Consecutive integers

[Brent@GMATPrepNow]

Okay, I took a question and spiced it up a bit for Cramya

Which of the following could be the sum of four consecutive integers?
A) 9,101,736
B) 9,101,737
C) 9,101,738
D) 9,101,739
E) 9,101,740

Answer: C

[cramya]

May not be the best approach but hey the spiciness could be the reason and not me Not the text book approach for sure


Sum of any 4 consecutive integers left a reminder of 2 when divided by 4 is what I saw when I added some consecutive integers. So the sum must be 2 more than this number

Last 2 digits of a number divisible by 4 then the number is divisible by 4

Choice A) and E) divisible.

Only choice A) + 2 is part of the answer choice

Choose C)

[Brent@GMATPrepNow]

Oops, I posted this in DS and not PS - my bad.

This looks like a great solution to me. The only thing missing, perhaps, is the rationale for why the sum of 4 consecutive integers will always have a remainder of 2 when divided by 4.

Here's the reason:
Let the 4 consecutive numbers be x, x+1, x+2, and x+3
The sum is 4x+6 or 4x+4+2 or 4(x+1) + 2
Here we can see that the sum will have a remainder of 2 when divided by 4.

Nice work!

[cramya]

Thanks Brent!

Got up to 4x+6 but coudnt think of the split(4x+4+2) and started using numbers...