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If a, b, and c are consecutive integers and a < b < c, which of the

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Bunuel
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If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   Updated on: 10 Jul 2019, 23:52
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If a, b, and c are consecutive integers and a < b < c, which of the following must be true?

(A) b^2 is a prime number
(B) (a + c)/2 = b
(C) a + b is even
(D) ab/3 is an integer
(E) c – a = b

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B

Originally posted by Bunuel on 21 May 2017, 12:53.
Last edited by Sajjad1994 on 10 Jul 2019, 23:52, edited 1 time in total.
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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   21 May 2017, 13:00
Bunuel wrote:
If a, b, and c are consecutive integers and a < b < c, which of the following must be true?

(A) b^2 is a prime number
(B) (a + c)/2 = b
(C) a + b is even
(D) ab/3 is an integer
(E) c – a = b



Answer is B.
Two cases can be there.
1<2<3
-3<-2<-1
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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   21 May 2017, 13:07
Let the three consecutive no: be n,n+1 and n+2

Therefore always n+n+2/2 = n+1.

For example : 1,2,3 be a,b and c

(1+3)/2 = 2 .

The above examples can be changed to 5,6,7 or 87,88,89 or 150,151,152 etc .. all of them will yield similar result as shown above.

Hence option B is always true.
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goalMBA1990
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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   21 May 2017, 14:02
Please correct me: why D option is wrong? I think it is always true.

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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   23 May 2017, 06:49
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goalMBA1990 wrote:
Please correct me: why D option is wrong? I think it is always true.

goalMBA1990, I think you are reading the numerator incorrectly.

It does not say \(\frac{abC}{3}\).

Just ab in the numerator. Only two of the three consecutive integers are in the numerator. Does that help?
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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   23 May 2017, 06:52
as 'a', 'b' and 'c' are consecutive integers and that implies they must in AP for sure and hence option B stands out
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generis
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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   23 May 2017, 07:00
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Bunuel wrote:
If a, b, and c are consecutive integers and a < b < c, which of the following must be true?

(A) b^2 is a prime number
(B) (a + c)/2 = b
(C) a + b is even
(D) ab/3 is an integer
(E) c – a = b


1. Because a, b, and c, are consecutive integers, they constitute an arithmetic sequence with common difference of 1.

2. In any arithmetic sequence, median equals mean.

3. In this case with three integers, the middle integer, b, is the median, which is also the mean, and

4. Mean of arithmetic sequence equals First + Last divided by 2, i.e. (a + c)/2, where a is first term and c is last term

Answer B.
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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink] New post   27 Jul 2020, 20:19
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Re: If a, b, and c are consecutive integers and a < b < c, which of the [#permalink]
27 Jul 2020, 20:19
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