The sum of three consecutive positive integers must be divisible by wh

Question

The sum of three consecutive positive integers must be divisible by which of the following?

(A) 2

(B) 3

(C) 4

(D) 5

(E) 6

Source: Nova GMAT

BrentGMATPrepNow · Answer

Let x = the smallest integer
So, x + 1 = the next integer
And x + 2 = the biggest integer

Sum = x + (x + 1) + (x + 2) 
= 3x + 3
=  3  (x + 1)

Since the sum MUST be a multiple of   3  , we can also say that the sum MUST be divisible by   3

Answer: B

Cheers,
Brent

BrentGMATPrepNow · Answer

Approach #2:  test sets of of three consecutive positive integers

For example, the 3 numbers COULD be 2, 3 and 4
SUM = 2 + 3 + 4 = 9
Since 9 is NOT divisible by 2, 4, 5 or 6, we can ELIMINATE A, C, D and E

Answer: B

Cheers,
Brent

Kinshook · Answer

Let the number be x, x+1, x+2
Sum = x + x +1 + x + 2 = 3 (x+1)
Divisible by 3.

IMO B

prateekchugh · Answer

Rule:- n consecutive integers------> 1 number must be divisible by n

So 3 consecutive +ve integers must be divisible by 3. B

ZahidPavel · Answer