Zero is a even integer

[leyley1390]

Hi,
I had this question on the GMAT:

if x,y,z are three integers, are they consecutive integers?

(1) z=x+2
(2) None of the three are multiple of 3.

I would select E because 0,1,2 are three consecutive integers, and none of them are multiple of 3.
But my book said that B is the correct answer because in any set of three consecutive integers, on of the three is automaticlly multiple of 3.

Who is right, me or my book?

[Anurag@Gurome]

I would select E because 0,1,2 are three consecutive integers, and none of them are multiple of 3.

0 is multiple of every integer.

[Brent@GMATPrepNow]

Hi,
I had this question on the GMAT:

if x,y,z are three integers, are they consecutive integers?
(1) z=x+2
(2) None of the three are multiple of 3.

Target question: Are the three integers consecutive?

Statement 1: z=x+2
There are several sets of values that meet this condition. Here are two:
Case a: x=1, y=2, z=3, in which case the 3 integers are consecutive.
Case b: x=1, y=8, z=3, in which case the 3 integers are not consecutive.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: None of the three are multiple of 3.
There's a nice rule that says: If there are n consecutive integers, then exactly 1 of them is divisible by n
Example: Of the 5 consecutive integers 7, 8, 9, 10, 11, exactly one is divisible by 5 (or we can say one is a multiple of 5.
Since, none of the 3 integers is divisible by 3, then the 3 integers must not be consecutive.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent

[leyley1390]

Ok thanks

[The Iceman]

There's a nice rule that says: If there are n consecutive integers, then exactly 1 of them is divisible by n

Exactly! For the same reason the product of k consecutive integers is perfectly divisible by k! (factorial of k)