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What is the value of x - y ?

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What is the value of x - y ?  [#permalink]

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What is the value of x - y ?

(1) 3x - z = 42 and y - z = 5.

(2) x^2 - xy - xz + yz = 84 and x - z = 12.

Originally posted by grantcke on 16 Oct 2016, 09:28.
Last edited by Bunuel on 18 Jan 2018, 15:50, edited 2 times in total.
Renamed the topic and edited the question.
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Re: What is the value of x - y ?  [#permalink]

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New post 16 Oct 2016, 10:26
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2. Taking common term out in first equation
x(x-y) -z(x-y) = 84
(x-z)(x-y) = 84
We also know that x-z=12
12(x-y) = 84 or x-y = 7(Sufficient - Option B)
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Re: What is the value of x - y ?  [#permalink]

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New post 17 Oct 2016, 08:48
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grantcke wrote:
What is the value of x - y ?

(2)\(x^2 - xy - xz + yz = 84\) \(and\) \(x - z = 12.\)

Please explain for (2). Thanks.


Posting only (2)


\(x^2 - xy - xz + yz = 84\) \(and\) \(x - z = 12.\)

Or, \(x^2 - xz - xy + yz = 84\)

Or, \(x( x - z )- y ( x - z ) = 84\)

Or, \(x(12)- y(12) = (12)(7)\)

So, \(x - y = 7\)

So , We can find the value of x - y from statement II

Answer will be (B)

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Re: What is the value of x - y ?  [#permalink]

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New post 03 Nov 2016, 11:48
What is the value of x - y ?

(1) 3x - z = 42 and y - z = 5.

(2) x^2 - xy - xz + yz = 84 and x - z = 12.

(1) 3x - z = 42 and y - z = 5.

From here we can either multiply y-z=12 by -1 and add the two equations or solve for Z and plug back in. Either way you end up with 3x-y=37 and this you cannot rearrange to x-y insuff.

(2) x^2 - xy - xz + yz = 84 and x - z = 12.

From here solve for z
-z=12-x
z=x-12

When you plug in x-12 for z you get

x²-xy-x²+12x+xy-12y=84

12x-12y=84
divide by 12
x-y=7
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Re: What is the value of x - y ?  [#permalink]

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New post 18 Jan 2018, 23:00
grantcke wrote:
What is the value of x - y ?

(1) 3x - z = 42 and y - z = 5.

(2) x^2 - xy - xz + yz = 84 and x - z = 12.


This is that kind of question which seems full of variables(algebra) and thus scares us away, but a slight thinking-on-feet ability and re-arranging the given data often makes the question simple.

(1) 3x - z = 42 and y - z = 5.
Clearly, z can be eliminated if we subtract any equation from the other. If we subtract second equation from first, we get:
3x - y = 42-5 = 37. But this gives us 3x-y, while we need x-y. Nothing else is given. So Insufficient.

(2) x^2 - xy - xz + yz = 84 and x - z = 12.
Can we somehow use x-z = 12 here. Lets factorise the first equation:
x(x-y) - z(x-y) = 84 OR (x-z)(x-y) = 84. We can now substitute x-z = 12 and that will give us a single value of x-y. That's what we need. Sufficient.

Hence B answer
Re: What is the value of x - y ? &nbs [#permalink] 18 Jan 2018, 23:00
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