Question

From a set of 100 numbers, half were selected to form group I, and 60 percent of the remaining numbers were selected to form group II. The average (arithmetic mean) of the numbers in group I is 24.4, and the average of the numbers in group II is 31.5. Which of the following is closest to the average of the numbers in groups I and II combined?

A. 27.1
B. 27.6
C. 27.8
D. 28.0
E. 28.3

Answer 1

The correct option is A.

27.1 is the closest to the average of the numbers in Group I and Group II combined.

Explanation:

There is a set of 100 numbers.

- Half were selected to form Group I.

This means

Group I = 50 numbers

- 60 percent of the remaining numbers were selected to form Group II

This means

Group II = 0.6×50 = 30 numbers.

- Average of the numbers in Group I = 24.4

Total numbers = 24.4 × 50 = 1220

- Average of numbers in Group II = 31.5

Total numbers = 31.5 × 30 = 945

Therefore the Average of the numbers in Group I and Group II combined is

(1220 + 945)/(50 + 30)

= 2165/80

=27.06

This is approximately 27.1