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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
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    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?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    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

    Cheers,
    Brent

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