A set of 5 integers has an arithmetic mean of 12. If four of the integers are 8, 10, 14, a… — GMAT

A set of $5$ integers has an arithmetic mean of $12$ . If four of the integers are $8$ , $10$ , $14$ , and $15$ , what is the value of the fifth integer?

Answer: 13

Answer

The value of the fifth integer is

13

The total sum of a set of numbers is given by the formula

\text{Sum} = \text{Mean} \times n

. For

5

numbers with a mean of

12

, the total sum is

5 \times 12 = 60

. The sum of the four provided numbers is

8 + 10 + 14 + 15 = 47

. Subtracting

47

from

60

yields

13

, which is the value of the fifth integer.

Step-by-Step Solution

Find the total sum of the 5 integers

The total sum is

60

The sum of a set of numbers equals the arithmetic mean multiplied by the total count of numbers (

12 \times 5 = 60

Sum the four given integers

The sum of the four integers is

47

Adding the given numbers:

8 + 10 + 14 + 15 = 47

Subtract the sum of the known integers from the total sum

The fifth integer is

13

Subtracting

47

from

60

gives

60 - 47 = 13

Key Concept

Arithmetic Mean

Estimated Time:45s

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