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If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2

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Joined: 02 Sep 2009
Posts: 54440
If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2  [#permalink]

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New post 22 Jun 2017, 23:48
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A
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D
E

Difficulty:

  55% (hard)

Question Stats:

63% (01:36) correct 37% (01:25) wrong based on 91 sessions

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If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2  [#permalink]

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New post 23 Jun 2017, 00:15
1
Bunuel wrote:
If 3x + 2y = -2z, what is x?


(1) x – y – z = 10

(2) x + y + z = -2


Known : 3x + 2y = -2z
DS: x

Option 1: x-y-z = 10
z = x-y-10

3x +2y = -2(x-y-10) = -2x + 2y +20
5x = 20
x =4............... SUFFICIENT

Option 2: x +y +z = -2
z = -2 -x -y

3x +2y = -2 (-2-x-y) = 4 +2x +2y
x = 4..........SUFFICIENT


Answer D.
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If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2  [#permalink]

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New post 23 Jun 2017, 00:18
Bunuel wrote:
If 3x + 2y = -2z, what is x?


(1) x – y – z = 10

(2) x + y + z = -2


\(3x + 2y = -2z\)
\(3x + 2y + 2z = 0\) ------- (i)

(1) \(x – y – z = 10\)
Multiplying 2 in above equation we get;
\(2x - 2y - 2z = 20\) ---------- (ii)

Adding equation (i) and (ii), we get;

\(3x + 2y + 2z = 0\)
\(2x - 2y - 2z = 20\)
\(5x = 20\)
\(x = 4\) ------------- (I is Sufficient)

(2) \(x + y + z = -2\)
Multiplying 2 in above equation we get;
\(2x + 2y + 2z = -4\) ---------- (iii)

Subtracting equation (i) and (iii), we get;

\(3x + 2y + 2z = 0\)
\(-(2x + 2y + 2z = -4)\)
\(-2x -2y -2z = 4\)
\(x = 4\) ------------- (II is Sufficient)

Answer (D) ...
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If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2  [#permalink]

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New post 23 Jun 2017, 00:23
Bunuel wrote:
If 3x + 2y = -2z, what is x?


(1) x – y – z = 10

(2) x + y + z = -2


Rearrange the equation

\(\frac{x=-2(z+y)}{3}\) x=?

St1 : \(y +z= x-10\) Suff
St2: \(y+z=-2-x\) Suff

D
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Re: If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2  [#permalink]

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New post 01 Oct 2017, 06:01
If 3x + 2y = -2z, what is x?

3x= -2z-2y
3x=-2(y+z) ................ (1)


(1) x – y – z = 10
x-(y+z)=10
2x-2(y+z)=20
By eq 1
2x+3x=20
x=4
Sufficient

(2) x + y + z = -2
2x+2(y+z)=-4
by eq 1
2x+(-3x) = -4
x=4
Sufficient

Answer: D
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Re: If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2  [#permalink]

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Re: If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2   [#permalink] 22 Mar 2019, 00:05
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