gmattesttaker2 wrote:Hello,

Can you please assist with this:

If n is a positive integer between 1 and 99, inclusive, what is the probability that
n(n + 1) is a multiple of 3?

(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 5/6

n and (n + 1) are consecutive integers.

The product n(n + 1) will be a multiple of 3 if n is a multiple of 3 OR (n + 1) is a multiple of 3

So, P(the product is a multiple of 3) = P(n is a multiple of 3 OR n+1 is a multiple of 3)
= P(n is a multiple of 3) + P(n+1 is a multiple of 3)
= 1/3 + 1/3
= [spoiler]2/3[/spoiler]
= D

Aside: Every 3rd integer from 1 to 99 inclusive is a multiple of 3. So, P(n is a multiple of 3) = 1/3
Likewise, P(n+1 is a multiple of 3) = 1/3

Cheers,
Brent

Hi Sri,

Your idea to decipher the pattern behind the sequence was a good option. Sequence prompts on the GMAT will follow type of pattern; your ability to figure out that pattern might be essential to the question (such as this question) or helpful in finding an easy approach to answering whatever specific question that the prompt asks for.

You figured out the first 4 numbers in the sequence...

N=1; 1(1+1) is not a multiple of 3
N=2; 2(2+1) IS a multiple of 3
N=3; 3(3+1) iS a multiple of 3
N=4; 4(4+1) is not a multiple of 3

Now go just a little further....
N=5; 5(5+1) IS a multiple of 3
N=6; 6(6+1) IS a multiple of 3

Now we can see the sequence: NOT, IS, IS, NOT, IS, IS

So, 2 out of every 3 numbers in the sequence will give you a multiple of 3. This pattern repeats. Working up to 99, we would have 33 "sets" of NOT/IS/IS.

It will clearly be 2/3.

Final Answer: D

Keep this logic/approach in mind, especially if you don't immediately see the pattern behind a question. There's NO time to stare on Test Day; you're better served brute-forcing your way through this question and discovering the pattern than hoping that it will just "come to you."

GMAT assassins aren't born, they're made,
Rich