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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the

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by VJesus12 » Mon Mar 19, 2018 3:50 am
Given

2x + y + z = 3
and

5x + 3y + z = 8,

what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2

The OA is E.

How can I know the value of x + y - z if I know just two equations? Can any expert give me some help here? Thanks in advanced.
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by GMATGuruNY » Mon Mar 19, 2018 4:10 am
VJesus12 wrote:Given

2x + y + z = 3
and

5x + 3y + z = 8,

what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2.
If we multiply 2x+y+z=3 by 2, we get:
4x+2y+2z=6.
If we subtract the equation in blue from 5x+3y+z=8, we get:
(5x+3y+z) - (4x+2y+2z) = 8-6
x+y-z = 2.

The correct answer is E.
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by Brent@GMATPrepNow » Mon Mar 19, 2018 6:05 am
VJesus12 wrote:Given

2x + y + z = 3
and
5x + 3y + z = 8,

What is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2
Another approach is to look for values of x, y and z that satisfy BOTH equations (2x + y + z = 3 and 5x + 3y + z = 8).
One set of values is x = 1, y = 1 and z = 0 (there are infinitely many sets of values that satisfy both equations)

What is the value of x + y - z ?
x + y - z = 1 + 1 - 0 = 2

Answer: E

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Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Tue Mar 20, 2018 4:03 pm
VJesus12 wrote:Given

2x + y + z = 3
and

5x + 3y + z = 8,

what is the value of x + y - z ?

A. -2
B. -1
C. 0
D. 1
E. 2
We can multiply the first equation by -2, and we have:

-4x - 2y - 2z = -6

Adding the above equation with the equation 5x + 3y + z = 8, we have:

x + y - z = 2

Answer: E

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by deloitte247 » Fri Mar 23, 2018 11:23 pm
$$2x+y+z=3---\left(i\right)$$
$$5x+3y+z=8---\left(ii\right)$$
$$mutiply\ eqn\ \left(i\right)\ by\ \left(2\right)$$
$$\left(2x\cdot2\right)+\left(2\cdot y\right)+\left(2\cdot z\right)=2\cdot3$$
$$4x+2y+2z=6---\left(iii\right)$$
Subtract eqn (iii) from (ii)
$$5x+3y+z=8---\left(ii\right)$$
$$4x+2y+2z=6---\left(iii\right)$$
$$we\ have\ x+y-z=2$$
The correct option is E
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