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If the average (arithmetic mean) of five distinct positive integers is
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25 Jan 2024, 02:05
25 Jan 2024, 02:05
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If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five integers?
(A) 11
(B) 12
(C) 24
(D) 40
(E) 46
(A) 11
(B) 12
(C) 24
(D) 40
(E) 46
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If the average (arithmetic mean) of five distinct positive integers is
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26 Jan 2024, 16:46
26 Jan 2024, 16:46
1
Let x = the smallest integer of the set.
Since the numbers are all distinct integers:
the LEAST possible value for the 2nd integer = x + 1
the LEAST possible value for the 3rd integer = 2nd integer + 1 = x + 2
the LEAST possible value for the 4th integer = 3rd integer + 1 = x + 3
the LEAST possible value for the 5th integer = 4th integer + 1 = x + 4
The average of the five integers =
\(\frac{x+x+1+x+2+x+3+x+4}{5} = \frac{5x+10}{5} = 10\)
\(5x + 10 = 50\)
\(5x = 40\)
\(x = 8\)
The greatest of the five integers =
\(x + 4 = 8 + 4 =12\)
Since the numbers are all distinct integers:
the LEAST possible value for the 2nd integer = x + 1
the LEAST possible value for the 3rd integer = 2nd integer + 1 = x + 2
the LEAST possible value for the 4th integer = 3rd integer + 1 = x + 3
the LEAST possible value for the 5th integer = 4th integer + 1 = x + 4
The average of the five integers =
\(\frac{x+x+1+x+2+x+3+x+4}{5} = \frac{5x+10}{5} = 10\)
\(5x + 10 = 50\)
\(5x = 40\)
\(x = 8\)
The greatest of the five integers =
\(x + 4 = 8 + 4 =12\)
gmatclubot
If the average (arithmetic mean) of five distinct positive integers is [#permalink]
26 Jan 2024, 16:46
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