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

_________________

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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