Hi,

Statement says that in a serie os five numbers {x1, x2, x3, x4, x5}, the large number, x5, is 4 greater than the median, i.e. x5=x3+4, and it asks if the mean is greater than the median (x1+....+x5)/5>x3?

(1) it says that x5+x3=34, combining it with x5=x3+4 from the statement we get, x3=15 and x5=19, but we still don't know what happens with x1 and x2, so INSUFF.

(2) it says that x3-x1=10, or 15-x1=10, or x1=5, but alone it doesnt give us any information about the other numbers, so INSUFF

(1+2) we have x1=5, x3=15, and x5=19, and the mean is maximize when x2 and x4 assume the greatest possible values x2=15 and x4=19 and minimezed when x2 and x4 assume the minimum possible values x2=5 and x4=15.

The mean of the serie {5;15;15;19;19} is 14,4 which IS greater than the median.

The mean of the serie {5;5;15;15;19} is 11,8 which IS NOT greater than the median.

Also INSUFF.

So my pick goes to E.

Hope it helps.

BTW: it took me more than 2min



Oooops, STUPID MISTAKE. For any of the above series the mean is not greater than the median, and so (1+2) is SUFF.

Statement 1 says: Largest number + median = 34
We know that largest number is 4 greater than median.

So we can setup equation:

L - 4 = M
L + M = 34

On combining and solving these equations we get.

L = 19
M = 15

This information is not enough to answer question. Hence choice A and D are out.

Statement 2 gives information about smallest number and that is not enough to answer question as well, so choice B is out too.

On combining both statements we can figure out that smallest number is 5, largest is 19 and Median is 15.

So we can calculate that mean is less than median (15) with any values.

For eg. 5, 14, 15, 18 and 19 have mean as 14.1. This the highest value of mean with combination of lower, median and largest value dervied from above equations.

Answer IMO = C.

the official answer is B

Makes sense, information provided in statement B is sufficient, we can answer question by substituting any value for X. Statement 1 is not required.