Which of the following must true?

[Gmat_mission]

A list of five integers has the following criteria:

I. The median of the list is 6
II. The mode of the list is 2
III. The mean of the list is 5

Which of the following must true?

A. The sum of the five integers is 30.
B. The sum of the five integers is 10.
C. The median of the three largest integers is 6.
D. The largest of the integers is 9.
E. The largest of the integers is 8.

Answer: E

Source: Veritas Prep

[swerve]

A list of five integers has the following criteria:

I. The median of the list is 6
II. The mode of the list is 2
III. The mean of the list is 5

Which of the following must true?

A. The sum of the five integers is 30.
B. The sum of the five integers is 10.
C. The median of the three largest integers is 6.
D. The largest of the integers is 9.
E. The largest of the integers is 8.

Answer: E

Source: Veritas Prep

The list should be \(2, 2, 6, x, y\).

given mean \(= 5\), so total \(= 25\)

median \(= 6\)

\(x+y = 15\)

\(x\) and \(y\) could be \(6, 9\) or \(7, 8\)

Since the given mode is 2, then the possible set is \(2, 2, 6, 7, 8\Longrightarrow\)E

[Scott@TargetTestPrep]

A list of five integers has the following criteria:

I. The median of the list is 6
II. The mode of the list is 2
III. The mean of the list is 5

Which of the following must true?

A. The sum of the five integers is 30.
B. The sum of the five integers is 10.
C. The median of the three largest integers is 6.
D. The largest of the integers is 9.
E. The largest of the integers is 8.

Answer: E

Solution:

Since the mean is 5 and there are 5 integers, the sum of the integers is 25. Therefore, we can see both A and B are false. Since the mode is 2 and the median is 6, we see that the five integers are 2, 2, 6, x, y where 6 < x < y. Since the sum of the integers is 25, the sum of x and y is 25 - (2 + 2 + 6) = 15. Therefore, x must be 7 and y must be 8 since 6 < x < y and x + y = 15. We see that the largest of the integers is 8.

Answer: E