a,b and c are consecutive

[Harris]

if a,b,c are consecutive positive integers and a<b<c, which of the following must be true?

I. c-a=2
II. abc is an even integer
III. a+b+c/3 is an integer

a. I only
b. II only
c. I and II only
d. II and III only
e. I, II, and III

I don't understand why I is correct. If we use numbers such as 1,2,3 or 2,3,4 or 3,4,5 the statements seems correct, but what if we use consecutive numbers such as 5,10,15 that statement is false. Can anyone explain why we can not use consecutive multiples; them stem does not really have any restrictions for consecutive multiples?

please explain, thanks!

[Rustic Myth]

In GMAT positive integers is used for Number. But they cannot put just specify numbers as it can be Whole number / Real Number / Positive Number / Negative number / Fractions.

If it would have been multiples it would have been explicitly mentioned.

Hope this clarifies your doubt.

[Guest]

I dont think 5,10,15 are consecutive positive integers.

5,6,7
10,11,12
15,16,17

[sanju]

Since they are consutive positive integers, we can assume the numbers to be a, a+1, a+2 where b = a+1 and c = a+2
c-a = 2.

[Guest]

I agree with sanju. The way to go here is to make

a = a
b = a + 1
c = a + 2

Now substitute for the expression given in Statement I:

c - a = 2
(a + 2) - a = 2

The a's cancel each other out, meaning that the difference between c and a will indeed always be 2.

[RonPurewal]

Can anyone explain why we can not use consecutive multiples; them stem does not really have any restrictions for consecutive multiples?

actually it does: "consecutive integers" (or "consecutive positive integers") means integers that would actually be consecutive if you listed the integers in order. this means that they have to come right after one another in "normal" counting.
5, 10, and 15 aren't consecutive, because there are other integers in the way - in exactly the same way that, say, 1986, 1991, and 1996 aren't consecutive years.

don't mistake "consecutive" for "in arithmetic progression" / "evenly spaced", which is a much more general concept. consecutive means consecutive.