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# If x + 2y = z, what is the value of x?

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Manager
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If x + 2y = z, what is the value of x? [#permalink]

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19 Nov 2009, 07:10
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25% (medium)

Question Stats:

68% (00:50) correct 32% (00:53) wrong based on 396 sessions

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If x + 2y = z, what is the value of x?

(1) 3y = 4.5 + 1.5z

(2) y = 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Mar 2015, 07:28, edited 1 time in total.
Renamed the topic, edited the question and added the OA.

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Re: If x + 2y = z, what is the value of x? [#permalink]

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19 Nov 2009, 08:24
kairoshan wrote:
If x + 2y = z, what is the value of x?

(1) 3y = 4.5 + 1.5z

(2) y = 2

A

1.equating this in x+2y =z we can find the value of x.suff
2. we do not know value of z hence insuff

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Re: If x + 2y = z, what is the value of x? [#permalink]

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17 Mar 2015, 06:16
with 1, we get this equation:
y=1.5+0.5z
rearranging the first equation, we get: x+3+z=z
cancel Z's: z+3 = 0 -> x=-3
2. we still have Z for which we have no information.

answ. A

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Re: If x + 2y = z, what is the value of x? [#permalink]

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17 Mar 2015, 07:46
Expert's post
1
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kairoshan wrote:
If x + 2y = z, what is the value of x?

(1) 3y = 4.5 + 1.5z

(2) y = 2

This is an example of a C-Trap question. For more check HERE.
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Re: If x + 2y = z, what is the value of x? [#permalink]

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17 Mar 2015, 09:34
If you try to solve this question without using pen then mostly you will get wrong answer as the equations are written to manipulate.
Simplify equations , using only statement 1 , you will get answer as x=-3.
Hence , statement 1 is enough.
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Re: If x + 2y = z, what is the value of x? [#permalink]

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18 Mar 2015, 19:54
1
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Expert's post
HI All,

This DS question is based on the idea of spotting a common 'multiple' among variables (and it's a concept that you'll likely see at least once on Test Day).

If you don't spot the multiple though, you can still get to the correct answer. While the work will take a little more effort, you can TEST VALUES and prove that a pattern exists.

We're told that X + 2Y = Z. We're asked for the value of X.

Fact 1: 3Y = 4.5 + 1.5Z

IF.....
Z = 0
3Y = 4.5
Y = 1.5

X + 2(1.5) = 0
X + 3 = 0
X = -3
The answer to the question is -3

IF...
Z = 2
3Y = 7.5
Y = 2.5

X + 2(2.5) = 2
X + 5 = 2
X = -3
The answer to the question is -3

IF....
Z = -3
3Y = 0
Y = 0

X + 2(0) = -3
X = -3
The answer to the question is -3

This is clearly a pattern. X is ALWAYS equal to -3
Fact 1 is SUFFICIENT

Fact 2: Y = 2

With this information, the original equation becomes....
X + 2(3) = Z
X + 6 = Z

Without the value of Z, we cannot figure out the value of X.
Fact 2 is INSUFFICIENT

[Reveal] Spoiler:
B

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If x + 2y = z, what is the value of x? [#permalink]

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18 Sep 2016, 18:06
Correct answer is A. Here's why:

(1) 3y = 9/2 + (3/2)z --> Multiply by 2

6y = 9 + 3z

Plug in main equation & you get...6y = 9 + 3(x+2y)

This simplifies down to 3x = -9 --> x = -3

SUFFICIENT

(2) y = 2

INSUFFICIENT - we cannot get the value of x with just the value of y alone; we need z as well (or some relationship between y and z)

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Re: If x + 2y = z, what is the value of x? [#permalink]

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29 May 2017, 11:27
kairoshan wrote:
If x + 2y = z, what is the value of x?

(1) 3y = 4.5 + 1.5z

(2) y = 2

The goal here is to find the unique value of x. Note that you don't need to find y and z independently as long as you find the value of x. It's important to keep this goal in mind.

You can restate the question as x = z - 2y.

Statement 1) 3y = 4.5 + 1.5z

You should immediately note that all are multiples of 3.

y = 1.5+0.5z

y - 0.5 z = 1.5

2y - z = 3

Sufficient since it matches the restated question.

Statement 2) y =2

We need to know the value of z in this case. Insufficient.

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Re: If x + 2y = z, what is the value of x? [#permalink]

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08 Sep 2017, 20:32
kairoshan wrote:
If x + 2y = z, what is the value of x?

(1) 3y = 4.5 + 1.5z

(2) y = 2

x +2y =z ... can't really rewrite this so dig into statements- will there be a way to substitute and cancel any variables?

St 1

3y= 4.5 + 1.5z
3y -4.5 =1.5Z
y - 1.5 = 0.5 Z - multiply by 2
2y- 3 =z

substitute

x +2y = 2y-3

x= -3

suff

St 2

X + 4 =z

insuff

A

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Re: If x + 2y = z, what is the value of x?   [#permalink] 08 Sep 2017, 20:32
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# If x + 2y = z, what is the value of x?

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