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555-605 (Medium)|   Algebra|      
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Bunuel
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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 09 Dec 2015, 08:41
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E
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35% (medium)

Question Stats:

76% (01:56) correct 24% (02:34) wrong based on 451 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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E
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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 09 Dec 2015, 08:54
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Bunuel
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
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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

Answer: E

Cheers,
Brent
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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 09 Dec 2015, 10:20
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Bunuel
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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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
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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 09 Dec 2015, 17:05
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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
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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 09 Dec 2015, 18:31
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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
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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 16 Jul 2017, 14:22
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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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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 17 Jul 2017, 11:20
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Bunuel
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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ANSWER:
====

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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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 20 Jul 2017, 16:37
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Bunuel
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
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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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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 22 Aug 2019, 19:20
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Bunuel
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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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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Given 2x + y + z = 3 and 5x + 3y + z = 8, what is the value of x + y - 22 Sep 2022, 10:24
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Quick solution:

Plug in numbers x=1, y=1, z=0 which satisfies both equations which is easy to guess.

Therefore, x+y-z = 1+1-0 = 2
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