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

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

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New post 30 Mar 2019, 13:43
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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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New post 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. \(z_{max} = 43\)

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

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

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