What is the value of x ? (1) y - x = y - 6 (2) x + 2y = 10

Question

What is the value of x ?

(1) y - x = y - 6

(2) x + 2y = 10

D3N0 · Answer

Ans: A
from stat 1) y-x=y-6
-x =-6 so x=6 (Suff)
from stat 2) x+2y =10
x=10-2y (Unless we know y, we can not find out value of x so) (Not Suff.)

KSBGC · Answer

we are looking for the value of x.

Statement 1:

y-x = y-6

x = 6

Sufficient .

Statement 2 :

x + 2y = 10

As we don't know the value of y , it is not possible to determine the value of x.

NOT Sufficient .

Thus the best answer is A.

MathRevolution · Answer

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution. Visit https://www.mathrevolution.com/gmat/lesson for details. The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify conditions if necessary. Condition 1) y - x = y - 6 is equivalent to x = -6. Since condition 1) yields a unique solution, it is sufficient. Condition 2) x = 2, y = 4 and x = 4 and y = 3 are solutions Since condition 2) does not yield a unique solution, it is not sufficient. Therefore, A is the answer.

BrentGMATPrepNow · Answer

Target question :    What is the value of x ?

Statement 1 : y - x = y - 6 
  Note: In most cases, there are infinitely many solutions to a linear equation with two variables. However, in this case, one of the variables cancels, leaving us an equation with ONE variable   
Subtract y from both sides of the equation to get:  -x = -6 
Multiply both sides of the equation by -1 to get:   x = 6  
Since we can answer the  target question  with certainty, statement 1 is SUFFICIENT

Statement 2 : x + 2y = 10 
This case, none of the variables cancel, which means there are infinitely many solutions to the equation  x + 2y = 10 
Here are two possible solutions: 
 Case a : x = 0 and y = 5. In this case, the answer to the target question is  x = 0 
 Case b : x = 10 and y = 0. In this case, the answer to the target question is  x = 10 
Since we can’t answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent

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What is the value of x ? (1) y - x = y - 6 (2) x + 2y = 10

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GMAT Data Sufficiency (DS) Questions

What is the value of x ? (1) y - x = y - 6 (2) x + 2y = 10

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