The average of 4 numbers is 9. If one of the numbers is 7, what is the sum of the other 3 numbers?

Rationale

The sum of the other 3 numbers is 29.

To find the sum of the remaining three numbers, we first calculate the total sum of all four numbers based on their average. Since the average is 9, the total sum is 4 times 9, which equals 36. By subtracting the known number 7 from this total, we find that the sum of the other three numbers must be 29.

A (2) YOUR ANSWER

This choice represents a sum that is too low given the average of the four numbers. If three numbers summed to 2, adding the known number 7 would yield a total of 9, which would not match the required total of 36. Thus, this option cannot be correct.

B (12) YOUR ANSWER

Adding the number 7 to a sum of 12 would provide a total of 19, which is significantly less than the required total of 36. Since the average is 9, this sum cannot be valid, making this option incorrect as well.

C (29) CORRECT

This choice accurately reflects the sum of the other three numbers. With a total sum of 36 and one number being 7, the calculation is 36 - 7 = 29. This outcome confirms that the remaining three numbers must indeed sum to 29, validating this option as correct.

D (36) YOUR ANSWER

This choice suggests that the sum of the other three numbers is equal to the total sum of all four, which is impossible since one number is already contributing to that total. If the sum of the other three were 36, that would mean the total would be 36 + 7 = 43, which far exceeds the required total of 36.

Conclusion

The problem requires understanding averages and total sums. Given that the average of four numbers is 9, the total must be 36. By subtracting the known number 7, we determine that the sum of the other three numbers is 29. This highlights the importance of both arithmetic operations and the concept of averages in solving such problems.