The mean of five numbers in a set is 12. If the set contains a total of six numbers and the mean of all six is 14, which of the following is the sixth number?
(1) 24
(3) 32
(2) 13
(4) 18

Explanation:

The process of finding the arithmetic mean involves two steps

The first bit of info your teacher gave you is "the mean of five numbers in a set is 12". While we don't know the actual individual values themselves, we know that they must add to some variable y. Dividing y over n gets us the mean

y/n = mean

y/5 = 12

y = 5*12

y = 60

The five values add to 60.

The next bit of info is that "the mean of all six is 14". That allows us to say:

(sum of all 6 values)/6 = mean

(sum of all 6 values)/6 = 14

( (sum of 5 values) + (6th value) )/6 = 14

(y + x)/6 = 14

(60 + x)/6 = 14

where x is the 6th number we want to find.

Solve for x

(60 + x)/6 = 14

60+x = 6*14

60+x = 84

x = 84-60

x = 24 so choice (1) is the answer

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