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GMAT Official Guide 2019 Which of the following statements

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GMAT Official Guide 2019 Which of the following statements

by BTGmoderatorDC » Wed Jun 27, 2018 4:25 am

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Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.


A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III
Last edited by BTGmoderatorDC on Wed Jun 27, 2018 8:23 pm, edited 1 time in total.
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by Brent@GMATPrepNow » Wed Jun 27, 2018 5:00 am
BTGmoderatorDC wrote:Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.

A. I only
B. II only
C. III only
D. I and II only
E. I, II, and III
There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
For example, in each of the following sets, the mean and median are equal:
{7, 9, 11, 13, 15}
{-1, 4, 9, 14}
{3, 4, 5, 6}

Since consecutive integers are equally spaced, the average (mean) of this set of 5 integers will equals its median.
So, statement III is true
Check the answer choices.....ELIMINATE A, B and D

Also, since the set has an ODD number of values, the median will be the middle value (when the numbers are arranged in ascending order).
Since the set consists of INTEGERS only, and since the median equals the middle value, the median must be an integer
So, statement II is true
Check the answer choices.....ELIMINATE C

By the process of elimination, the correct answer must be E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Jeff@TargetTestPrep » Mon Jul 02, 2018 9:04 am
BTGmoderatorDC wrote:Which of the following statements must be true about the average (arithmetic mean) and the median of 5 consecutive integers?

I. The average is one of the integers.
II. The median is one of the integers.
III. The median equals the average.


A. I only

B. II only

C. III only

D. I and II only

E. I, II, and III
For a set of 5 consecutive integers, the median = average. Furthermore, both the mean and the median are one of the given integers.

For example:

1, 2, 3, 4, 5

Average = 15/5 = 3 = median.

Answer: E

Jeffrey Miller
Head of GMAT Instruction
[email protected]

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