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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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Math Expert
Joined: 02 Sep 2009
Posts: 43862
If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2 [#permalink]

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22 Jun 2017, 22:48
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45% (medium)

Question Stats:

58% (01:17) correct 42% (00:45) wrong based on 66 sessions

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If 3x + 2y = -2z, what is x?

(1) x – y – z = 10

(2) x + y + z = -2
[Reveal] Spoiler: OA

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Director
Joined: 13 Mar 2017
Posts: 562
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2 [#permalink]

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22 Jun 2017, 23:15
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

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Director
Joined: 04 Dec 2015
Posts: 696
Location: India
Concentration: Technology, Strategy
Schools: ISB '19, IIMA , IIMB, XLRI
WE: Information Technology (Consulting)
If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2 [#permalink]

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22 Jun 2017, 23:18
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)

Manager
Joined: 17 Feb 2016
Posts: 106
Location: India
Concentration: General Management, Entrepreneurship
GMAT 1: 660 Q47 V36
GPA: 3.12
WE: Education (Internet and New Media)
If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2 [#permalink]

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22 Jun 2017, 23:23
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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Senior Manager
Joined: 02 Jul 2017
Posts: 288
GMAT 1: 730 Q50 V38
Re: If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2 [#permalink]

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01 Oct 2017, 05:01
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

Re: If 3x + 2y = -2z, what is x? (1) x – y – z = 10 (2) x + y + z = -2   [#permalink] 01 Oct 2017, 05:01
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