XAT 2015 — QA & DI Question 16
The median of 11 different positive integers is 15 and seven of those 11 integers are 8, 12, 20, 6, 14, 22, and 13.
Statement I: The difference between the averages of four largest integers and four smallest integers is 13.25.
Statement II: The average of all the 11 integers is 16.
Which of the following statements would be sufficient to find the largest possible integer of these numbers?
Answer & solution
- A
Statement I only.
- B
Statement II only.
- C
Both Statement I and Statement II are required.
- D
Neither Statement I nor Statement II is sufficient.
Either Statement I or Statement II is sufficient.
Three integers are not known.
Using Statement I:
Average of four smallest integers
= (6 + 8 + 12 + 13)/4 = 39/4
∴ Average of four largest integers
In order to get the largest possible integer, two of the three unknown integers must be lowest possible i.e., 16 and 17.
So, the largest possible integer
= 92 – 22 – 20 – 17 = 33
Statement I can answer the question independently.
Using Statement II:
Sum of 11 integers = 11 × 16 = 176
Sum of the given integers = 110
∴ Sum of three unknown integers = 66
In order to get the largest possible integer, two of the three unknown integers must be lowest possible i.e., 16 and 17.
So, the largest possible integer
= 66 – 16 – 17 = 33
Statement II also answers the question independently.
Hence, option (e).