Mo2men wrote:The average age of a group of n people is 15 yrs. One more person aged 39 joins the group and the new average is 17 yrs. What is the value of n?
(A) 9
(B) 10
(C) 11
(D) 12
(E) 13
An alternate approach is to PLUG IN THE ANSWERS, which represent the value of n.
When the correct answer choice is plugged in, the age of the added person will be 39.
B: n=10
Sum of the ages of the 10 original people = (original number of people)(original average) = 10*15 = 150.
Sum of the ages after 1 person is added = (new number of people)(new average age) = 11*17 = 187.
Age of the added person = (new sum) - (old sum) = 187-150 = 37.
Here, the age of the added person is TOO SMALL.
D: n=12
Sum of the ages of the 12 original people = (original number of people)(original average) = 12*15 = 180.
Sum of the ages after 1 person is added = (new number of people)(new average age) = 13*17 = 221.
Age of the added person = (new sum) - (old sum) = 221-180 = 41.
Here, the age of the added person is TOO GREAT.
Since the age of added person is TOO SMALL when n=10 but TOO GREAT when n=12, the correct answer choice must be BETWEEN 10 and 12.
The correct answer is
C.
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