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

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by Vincen » Wed Sep 20, 2017 6:50 am
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?
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by Brent@GMATPrepNow » 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

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

by Brent@GMATPrepNow » 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

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Brent
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by Scott@TargetTestPrep » Wed Dec 20, 2017 10:54 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
We are given three different-valued quantities x, y, z, with x having the largest value. Thus, the average of the three quantities can't be x (the average of any set of numbers is always less than the largest number in the set).

Answer: A

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by [email protected] » Wed Dec 20, 2017 12:26 pm
Hi Vincen,

We're told that X > Y > Z. We're asked which CANNOT be the average (arithmetic mean) of X, Y and Z. This question can be dealt with conceptually or by TESTing VALUES.

IF....
X=3, Y=2, Z=1, then the average is (3+2+1)/3 = 2

If you plug in those 3 values, you'll get 2 in four of the five answer choices. The one answer that you DON'T get 2 is the correct answer...

Final Answer: A

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