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20 Jun 2018, 00:23
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
88% (00:42) correct
12%
(00:48)
wrong
based on 2823
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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
(PS00984)
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
(PS00984)
20 Jun 2018, 02:21
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Solution
Given:
- • We are given 5 consecutive integers.
To find:
- • We need to find the average and median of 5 consecutive integers.
Approach and Working:
Let us assume that 5 consecutive numbers are: a-2, a-1, a, a+1, a+2.
- • Thus, the average of the 5 integers = \(\frac{(a-2)+ (a-1) + (a) + (a+1) + (a+2)}{5}\)= \(\frac{5a}{5}\)= a
• And their median= a.
Thus, average and median both are the same and are one of the integers among 5 consecutive integers.
Hence, option E is the correct answer.
Answer: E
27 Jun 2018, 06:07
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Bunuel
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
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