Does x + c = y + c ? (1) x = y (2) x = c

Question

Does x + c = y + c ?

(1) x = y
(2) x = c

racingip · Answer

The solution is supposed to be A. Yet, I am not clear about that.

My approach is as follows:

First, I simplify the equation: x+c=y+c, so I get x=y. The question becomes, is x=y?

Statement 1: x=y. Sufficient
Statement 2: x=c. Substituting x in the original equation we get x+x=y+x; 2x =y+x, and then x=y. So statement 2 is sufficient.

Solution is option D.

I am not sure what I am missing.

mvictor · Answer

you are not correct, and I will provide few examples.

statement 1 is sufficient as you say.
x=y, that means c=c all the times
say x=2, y=2, c=-2
2-2=2-2 = always true.

statement 2 is not sufficient, and here is why:
case 1:
x=c
x=2, c=2, y=2
2+2=2+2 - true

case 2:
x=c
x=2, c=2. y=-2
2+2=y+2 - not true
Y can be ANY number, therefore, it's an additional coefficient that we don't know

A is the answer.

don't take the QUESTION as a statement - you are asked whether x+c=y+c, not given it as a FACT!

Nunuboy1994 · Answer

You're making the mistake of already assuming what you're attempting to prove either incorrect or correct in the problem. Be careful- this is a huge trap on data sufficiency; you can only reduce the equation in the stimulus to x=c if the stated equation x + c = y + c is already known to be true.

varun4s · Answer

(1) x=y, add C on both sides of the equation
 x+c= y+c  
(2) x=c, if x=y then answer is yes
 if x>y then answer is no.Two different answer,

Answer: A.

Kudos please if you like my explanation!

BrentGMATPrepNow · Answer

Target question :    Does x + c = y + c ?  
This is a good candidate for  rephrasing the target question.  
Take the equation  x + c = y + c , and subtract c from both sides to get:  x = y

REPHRASED target question :    Does x = y ?

Aside: the video below has tips on rephrasing the target question

Statement 1 : x = y  
Perfect!The answer to the REPHRASED target question is  YES, x = y 
Since we can answer the  REPHRASED target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : x = c 
Since we know nothing about the value of y, we cannot answer the REPHRASED target question 
Statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

RELATED VIDEO 
 https://www.youtube.com/watch?v=MyG1K3ee69w

bumpbot · Answer

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Does x + c = y + c ? (1) x = y (2) x = c

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