Originally posted by CAMANISHPARMAR on 11 Jul 2018, 08:46.
Last edited by Bunuel on 11 Jul 2018, 10:11, edited 1 time in total.
Edited the question.
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Re: What is the value of x − 3z?  [#permalink]

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New post 11 Jul 2018, 09:07
I think the OA is C.

Here is my aporoach.

We need to find x-3z? and equations are in terms of x,y and z .
So we would like to eliminate the y factor.

Clearly individual statements are not sufficient so directly checking the combined case.

STAT1 and STAT2
x+4y=3
implies
4y=3-x(putting in terms of y)

Now substituting value of y in equation 2

x^2 +4x(3-x)/4 -3xz- (3-x)*3z=24

implies

3x-9z=24
x-3z=8 (Clearly this is what we are supposed to find )

So combined statements are sufficient.

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Re: What is the value of x − 3z?  [#permalink]

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New post 11 Jul 2018, 11:10
CAMANISHPARMAR wrote:
What is the value of \(x − 3z?\)

(1) \(x + 4y = 3\)
(2) \(x^2 + 4xy − 3xz − 12yz = 24\)


St1:- x+4y=3
No info on z, hence x-3z can't be determined.
Insufficient.
St2:-\(x^2 + 4xy − 3xz − 12yz = 24\)
Since it is a 2 degree equation, hence it yields 2 solutions, hence x-3z have more than one value.
So, insufficient. Moreover, there are more than one combination of (x,y,z) for which LHS=0.

Combining, from st2, we have
x(x+4y)-3z(x+4y)=24
Or, (x+4y)(x-3z)=24
Or, 3(x-3z)=24 (Substituting the value of x+4y from st1)
So we are able to determine an unique value of (x-3z).
Sufficient.

Ans. (C)
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Re: What is the value of x − 3z? &nbs [#permalink] 11 Jul 2018, 11:10
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