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# If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?

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If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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14 Jul 2016, 01:48
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35% (medium)

Question Stats:

78% (02:25) correct 22% (02:56) wrong based on 192 sessions

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If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?

A. -4.5.
B. -2.
C. -1.7.
D. 3.
E. 2.5.

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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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14 Jul 2016, 02:10
1
Bunuel wrote:
If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?

A. -4.5.
B. -2.
C. -1.7.
D. 3.
E. 2.5.

If we keep on solving the question it'll take a lot of time.

Quick way.

Given : X+Y = 2X-2Z, --> eq 1
X-2Y = 4Z --> eq 2
X+Y+Z = 21 -->eq 3.

Now we are asked to find the value of Y/Z.

Now let choose some option randomly,

Take C , which is 3, I randomly chose this value as it is positive

Y/Z = 3 , this is the value we need to get.

Then Y = 3Z -- eq 4
Sub this in eq 1.
X + 3Z = 2X - 2Z
=> X = 5Z -->eq 5.

Sub X and Y value in eq 3.

5Z + 3Z + Z = 21
=> Z = 21/9. Now sub this value to get Y , we get Y = 21/3.

Then Y/Z = 21/3 / 21/9 = we get 3 again. So this option is correct.

Hope this helps.

IMO option C is correct.
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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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14 Jul 2016, 03:35
1
X+Y=2X-2Z => Y-X=-2Z....(1)

X-2Y =4Z...(2)

-Y=2Z => Y/Z=-2

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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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14 Jul 2016, 04:11
2
Bunuel wrote:
If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?

A. -4.5.
B. -2.
C. -1.7.
D. 3.
E. 2.5.

X+Y = 2X-2Z
Y= X-2Z---------- 1

X-2Y = 4Z
X-4Z= 2Y--------- 2

Subtracting equation 1 from equation 2
-2Z= Y
Y/Z= -2

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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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14 Jul 2016, 09:16
1. X + Y = 2X - 2Z
Solve for X: X = Y + 2Z

2. X - 2Y = 4Z
Substitute X with the value we found above: (Y + 2Z) - 2Y = 4Z

3. (Y + 2Z) - 2Y = 4Z
Combine like terms: -Y = 2Z --> Y/Z = -2

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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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15 Jul 2016, 14:27
From the 3 equations you choose from where you want to substitute x.

I chose the 2nd one:

1) x+y=2x-2z
2) x-2y=4z --> x=4z+2y
3) x+y+z=21

in 1) (4z+2y) + y = 2(4z+2y) - 2z

4z+3y=8z+4y-2z
-4y+3y=6z-4z
-y=2z
y/z=-2

Ans: B.
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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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15 Jul 2016, 16:52
\text{Original information}\\ \begin{align} &X+Y = 2X-2Z &&&& (1)\\ &X-2Y = 4Z &&&& (2)\\ &X+Y+Z = 21 &&&& (3)\\ \hline \\ &Y = X-2Z && \text{rearrange (1)} && (4)\\ &X = 4Z+2Y && \text{rearrange (2)} && (5)\\\\ &Y = 2Z + 2Y && \text{sub (5) into (4)} &&\\ &Y = -2Z\\ &\frac{Y}{Z} = -2\\\\ &\text{Answer: (B) -2} \end{align}
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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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23 Mar 2017, 11:46
Can be solved just by solving the 1st 2 equations

x+y=2x-2z= x-y=2z

x-y=2z
x-2y=4z x -1= -x+2y=-4z

x-y=2z
-x+2y=-4z

y=-2z
y/z=-2

option b
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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?  [#permalink]

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16 Dec 2018, 12:17

Solution

Given:
• X+Y = 2X-2Z
• X-2Y = 4Z
• X+Y+Z = 21

Approach and Working:
• X+Y = 2X-2Z
o Y= X-2Z------(1)

• X-2Y = 4Z
o Substituting the value of y from equation 1, we get: X – 2(X-2Z) = 4Z
o X-2X +4Z=4Z
o -X=0
o Thus, Y= -2Z or Y/Z= -2

Therefore, the correct answer is option B.
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Re: If X+Y = 2X-2Z, X-2Y = 4Z and X+Y+Z = 21, what is the value of Y/Z?   [#permalink] 16 Dec 2018, 12:17
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