anurag_7 wrote:The average of 5 different numbers is 14. What is the average (arithmetic mean) of the 3 largest numbers?
(1) The average (arithmetic mean) of the two smallest numbers is 5.
(2) The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
For average problems, remember the following:
sum = (number)(average).
number = sum/average.
average = sum/number.
Let a, b, c, d, and e be the 5 values, in ascending order.
a+b+c+d+e = (number)(average) = 5*14 = 70.
Statement 1: The average (arithmetic mean) of the two smallest numbers is 5.
a+b = (number)(average) = 2*5 = 10.
c+d+e = (a+b+c+d+e) - (a+b) = 70-10 = 60.
Average of c, d, and e = sum/number = 60/3 = 20.
SUFFICIENT.
Statement 2: The average (arithmetic mean) of the two smallest numbers is 1/4 of the average of the 3 largest numbers.
Statement 1 implies the following values:
Average of a and b = 5.
Average of c, d, and e = 20.
Sum of a+b+c+d+e = 70.
Notice that the two averages -- 5 and 20 -- also satisfy statement 2, since 5 is 1/4 of 20.
If these two averages both increase or both decrease, then the SUM will also increase or decrease.
Not possible, since the sum must be 70.
Implication:
Statement 2 is satisfied only by the SAME combination of values that satisfy statement 1.
Thus, the average of c, d and e = 20.
SUFFICIENT.
The correct answer is
D.
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