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Math Expert V
Joined: 02 Sep 2009
Posts: 58402
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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10 00:00

Difficulty:   35% (medium)

Question Stats: 73% (01:55) correct 27% (02:34) wrong based on 206 sessions

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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

Source: GMATQuantum

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GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4007
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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4
3
Bunuel 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

Given: 2x + y + z = 3 and 5x + 3y + z = 8
Take 2x + y + z = 3 and multiply both sides by 2 to get the EQUIVALENT fraction: 4x + 2y + 2z = 6

We now have:
5x + 3y + z = 8
4x + 2y + 2z = 6

Subtract the bottom equation from the top equation to get:
x + y - z = 2

Cheers,
Brent
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Manager  Joined: 15 Feb 2015
Posts: 92
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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1
Bunuel 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

Source: GMATQuantum

A quick one!

Subtract Eq 1 from Eq2 ( both are given)

I got 3x+2y=5 wheni did that.

Again, from this equation, subtract eq1 ( 2x+y+z=3)

The answer is x+y-z=2

Hence E
Senior Manager  B
Joined: 28 Feb 2014
Posts: 291
Location: United States
Concentration: Strategy, General Management
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

5x + 3y + z = 8
-2(2x + y + z = 3)

which equals x + y - z = 2

E. 2
Intern  Joined: 27 Oct 2015
Posts: 25
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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

Multiply the first equation by 2 and subtract it from the 2nd equation
x+y-z = 8 - 6 = 2
Retired Moderator P
Joined: 19 Mar 2014
Posts: 922
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - z ?

$$2x + y + z = 3$$ ====> 1

$$5x + 3y + z = 8$$ ====> 2

Multiply Eq. 1 by 2

$$4x + 2y + 2z = 6$$ ===> 3

Substract Eq. 3 from 2

$$5x + 3y + z = 8$$
-$$(4x + 2y + 2z = 6)$$

We Get:

$$x + y - z = 2$$

Hence, Answer is E

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Manager  G
Joined: 18 Jan 2017
Posts: 127
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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Bunuel 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

Source: GMATQuantum

====

2x + y + z = 3 and 5x + 3y + z = 8
Multiply both sides of 2x + y + z = 3 by 2
to get 4x + 2y + 2z = 6

5x + 3y + z = 8
4x + 2y + 2z = 6
Subtract them to get x + y - z = 2

Hence the answer is E
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Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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Bunuel 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

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SVP  P
Joined: 03 Jun 2019
Posts: 1699
Location: India
Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -  [#permalink]

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Bunuel 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

Source: GMATQuantum

Given:
2x + y + z = 3 (1)
5x + 3y + z = 8 (2)

Asked: what is the value of x + y - z?

(2)-2*(1) gives
x+y-z=8-2*3=2

IMO E

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E-mail : kinshook.chaturvedi@gmail.com Re: Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y -   [#permalink] 22 Aug 2019, 19:20
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