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# If the average (arithmetic mean) of five distinct positive integers is

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Math Expert
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If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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03 Jul 2017, 03:40
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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 numbers?

(A) 11
(B) 12
(C) 24
(D) 40
(E) 46
[Reveal] Spoiler: OA

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Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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03 Jul 2017, 05:15
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Since the average of 5 numbers is 10, the total must be 50.
The numbers, must be consecutive for the greatest number to be least (8,9,10,11,12)

The least possible value of the greatest number(as it has been given that the numbers are distinct) has to be 12(Option B)
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Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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03 Jul 2017, 06:15
Ans :A
9,10,10,10,11

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Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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03 Jul 2017, 06:18
Anannt wrote:
Ans :A
9,10,10,10,11

Sent from my Mi 4i using GMAT Club Forum mobile app

It cannot be 9,10,10,10,11 because it has been given that the integers are distinct.
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Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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03 Jul 2017, 09:01
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Bunuel wrote:
If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?

(A) 11
(B) 12
(C) 24
(D) 40
(E) 46

$$a + ( a + 1 ) + ( a + 2 ) + ( a + 3 ) + (a + 4) = 50$$ ( As the numbers are distinct )

Or, $$5a + 10 = 50$$

Or, $$5a = 40$$

Or, $$a = 8$$

So, The least value of the greatest of the five numbers is 8 + 4 = 12, answer , must be (B) 12
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Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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15 Nov 2017, 21:51
Hi,

I don't understand how to get the "least" possible value of the greatest. Could someone explain it please.

Thank you!
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Posts: 44298
Re: If the average (arithmetic mean) of five distinct positive integers is [#permalink]

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15 Nov 2017, 23:31
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shamsm wrote:
Hi,

I don't understand how to get the "least" possible value of the greatest. Could someone explain it please.

Thank you!

If the average (arithmetic mean) of five distinct positive integers is 10, what is the least possible value of the greatest of the five numbers?

(A) 11
(B) 12
(C) 24
(D) 40
(E) 46

Given: $$0<a < b < c< d< e$$ and $$a + b + c + d + e = 10*5$$.

We want to minimise e.

General rule for such kind of problems, when the sum is fixed:
to maximize one quantity, minimize the others;
to minimize one quantity, maximize the others.

So, here we should maximize a, b, c, and d. Since the integers are distinct, then the max value of d is e - 1, the max value of c is e - 2, the max value of b is e - 3 and the max value of a is e - 4.

Thus, $$(e - 4) + (e - 3) + (e - 2) + (e - 1) + e = 50$$;
e = 12.

14. Min/Max Problems

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Re: If the average (arithmetic mean) of five distinct positive integers is   [#permalink] 15 Nov 2017, 23:31
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