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02 Aug 2017, 12:04
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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:
45%
(medium)
Question Stats:
67% (02:04) correct
33%
(02:11)
wrong
based on 233
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The average of a series of consecutive integers is an even integer. Which of the following could be true?
I. There is an even number of integers in the series.
II. The smallest number in the series is odd.
III. The product of the smallest and largest number in the series is odd.
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
I. There is an even number of integers in the series.
II. The smallest number in the series is odd.
III. The product of the smallest and largest number in the series is odd.
A. I only
B. II only
C. III only
D. I and II only
E. II and III only
03 Aug 2017, 11:12
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cgalan6
Dear cgalan6,
I'm happy to respond.
This is a fabulous question! What is the source? It's great!
Let's think about that first statement:
The average of a series of consecutive integers is an even integer.
The average of a set of consecutive integers is always the median of the set. If we have an even number of consecutive integers, the average & median are non-integers: it's the half-integer between the two middle numbers. It's only if we have an odd number of consecutive integers that the average & median could be an integer at all. The average is the middle number of the set. The two possibilities are
a) even in middle: O E O E O E O or E O E O E O E O E
b) odd in middle: E O E O E O E or O E O E O E O E O
Thus, if we have an even number in the middle, so that the median & average are even, then it could be true that both the first & last are odd, or it could be true that the first & last are even.
Now, we can proceed to the three statements
I. There is an even number of integers in the series.
False. If there are an even number of consecutive integers in the series, then the average wouldn't be an integer at all.
II. The smallest number in the series is odd.
True. This is possible.
III. The product of the smallest and largest number in the series is odd.
True. If the first is odd, the last must also be odd, and their product would be odd. This is possible.
Thus, II and III are possible.
OA = (E)
Does all this make sense?
Mike
General Discussion
05 Aug 2017, 18:34
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mikemcgarry this makes complete sense, but can't a consecutive series of integers also be something like 2,4,6,8 and 3,5,7,9? That's why I was a bit confused because then statement 1 "could" be true. Obviously from the answer choices all three cannot be all true. the And I believe this question is from a kaplan bank. Thanks again.
