Is the median equal to 10

hardik.jadeja 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.

OA is E
IMO it should be C

My Logic:
Clearly 1 and 2 alone are insufficient. So A,B and D are ruled out. But when 1 & 2 are taken together..

We know we have 5 numbers in the set that are less than 10. (given in statement 1). Other 5 numbers can be 10(not all 5) or more than 10.
And we also know that 10 occurs more than once in the set as 10 is the mode of the set.

So when we arrange these numbers in ascending order we will have a number less than 10 on the fifth place and 10 on the 6th place. This is enough to figure out that median will not be 10 because the average of the 2 middle numbers(5th & 6th) will not be 10.

Correct me if I am wrong?

ontopofit wrote:it's E.

so here evryone agrees that it cud not be solved with either 1) or 2).

with C I will give one series.

1,2,3,4,5,6,7,10,10,52.

mode =10, mean =10, but median = 5.5.

avenus wrote:x2suresh, the example you were asking for:

{6 7 8 9 10 10 11 12 13 14}

Mean = 10
Median = 10
Mode = 10