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?
If x > y > z, which cannot be . . .
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One option is to plug in numbers that allow us to eliminate 4 of the answer choices.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
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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Another approach is to apply some number sense.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
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
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Brent
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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).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
Answer: A
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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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich