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An arithmetic progression is one in which each subsequent term is the

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An arithmetic progression is one in which each subsequent term is the [#permalink]

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New post 25 Oct 2017, 23:35
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An arithmetic progression is one in which each subsequent term is the sum of the preceding number and a constant. If a, b, c, d, e, and f are integers in arithmetic progression, what can be said about the six terms for sure?

I. The average is not an integer.
II. The median is not an integer.
III. The median and the mean are equal.


A. II only
B. III only
C. I and III only
D. II and III only
E. I, II, and III
[Reveal] Spoiler: OA

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Re: An arithmetic progression is one in which each subsequent term is the [#permalink]

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New post 26 Oct 2017, 01:25
a, b, c, d, e, and f are integers in arithmetic progression

Average may or may not be an integer.
Since there are 6 integers, median will be in between the 3rd and 4th number, and so may or may not be integer.
The median and the mean will be equal since in an evenly spaced set, median and mean are equal.
III must be true.
Answer B.

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An arithmetic progression is one in which each subsequent term is the [#permalink]

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New post 27 Oct 2017, 15:57
nkmungila wrote:
An arithmetic progression is one in which each subsequent term is the sum of the preceding number and a constant. If a, b, c, d, e, and f are integers in arithmetic progression, what can be said about the six terms for sure?

I. The average is not an integer.
II. The median is not an integer.
III. The median and the mean are equal.


A. II only
B. III only
C. I and III only
D. II and III only
E. I, II, and III

The arithmetic progression could be integers, even integers, mulriples of 6 . . .

This progression has an even number of terms. The questions are centered around median, mean, and integers. Consecutive integers will NOT yield an integer for mean or median if number of terms is even, so try

2, 4, 6, 8, 10, 12

as an example. (We are trying to disprove each statement). Evaluate: what MUST be true?

I. The average is not an integer.
The average here is 7, an integer.
Sum of 42/6 = mean of 7. OR
mean = median = 7. REJECT

II. The median is not an integer.
The median, between the 3rd and 4th terms, is also 7. REJECT

III. The median and the mean are equal.
ALWAYS the case in an arithmetic progression.

Answer B

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An arithmetic progression is one in which each subsequent term is the   [#permalink] 27 Oct 2017, 15:57
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