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What is the value of x?

This topic has 1 expert reply and 0 member replies
ahmedshafea Junior | Next Rank: 30 Posts
Joined
30 Aug 2017
Posted:
19 messages

What is the value of x?

Post Mon Sep 11, 2017 12:56 pm
What is the value of x?

(1) 2x - 5y + 6 = 12

(2) 8x - (4x + 10y) + 27 = 39


Can you help me with the DS question? What's the best way to determine whether statement 1 is sufficient?

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GMAT/MBA Expert

Post Mon Sep 11, 2017 1:10 pm
ahmedshafea wrote:
What is the value of x?

(1) 2x - 5y + 6 = 12
(2) 8x - (4x + 10y) + 27 = 39
Target question: What is the value of x?

Statement 1: 2x - 5y + 6 = 12
Subtract 6 from both sides to get: 2x - 5y = 6
Since we have one equation with 2 variables, there are infinitely many solutions.
In other words, x can have infinitely many values, which means statement 1 is NOT SUFFICIENT.

ASIDE: If you're not 100% convinced that there are infinitely many solutions, you can always test some values
There are several values of x and y that satisfy the equation 2x - 5y = 6. Here are two:
Case a: x = 3 and y = 0, in which case x = 3
Case b: x = 8 and y = 2, in which case x = 8

Statement 2: 8x - (4x + 10y) + 27 = 39
Subtract 27 from both sides to get: 8x - (4x + 10y) = 12
Expand: 8x - 4x - 10y = 12
Simplify: 4x - 10y = 12
Here we have another equation with 2 variables, which means there are infinitely many solutions.
In other words, x can have infinitely many values, which means statement 2 is NOT SUFFICIENT.

Statements 1 and 2 combined
Statement 1 tells us that 2x - 5y = 6
Statement 2 tells us that 4x - 10y = 12
IMPORTANT: the two equations above are EQUIVALENT equations.
If we take the equation 4x - 10y = 12 and divide both sides by 2 we get the EQUIVALENT equation 2x - 5y = 6
Since the two statements provide the same information, and since each statement alone is NOT SUFFICIENT, we can conclude that the COMBIEND statements are NOT SUFFICIENT

Answer: E

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Brent

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