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# The arithmetic mean (average) of a set of 10 numbers is 10. Is the med

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Math Expert
Joined: 02 Sep 2009
Posts: 50627
The arithmetic mean (average) of a set of 10 numbers is 10. Is the med  [#permalink]

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19 May 2016, 23:19
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Difficulty:

85% (hard)

Question Stats:

36% (01:53) correct 64% (02:00) wrong based on 68 sessions

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The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

(1) Exactly half of the numbers are less than 10.
(2) The mode of the set of numbers is 10.

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Joined: 02 Aug 2009
Posts: 7036
The arithmetic mean (average) of a set of 10 numbers is 10. Is the med  [#permalink]

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20 May 2016, 05:31
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Bunuel wrote:
The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

(1) Exactly half of the numbers are less than 10.
(2) The mode of the set of numbers is 10.

slightly tricky...
we know that average is 10, so SUM = 100..
Is MEDIAN 10?
what does it mean...

the average of 5th and 6th should be 10....

lets see the statements--

(1) Exactly half of the numbers are less than 10.

it is possible that numbers are such that 5th is 9 and 6th is 11.. Median is 10..
8,8,8,9,9,11,11,12,12,12..... average = median=10...YES

it is possible that median is not 10..
8,8,8,9,9,10,12,12,12,12,... average =10, but median = 9.5...NO

Insuff

(2) The mode of the set of numbers is 10.

it is possible that numbers are such that average is 10 and Median is 10..
8,8,8,9,10,10,10,10,10,17..... average = median=10...YES

it is possible that median is not 10..
8,8,8,9,9,10,10,10,10,18,... average =10, but median = 9.5...NO

Insuff

Combined...
5 numbers are less than 10, but, since mode is 10, 6th number or 7th or 8th has to be 10...
so 5th < 10 and 6th is 10....so median cannot be 10 and will always be<10
5th < 10 and 6th is also < 10..median<10
.. ans is NO for all cases
Suff
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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

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Re: The arithmetic mean (average) of a set of 10 numbers is 10. Is the med  [#permalink]

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20 May 2016, 09:15
Bunuel wrote:
The arithmetic mean (average) of a set of 10 numbers is 10. Is the median value of the same set also equal to 10?

(1) Exactly half of the numbers are less than 10.
(2) The mode of the set of numbers is 10.

Given information:- Mean on 10 numbers is 10.

Question asked- Is the median 10?

Inference:-
Sum of 10 numbers = 10*10=100
Median will be 10 in below cases:-
1) if only 1 digit is 10 and others are either smaller or greater than 10
2) All digits are equal to 10

(1) Exactly half of the numbers are less than 10.
This means:-
-Remaining 5 numbers can be >10 (In this case the median will not be 10)
- 1 to 4 numbers can be equal to 10 and the last number is greater than 10 (in this case median will be 10)

Not sufficient
(2) The mode of the set of numbers is 10
Mode is 10 means 10 appears maximum number of times. There can be multiple possibilities in which the median 10 or not.

Not sufficient.

Combining both statements
5 digits are less than 10 and mode of set is 10. That means we have at least 2 10's, and the sequence will be:-

smaller 5 digits, 10, 10, any other digit

6th digit is 10 in this case

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Re: The arithmetic mean (average) of a set of 10 numbers is 10. Is the med  [#permalink]

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10 Nov 2017, 02:08
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The arithmetic mean (average) of a set of 10 numbers is 10. Is the med &nbs [#permalink] 10 Nov 2017, 02:08
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