Which of the following is always true?
(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
A. I and III
B. I, II and III
C. II
D. I and II
E. None
Can some experts explain how to find the best Option?
OA B
Which of the following is always true
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
- EconomistGMATTutor
- GMAT Instructor
- Posts: 555
- Joined: Wed Oct 04, 2017 4:18 pm
- Thanked: 180 times
- Followed by:12 members
Hi lheiannie07,Which of the following is always true?
(I) The average (arithmetic mean) of five negative consecutive integers is equal to the average of the largest and smallest of them.
(II) The average (arithmetic mean) of four positive consecutive integers is equal to the average of the largest and smallest of them.
(III) The average (arithmetic mean) of five consecutive integers is equal to the average of the largest and smallest of them.
A. I and III
B. I, II and III
C. II
D. I and II
E. None
Let's take a look at your question.
We will take some random values to check each statement.
Let's start from statement (I).
Let 5 negative consecutive integers be -1, -2, -3, -4, -5.
Average of five numbers = (-1-2-3-4-5)/5 = -15/5 = -3
Average of largest and smallest number = (-1-5) / 2 = -6/2 =-3
It means Statement (I) is correct.
We will now check statement (II).
Let 4 positive consecutive integers be 1, 2, 3, 4.
Average of four numbers = (1+2+3+4)/4 = 10/4 = 2.5
Average of largest and smallest number = (1+4) / 2 = 5/2 =2.5
Hence, statement (II) is also true.
Now check statement (III).
Let 5 consecutive integers be -1, 0, 1, 2, 3.
Average of five numbers = (-1+0+1+2+3)/5 = 5/5 = 1
Average of largest and smallest number = (-1+3) / 2 = 2/2 =1
Hence, statement (III) is also true.
Therefore, option B is correct, because statement I, II and III are true.
Hope it helps.
I am available if you'd like any follow up.
GMAT Prep From The Economist
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
![Image](https://partners.beatthegmat.com/uploads/BTGsig.jpg)
We offer 70+ point score improvement money back guarantee.
Our average student improves 98 points.
![Image](https://partners.beatthegmat.com/uploads/BTGsig.jpg)