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If x + y = 8, if x + z = 7, and if y + z = 6, then x = (A) 3.5 (B) 4

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Carcass
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If x + y = 8, if x + z = 7, and if y + z = 6, then x = (A) 3.5 (B) 4 [#permalink] New post   09 Jun 2022, 01:00
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If x + y = 8, if x + z = 7, and if y + z = 6, then x =

(A) 3.5
(B) 4
(C) 4.5
(D) 5
(E) 5.5

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C
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Re: If x + y = 8, if x + z = 7, and if y + z = 6, then x = (A) 3.5 (B) 4 [#permalink] New post   09 Jun 2022, 03:50
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\(x + y = 8\) so \(y = 8 - x\)

&

\(x + z = 7\), so \(z = 7 - x\)

Now, we are given \(y + z = 6\)

\(8 - x + 7 - x = 6\)

\(x = 4.5\)

Answer \(C\)
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Re: If x + y = 8, if x + z = 7, and if y + z = 6, then x = (A) 3.5 (B) 4 [#permalink] New post   09 Jun 2022, 09:38
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Carcass wrote:
If x + y = 8, if x + z = 7, and if y + z = 6, then x =

(A) 3.5
(B) 4
(C) 4.5
(D) 5
(E) 5.5


We're given the following system of equations:
x + y = 8
x + z = 7
y + z = 6

Strategy: I can see that, if we add the top 2 equations, we'll have 2x + y + z = 15.
So our system becomes:
2x + y + z = 15
y + z = 6

Subtract the bottom equation from the top equation to get: 2x = 9, which we can solve to get x = 4.5

Answer: C
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alsafaj
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Re: If x + y = 8, if x + z = 7, and if y + z = 6, then x = (A) 3.5 (B) 4 [#permalink] New post   09 Jun 2022, 12:29
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if y + z = 6, then z = 6 - y
and if x + z = 7, then x + 6 - y = 7 or y = x + 6 - 7 = x - 1

and if x + y = 8, then 2x = 9 or x = 4.5

The answer is (C)
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gmatclubot
Re: If x + y = 8, if x + z = 7, and if y + z = 6, then x = (A) 3.5 (B) 4 [#permalink]
09 Jun 2022, 12:29
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