The average(arithmetic mean) of 50 measurements is 34.6, and the least and the greatest of the measurements are 18.3 and 51.7 respectively.

Quantity A	Quantity B
The median of the 50 measurements	34.6

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.

D

we know the sum must be 34.6*50=1730

Try to prove theyre equal first then prove they are not equal to prove D.

1th 2-24 25 & 26 27-49 50th

18.3 34.6 34.6 51.7

to make the median 34.6 the 25th and 26th term's avg must be 34.6, the easiest case is 34.6 34.6
if you fill the rest with numbers less than 51.7 for 27-49 but greater or equal than 34.6 and the 2-24th term with numbers less than 34.6 , the sum can exceed 1730 and also make it equal

now try to check if you can get the same sum (1730) with differrent terms for the 25 and 26th slots.
then try to fill in the rest to make the sum 1730 or larger

18.3 33.6 34.6 51.7

if you choose about the same numbers as the first case you will get a sum larger or equal to 1730 but with a different median.

D

sorry i couldnt come up with a better solution there probably is.