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# A set contains five positive integers, for which the average is 3. Wha

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A set contains five positive integers, for which the average is 3. Wha  [#permalink]

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11 Apr 2018, 20:32
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Difficulty:

15% (low)

Question Stats:

86% (00:57) correct 14% (00:30) wrong based on 81 sessions

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A set contains five positive integers, for which the average is 3. What is the greatest possible value of an integer in that set?

A. 5
B. 7
C. 9
D. 11
E. 13

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Joined: 04 Apr 2018
Posts: 21
Re: A set contains five positive integers, for which the average is 3. Wha  [#permalink]

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11 Apr 2018, 23:11
Let the positive integers be {a1, a2, a3, a4, a5}.
According to the problem, (a1+a2+a3+a4+a5)/5 = 3; >> (a1+a2+a3+a4+a5) = 15.
The question nowhere mentions that the numbers has to be unique/distinct. So, let's just assume all the numbers to be the least positive integers i.e. 1 to maximize one number among the set.
So, (1+1+1+1+a5) = 15. >> a5 = 11. So option D.11 should be the answer !
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Re: A set contains five positive integers, for which the average is 3. Wha  [#permalink]

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12 Apr 2018, 00:09
Bunuel wrote:
A set contains five positive integers, for which the average is 3. What is the greatest possible value of an integer in that set?

A. 5
B. 7
C. 9
D. 11
E. 13

sum of 5 numbers: 5*3=15
now we have to find out greatest possible value. In order to to so we have to minimize all other values of the set. As mentioned all numbers are positive we can set 1 as minimum value for 4 numbers out of 5.
so, 1+1+1+1=4
now we can deduct to find out the max: (sum of of 5 numbers)-(minimum value of 4 numbers)
=15-4
= 11
thus option D is the correct answer.
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Re: A set contains five positive integers, for which the average is 3. Wha  [#permalink]

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16 Apr 2018, 15:10
Bunuel wrote:
A set contains five positive integers, for which the average is 3. What is the greatest possible value of an integer in that set?

A. 5
B. 7
C. 9
D. 11
E. 13

Using the average formula: average = sum/number, we see that the sum of the integers is 15.

We can let each of the first 4 integers = 1 (the smallest positive integer), so the fifth integer would be 15 - 4 = 11.

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Re: A set contains five positive integers, for which the average is 3. Wha  [#permalink]

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23 Apr 2018, 20:05
I go via options

Largest number in options is 13 ,it is not possible as number cannot be zero.

Other one is 11,which is possible if rest are 1.

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Re: A set contains five positive integers, for which the average is 3. Wha &nbs [#permalink] 23 Apr 2018, 20:05
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