Average Problem

[wawan.widiyo]

The average age of a team of 15 employees is 36. The youngest of them is 20 years old and the eldest is 56 years old. Two of them with average age 28 leave the team. If one of the two comes back on the condition that he will be made the team leader then which of the following can possibly be the average age of the new team so formed?
(A) 45
(B) 39
(C) 37
(D) 36
(E) 35

Ans. is D
total number= 15*36=540
left 2 peoples = 540-(2*28)=484
let 1 of x year people joint the team, (484+x)/14
from here, how the best way to finish it, in term of figure out x value? by plugging in number from 20-56?

thx in adv.
source: TM

[Pankaj.Dahiya]

The value of x is constrained by two statements:
1) Min age=20 & Max age=56, and
2) The avg. age of two men, who had left the team, were 28 yrs.

x can refer to any of these two men. Min.age=20 & avg.age=28, implies that x can have any value from 20 to 36.

Taking extreme values, we get that the new average as ranging from 36 to 37.14

So, the moral of the whole story is that it is a poorly constructed problem.

[esledge]

So, the moral of the whole story is that it is a poorly constructed problem.

You just made my day.

There is too much going on in this problem:
1. too many scenarios: before (15 person team)/after (2 leave the team)/hypothetical (1 conditionally rejoins)
2. multiple average-->sum calculations
3. a divisibility twist (since all the answers are integers, the 484 + x we are solving for must be divisible by 14)
4. the irrelevance of the age of the oldest player (except as a trap)

Plus, this sentence is not ideal, grammatically: "Two of them with average age 28 leave the team."