If a, b, and c are consecutive integers and a

Question

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

Source:   Nova GMAT  
Difficulty Level:   500

nishantt7 · Answer

Answer is B.
Two cases can be there.
1<2<3
-3<-2<-1

Kritesh · Answer

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.

goalMBA1990 · Answer

Please correct me: why D option is wrong? I think it is always true.

Sent from my XT1663 using  GMAT Club Forum mobile app

generis · Answer

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?

attari92 · Answer

as 'a', 'b' and 'c' are consecutive integers and that implies they must in AP for sure and hence option B stands out

generis · Answer

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

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