1

Problem

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?

2

Step

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.

3

Step

Calculate the sum of the 9 given integers:
Add up the 9 integers:

40 + 47 + 43 + 50 + 55 + 52 + 56 + 58 + 59

4

Step

The sum of the 9 integers is:

460

5

Step

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

6

Step

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

420 - 460 = - 40

7

Step

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

8

Step

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.

9

Step

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

10

Step

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

11

Step

The only positive integer among the options provided is

59, which satisfies this condition

12

Solution

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

13

Sumup

Please summarize steps

Choices

14

Choice-A

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

Correct 59

15

Choice-B

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

Wrong 60

16

Choice-C

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

Wrong 62

17

Choice-D

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

Wrong 64

18

Answer

Option

A

19

Sumup

Please summarize choices