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Which of the following must true?

Expert replies
by Gmat_mission » Thu Oct 08, 2020 6:02 am
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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
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Source: — Problem Solving |

Re: Which of the following must true?

by swerve » Thu Oct 08, 2020 5:31 pm
Gmat_mission wrote: ↑
Thu Oct 08, 2020 6:02 am
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
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Gmat_mission wrote: ↑
Thu Oct 08, 2020 6:02 am
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

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