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# The average (arithmetic mean) of 6 positive integers is 31/2. What is

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Math Expert
Joined: 02 Sep 2009
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The average (arithmetic mean) of 6 positive integers is 31/2. What is  [#permalink]

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16 Jul 2017, 03:12
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Difficulty:

65% (hard)

Question Stats:

47% (01:40) correct 53% (01:31) wrong based on 56 sessions

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The average (arithmetic mean) of 6 positive integers is 31/2. What is the largest integer?

(1) The integers are all distinct.
(2) The smallest integer is 13.

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Re: The average (arithmetic mean) of 6 positive integers is 31/2. What is  [#permalink]

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16 Jul 2017, 03:29
Bunuel wrote:
The average (arithmetic mean) of 6 positive integers is 31/2. What is the largest integer?

(1) The integers are all distinct.
(2) The smallest integer is 13.

Sum of the 6 integers = Average * Number of numbers
=$$\frac{31}{2}$$ * 6
=93

(1) Integers are distinct: Which clearly is not sufficient. It could be any 6 distinct numbers that should add up to 93. Insufficient

(2) Smallest integer is 13. Again multiple possibilities are there where the smallest number is 13 and the numbers should add up to 93. Insufficient.

Even if we combine, all we know is the numbers are distinct ad least number is 13. The largest number could have many possibilities.

Hence E.
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Re: The average (arithmetic mean) of 6 positive integers is 31/2. What is  [#permalink]

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16 Jul 2017, 20:36
IMO Answer will be C... Using details from question, total of all integers is 93. Now with Option 1, there could be various possible combination of integers possible. With Option 2, we know the smallest integer is 13 so sum of other integers is 80. Using option 1 & 2, since they are distinct integers and smallest is 13, take other integers as 14,15,16,17,18 -> Sum of which is 80... hence largest integer is 18.
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Re: The average (arithmetic mean) of 6 positive integers is 31/2. What is  [#permalink]

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16 Jul 2017, 20:55
varunjoshi31 wrote:
IMO Answer will be C... Using details from question, total of all integers is 93. Now with Option 1, there could be various possible combination of integers possible. With Option 2, we know the smallest integer is 13 so sum of other integers is 80. Using option 1 & 2, since they are distinct integers and smallest is 13, take other integers as 14,15,16,17,18 -> Sum of which is 80... hence largest integer is 18.

Totally missed that part. Thanks
Re: The average (arithmetic mean) of 6 positive integers is 31/2. What is   [#permalink] 16 Jul 2017, 20:55
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