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If x > y > z, which cannot be . . .

This topic has 2 expert replies and 0 member replies

If x > y > z, which cannot be . . .

Post Wed Sep 20, 2017 6:50 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    If x > y > z, which cannot be the average (arithmetic mean) of x, y and z?

    A. x
    B. y
    C. x - 1
    D. z + 1
    E. (z + x)/2

    The OA is A.

    How can I approach this PS question? Which formulas should I use? Or should I set a number for each variable?

    Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!
    Post Wed Sep 20, 2017 7:09 am
    Vincen wrote:
    If x > y > z, which CANNOT be the average (arithmetic mean) of x, y and z?

    A. x
    B. y
    C. x - 1
    D. z + 1
    E. (z + x)/2
    One option is to plug in numbers that allow us to eliminate 4 of the answer choices.
    In fact, we can use the same set of values to eliminate B, C, D and E:

    B) If x = 3, y = 2 and z = 1, then the average of x, y, and z is 2 (which is the same as y).
    Since the average CAN equal y, we can ELIMINATE B

    C) If x = 3, y = 2 and z = 1, then the average of x, y, and z is 2 (which is the same as x-1).
    Since the average CAN equal x-1, we can ELIMINATE C

    D) If x = 3, y = 2 and z = 1, then the average of x, y, and z is 2 (which is the same as z+1).
    Since the average CAN equal z+1, we can ELIMINATE D

    E) If x = 3, y = 2 and z = 1, then the average of x, y, and z is 2 (which is the same as z+x/2).
    Since the average CAN equal (z+x)/2, we can ELIMINATE E

    Answer: A

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
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    Thanked by: Vincen
    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
    Post Wed Sep 20, 2017 7:15 am
    Vincen wrote:
    If x > y > z, which cannot be the average (arithmetic mean) of x, y and z?

    A. x
    B. y
    C. x - 1
    D. z + 1
    E. (z + x)/2
    Another approach is to apply some number sense.

    Since y and z are smaller than x, we can say....
    y = a number smaller than x
    z = another number smaller than x

    So.....
    The average of x, y and z = the average of x, a number smaller than x, and another number smaller than x
    = (x + a number smaller than x + another number smaller than x)/3
    = (a number that's LESS THAN 3x)/3
    = a number LESS THAN x

    Since the average must be LESS THAN x, the average cannot equal x

    Answer: A

    RELATED VIDEO: https://www.youtube.com/watch?v=Y9f_0QJU1ug

    Cheers,
    Brent

    _________________
    Brent Hanneson – Founder of GMATPrepNow.com
    Use our video course along with Beat The GMAT's free 60-Day Study Guide

    Check out the online reviews of our course
    Come see all of our free resources

    GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!

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