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

This is an example of a C-Trap question. For more check HERE.

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.

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

Final Answer:

GMAT assassins aren't born, they're made,
Rich

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)

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.

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

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

To find: x?

(1) 3y = 4.5 + 1.5z
multiplying equation by 2
6y = 9 + 3z
dividing by 3
2y = 3 + z
z - 2y = -3 = x
sufficient

(2) y = 2
Insufficient as z is unknown

A is correct

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