Question

The average of 12 numbers is 15 and the average of the first two numbers is 1(D) What is the average of the remaining numbers?

• A. \( 15 \)
• B. \( 15.2 \)
• C. \( 14 \)
• D. \( 1(D)2 \)

Hint:

\textbf{Average Problems.} Remember that the sum of a set of numbers is equal to their average multiplied by the number of terms. You can use this relationship to find the sum of different subsets of the data and then calculate the required average.

Answer 1

The Correct Option is B

Let the 12 numbers be \(n_1, n_2, n_3, \ldots, n_{12}\). The average of these 12 numbers is 15. The sum of these 12 numbers is: $$ \text{Sum of 12 numbers} = \text{Average} \times \text{Number of terms} = 15 \times 12 = 180 $$ The first two numbers are \(n_1\) and \(n_2\). Their average is 1(D) The sum of the first two numbers is: $$ \text{Sum of first two numbers} = \text{Average} \times \text{Number of terms} = 14 \times 2 = 28 $$ The remaining numbers are \(n_3, n_4, \ldots, n_{12}\). There are \(12 - 2 = 10\) remaining numbers. The sum of the remaining 10 numbers is the total sum minus the sum of the first two numbers: $$ \text{Sum of remaining 10 numbers} = \text{Sum of 12 numbers} - \text{Sum of first two numbers} $$ $$ \text{Sum of remaining 10 numbers} = 180 - 28 = 152 $$ The average of the remaining 10 numbers is the sum of these numbers divided by the number of terms: $$ \text{Average of remaining 10 numbers} = \frac{\text{Sum of remaining 10 numbers}}{\text{Number of remaining numbers}} $$ $$ \text{Average of remaining 10 numbers} = \frac{152}{10} = 15.2 $$ Therefore, the average of the remaining numbers is 15.(B)