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# If the average (arithmetic mean) of positive integers x, y, and z is 1

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Senior Manager
Joined: 24 Oct 2016
Posts: 371
GMAT 1: 670 Q46 V36
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If the average (arithmetic mean) of positive integers x, y, and z is 1  [#permalink]

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30 Mar 2019, 13:43
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Difficulty:

15% (low)

Question Stats:

74% (00:37) correct 26% (00:56) wrong based on 27 sessions

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If the average (arithmetic mean) of positive integers x, y, and z is 15, what is the greatest possible value of z?

A. 18
B. 20
C. 30
D. 43
E. 45

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Re: If the average (arithmetic mean) of positive integers x, y, and z is 1  [#permalink]

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31 Mar 2019, 00:01
dabaobao wrote:
If the average (arithmetic mean) of positive integers x, y, and z is 15, what is the greatest possible value of z?

A. 18
B. 20
C. 30
D. 43
E. 45

x+y+z = 15*3 = 45

Since z has to be maximized therefore x and y must be minimized

The minimum values of x and y may be x=1 and y = 1 (Question does NOT mention that they are different)

i.e. $$1+1+z_{max} = 45$$

i.e. $$z_{max} = 43$$

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Re: If the average (arithmetic mean) of positive integers x, y, and z is 1  [#permalink]

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31 Mar 2019, 00:19
(X+Y+Z)/3=15. Sum= 45, Minimum value of X and Y is 1 each (as a positive integer). Maximum value is 43
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Re: If the average (arithmetic mean) of positive integers x, y, and z is 1   [#permalink] 31 Mar 2019, 00:19
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