Median of 15 Integer:

[s.pratibha14]

What is the median of 15 integers?
(1) Exactly seven of the numbers are greater than 7.
(2) Exactly seven of the numbers are less than 7

plz help me to solve this question with explanation.

[aspirant_gmat_2012]

Hi Pratibha,

I think the OA should be (C) for this one. Only after combining do we know that the 8th item would be '7'.

Regards,
Syed

[s.pratibha14]

Hi Syed,

so in this question are we assuming that 7 is in the list of the integer?

after combining both of the statement, cant we get the list of 15 integer like this {-1 -2 -3 1 2 3 0 8 9 10 11 12 13 14}.

Plz tell me what m missing?

[s.pratibha14]

M sorry, i got it.. when i read my 2nd post i got the logic..

In that case we will have only 14 integers and 15th integer shud be 7 to satisfy both of the statement together..

OA is C..

Thanx Syed..

[aspirant_gmat_2012]

Pratibha,

We need 15 integers. Your list has only 14 integers. What number can I add to the list now? Only: 7

because EXACTLY 7 integers are below '7' and EXACTLY 7 integers are above '7'

Rgds,
Syed

[aspirant_gmat_2012]

Cool, mst wlcmd

[amit1234]

i guess ans should be E

7 numbers are less than 7 so those can be -70, -69,-68,...
7 nubers greater than 7 can be 100, 101,102...

and 8th number can be anything ....

[aspirant_gmat_2012]

Yea, 8th number can be any number which is not greater than 7 and not less than 7 ;)

1) and 2) say EXACTLY 7 are less than and 7 are greater than seven

[tim]

good discussion. the answer is indeed C. let us know if you have any additional questions about this one..

[ayush.rastogi.13]

Hi,
request you to clarify my doubt - even if we combine the 2 statements and assume the 14 numbers to be 0,1,2,3,4,5,6 <7 or 8 < 10,11,12,13,14,15,16.

So both statements are satisfied yet my median can be either 7 or 8. Hence shouldn't the answer be E ??

[RonPurewal]

Hi,
request you to clarify my doubt - even if we combine the 2 statements and assume the 14 numbers to be 0,1,2,3,4,5,6 <7 or 8 < 10,11,12,13,14,15,16.

So both statements are satisfied yet my median can be either 7 or 8. Hence shouldn't the answer be E ??

no.
if your median is 8, then you're looking at a list in which eight integers -- not just seven of them -- are greater than 7.

just think about it this way: the numbers in the list don't even have to be integers.
the point is this: exactly seven of the numbers are greater than 7, and exactly seven of them are less than 7.
since there are fifteen numbers in the list, that leaves one number that's neither greater than 7 nor less than 7.
so, what is that number?
there you go.