Which one of the following could be an integer?

Question

(A) Average of two consecutive integers.

(B) Average of three consecutive integers.

(C) Average of four consecutive integers.

(D) Average of six consecutive integers.

(E) Average of 6 and 9.

Source:   Nova GMAT  
Difficulty Level:   550

CareerGeek · Answer

(A) Average of two consecutive integers.

(x + x+1)/2 = x + 0.5 -  NO

(B) Average of three consecutive integers.

(x + x+1 + x+2)/3 = (3x + 3)/3 = x + 1 -  YES

(C) Average of four consecutive integers.

(x + x+1 + x+2 + x+3)/4 = x + 6/4 = x + 1.5 -  NO

(D) Average of six consecutive integers.

(x + x+1 + x+2 + x+3 + x+4 + x+5)/6 = x + 15/6 = x + 2.5 -  NO

(E) Average of 6 and 9. = 7.5 -  NO

Option B.

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firas92 · Answer

For an evenly spaced set, Arithmetic Mean (average) = Median and of course, a set of consecutive integers is an evenly spaced set

In a set of even number of elements, median = average of the two middle elements

Since the average of two consecutive integers =  \frac{(odd+even)}{2} , it can never be an integer

Therefore, when the two middle elements are consecutive, the mean is not an integer
Eliminate (A), (C), (D) & (E)

In an evenly spaced set of odd number of elements, mean=median=middle term

Answer is  (B)

nide · Answer

A. ((n)+(n+1))/2 = (2n+1)/2 = n + 0.5 
B. (n+n+1+n+2)/3 = (3n+3)/3 = n+1
C. (n+n+1+n+2+n+3)/4 = (4n+6)/4 = n+ 6/4
D. (n+n+1+n+2+n+3+n+4+n+5)/6 = (6n+15)/6 = n + 5/2
E. (6+9)/2 = 7.5

So right answer is B

Rule:
The average of three consecutive integers is always an integer
(since they sum up to the form 3n+3 which is divisible by 3)

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ScottTargetTestPrep · Answer

Since the average of 3 consecutive integers is equal to the median, and since the median would be the middle integer of 3 consecutive integers, we see that the average of 3 consecutive integers must be an integer.

Answer: B

bumpbot · Answer

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Which one of the following could be an integer?

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Which one of the following could be an integer?

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