Question

4, 6, 8, 10, 12, 14, 16, 18, 20, 22
List M (not shown) consists of 8 different integers, each of which is in the list shown. What is the standard deviation of the numbers in list M?
(1) The average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list shown.
(2) List M does not contain 22.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

Answer: (C)

Both statements together are sufficient, but neither statement alone is sufficient.

• From statement 1, the average (arithmetic mean) of the numbers in list M is equal to the average of the numbers in the list. The mean of list M is also $13$. Thus, the sum of the integers in list M is $13\times 8=104$, which means that the sum of the $2$ integers removed is $130-104=26$. The $2$ integers removed could be any pairs. From statement 2, list M does not contain $22$. We know only one of the numbers is removed.
• From statement 1, we know that the sum of the $2$ integers removed is $26$ and from statement $2$, we know that one of the integers removed is $22$. Therefore, the second integer removed is $26-22=4$. List M consists of the following $8$ integers: $6,8,10,12,14,16,18,20$. So, we can determine its standard deviation considering both the statements.