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

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Re: What is the value of x ? (1) y - x = y - 6 (2) x + 2y = 10 [#permalink]
Bunuel wrote:
What is the value of x ?

(1) y - x = y - 6

(2) x + 2y = 10

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.

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Re: What is the value of x ? (1) y - x = y - 6 (2) x + 2y = 10 [#permalink]
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Bunuel wrote:
What is the value of x ?

(1) y - x = y - 6
(2) x + 2y = 10

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

Cheers,
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Re: What is the value of x ? (1) y - x = y - 6 (2) x + 2y = 10 [#permalink]
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Re: What is the value of x ? (1) y - x = y - 6 (2) x + 2y = 10 [#permalink]
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