Quantitative Ability Question of the Day

QUESTION:-
If the mean and median of a set containing 5 natural numbers is 10 and 15 respectively, what can be the maximum value of a number that belongs to the set?


OPTIONS
1) 19
2) 18
3) 17
4) 16

Solution

Sum of the 5 numbers = 5 × 10 = 50
Since the median is 15, the third number when the numbers are arranged in an ascending order is 15.
Because we want the 5th number to have the largest possible value, we have to minimize all the other numbers.
The minimum value that the 1st and 2nd number can take is 1.
To minimize the fourth number, it has to be equal to the third number i.e. 15.
The four numbers we now have are 1, 1, 15 and 15. Their total is 32.
So, the fifth number must be equal to 50 − 32 = 18, which is the largest possible value.
Hence, option 2.