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Which one of the following could be an integer?
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16 Apr 2018, 11:09
16 Apr 2018, 11:09
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Question Stats:
93% (00:37) correct
6% (01:23) wrong based on 44 sessions
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Which one of the following could be an integer?
(A) The average of two consecutive integers
(B) The average of three consecutive integers
(C) The average of four consecutive integers
(D) The average of six consecutive integers
(E) The average of 6 and 9
(A) The average of two consecutive integers
(B) The average of three consecutive integers
(C) The average of four consecutive integers
(D) The average of six consecutive integers
(E) The average of 6 and 9
Re: Which one of the following could be an integer?
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18 Apr 2018, 01:42
18 Apr 2018, 01:42
2
Lets start with option A
let \(x\)be the first integer than 2nd integer is\(x+1\)
There average will be \(\frac{2x + 1}{2} = x + \frac{1}{2}\) which is not a integer
For option B
1st integer = \(x\)
2nd integer = \(x+1\)
3rd integer = \(x+2\)
Hence there average \(= \frac{3x +3}{3}\) or, \(\frac{3(x+1)}{3} = x + 1\)
since x is an integer \(x +1\) is also a integer
option B
let \(x\)be the first integer than 2nd integer is\(x+1\)
There average will be \(\frac{2x + 1}{2} = x + \frac{1}{2}\) which is not a integer
For option B
1st integer = \(x\)
2nd integer = \(x+1\)
3rd integer = \(x+2\)
Hence there average \(= \frac{3x +3}{3}\) or, \(\frac{3(x+1)}{3} = x + 1\)
since x is an integer \(x +1\) is also a integer
option B
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Re: Which one of the following could be an integer?
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11 Jun 2019, 19:17
11 Jun 2019, 19:17
1
Expert Reply
Carcass wrote:
Which one of the following could be an integer?
(A) The average of two consecutive integers
(B) The average of three consecutive integers
(C) The average of four consecutive integers
(D) The average of six consecutive integers
(E) The average of 6 and 9
(A) The average of two consecutive integers
(B) The average of three consecutive integers
(C) The average of four consecutive integers
(D) The average of six consecutive integers
(E) The average of 6 and 9
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
