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# What is the median of a set of seven different positive integers?

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Math Expert
Joined: 02 Aug 2009
Posts: 7335
What is the median of a set of seven different positive integers?  [#permalink]

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01 Feb 2019, 22:09
00:00

Difficulty:

95% (hard)

Question Stats:

27% (01:53) correct 73% (01:20) wrong based on 37 sessions

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What is the median of a set of seven different positive integers?
(1) The range of the set is 6.
(2) The arithmetic mean of the set is 4.

New question!!...

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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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Re: What is the median of a set of seven different positive integers?  [#permalink]

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01 Feb 2019, 22:18
Seven different positive integers.

From statement 1:

The range of the set is 6.
The Set can contain {1,2,3,4,5,6,7} or {2,3,4,5,6,7,8} or a set with different combinations
Here the median of the set is not the same.
Hence 1 is Insufficient.

From statement 2:

AM = 4.
As the set contains only positive integers. The only set, which satisfies the criteria is {1,2,3,4,5,6,7}
Hence the median is the mean of the set, which is 4.
B is sufficient.

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Re: What is the median of a set of seven different positive integers?  [#permalink]

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01 Feb 2019, 22:46
chetan2u wrote:
What is the median of a set of seven different positive integers?
(1) The range of the set is 6.
(2) The arithmetic mean of the set is 4.

New question!!...

IMO B

Range = highest - lowest

from 1) we can get multiple values for the median, such as 4,11...
1,2,3,4,5,6,7 => R = 6
8,9,10,11,12,13,14 => Range = 6

from 2) the arithmetic mean is 4, sum will be 4*7 =28
since the terms are different +ive integers, there is only one way of getting the sum as 28
1,2,3,4,5,6,7
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Re: What is the median of a set of seven different positive integers?  [#permalink]

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02 Feb 2019, 02:00
chetan2u wrote:
What is the median of a set of seven different positive integers?
(1) The range of the set is 6.
(2) The arithmetic mean of the set is 4.

New question!!...

#1
range of set = highest no - smallest no
since set has 7 different + integers so we can have many different possibilites of type of integers within set ; in sufficient

#2
AM = 4
so sum of digits = 28
only possible set of integers
consective integers from 1 to 7
so sufficient
IMO B
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Re: What is the median of a set of seven different positive integers?   [#permalink] 02 Feb 2019, 02:00
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