Data set A consists of 10 positive integers less than 60.
The list shown gives 9 of the integers from data set A. 40, 47, 43, 50, 55, 52, 56, 58, and 59.
The mean of these 9 integers is 42.
If the mean of data set A is an integer that is greater than 42, what is the value of the largest integer from data set A?

Given information:
Data set A consists of 10 positive integers less than 60.
The list provided contains 9 integers from data set A, along with their mean.

Calculate the sum of the 9 given integers:
Add up the 9 integers: 40 + 47 + 43 + 50 + 55 + 52 + 56 + 58 + 59

Sum of the 9 integers is

460

Calculate the mean of all 10 integers:
Since the mean of the 9 given integers is 42, the total sum of all 10 integers must be

\$42 \times 10\$ = 420

Find the missing integer:
Subtract the sum of the 9 given integers from the sum of all 10 integers:

420 - 460 = - 40

However, since we’re dealing with positive integers, this doesn’t fit. So, we need to find the missing integer in a different way

Determine the value of the largest integer:
Since the mean of data set A is an integer greater than 42, we need to add an integer greater than 42 to the data set

This means the missing integer will be the difference between the desired mean and the mean of the given integers: x - 42, where x is the value of the missing integer

Since the mean of data set A must be an integer, x - 42 must be a positive integer

The only positive integer among the options provided is 59, which satisfies this condition

The value of the largest integer from data set A is 59.

This option suggests that the largest integer from data set A is 59. According to our calculation, we found that the mean of the given 9 integers is 42. Since the mean of data set A is stated to be an integer greater than 42, adding an integer greater than 42 will require the last integer in the set to be larger. Therefore, 59 fits this requirement

59

This option proposes that the largest integer is 60. However, since the mean of the given 9 integers is 42, adding an integer larger than 42 would push the mean higher than desired

60

This option suggests that the largest integer is 62. Again, adding an integer larger than 42 would push the mean even higher, which contradicts the requirement that the mean must be an integer greater than 42

62

This option proposes that the largest integer is 64. Similar to options B and C, adding such a large integer would result in a mean greater than desired

64

Option

A

Can you summarize what you’ve understood in the above steps?