For a positive integer n, what is the remainder when n(n+1) is divided

Question

For a positive integer n, what is the remainder when n(n+1) is divided by 12? 
1) n is divisible by 3.
2) n is divisible by 4.

BrentGMATPrepNow · Accepted Answer

Target question :    What is the remainder when n(n+1) is divided by 12?

Statement 1 : n is divisible by 3  
Let's TEST some values.
There are several values of n that satisfy statement 1. Here are two: 
Case a: n = 3, in which case n(n+1) = 3(3+1) = 12. Here,  12 divided by 12 leaves remainder 0 
Case b: n = 6, in which case n(n+1) = 6(6+1) = 42. Here,  42 divided by 12 leaves remainder 6 
Since we cannot answer the  target question  with certainty, statement 1 is NOT SUFFICIENT

Statement 2 : n is divisible by 4  
There are several values of n that satisfy statement 2. Here are two: 
Case a: n = 4, in which case n(n+1) = 4(4+1) = 20. Here,  20 divided by 12 leaves remainder 8 
Case b: n = 8, in which case n(n+1) = 8(8+1) = 72. Here,  72 divided by 12 leaves remainder 0 
Since we cannot answer the  target question  with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined    
Statement 1 tells us that n is divisible by 3
Statement 2 tells us that n is divisible by 4 
COMBINED, we know that n is divisible by 12. 
If n is divisible by 12, then we can be certain that  (n)(n+1) is divisible by 12 .
If (n)(n+1) is divisible by 12, then  (n)(n+1) divided by 12 will leave remainder 0 
Since we can answer the  target question  with certainty, the combined statements are SUFFICIENT

Answer =  C

RELATED VIDEO
 https://www.youtube.com/watch?v=XCxgIR042tE

msk0657 · Answer

12 = 4*3

We need to know if n is divisible by 4 and 3.

Stat 1: Insufficient...since we don't know about n is divisible by 4.

Stat 2: Insufficient...since we don't know about n is divisible by 3.

Both : Sufficient...n is divisible by 4 and 3...i.e n ( n+1) is divisible by 12...

s1d1 · Answer

ques- For a positive integer n, what is the remainder when n(n+1) is divided by 12? 
1) n is divisible by 3.
2) n is divisible by 4.

answer-

when N is divisible by 3, then N is a multiple of 3 (N can be 3,6,9,12...etc)
so this case can have both situations where N(N+1) is divisible by 12 and not divisible by 12. 
For example- let N=3, thus 3*4 is divisible by 12, but if N=6 then 6*7 is not divisible by 12. 
we are not certain what the remainder will be. It can either be Zero or any other number

this statement is NOT SUFFICIENT. Thus we can eliminate choices A and D. we are now left with choices B,C,E

following the same above approach for statement 2 when N is divisible by 4, we can have two situations where N(N+1) is divisible by 12 ( for N=8) but N(N+1) is not divisible by 12 (for N=4,16..etc). thus again we are not certain what will be the remainder. it can either be Zero or any other number

So this statement is also NOT SUFFICIENT. We can eliminate choice B. 2 choices are left-C,E

now if we are given N is divisible by both 3 and 4, then N is a multiple of 12. Thus, N(N+1) is divisible by 12. now we are certain about the remainder
ANswer is C

MathRevolution · Answer

==> In the original condition, there is 1 variable (n), so D is highly likely to be the answer. In the case of 1), if =3, n(n+1)=12 with the remainder of 0,and if n=6, n(n+1)=42=12*3+6 with the remainder of 6, hence not sufficient. In the case of 2), if n=4, n(n+1)=20=12*1+8 with the remainder of 8, if n=8, n(n+1)=72=12*6 with the remainder of 0, hence not sufficient. Through 1) & 2), n=12, 24, 36… all have the remainder of 0, hence unique, and sufficient. C is the answer. 
Answer: C

Kinshook · Answer

Asked: For a positive integer n, what is the remainder when n(n+1) is divided by 12? 
1) n is divisible by 3.
n = 3k
n(n+1) = 3k(3k+1) = 9k^2 + 3k
The remainder when n(n+1) is divided by 12 = {0, 6}
NOT SUFFICIENT

2) n is divisible by 4.
n = 4k
n(n+1) = 4k(4k + 1) = 16k^2 + 4k 
The remainder when n(n+1) is divided by 12 = 4k(k+1) = {8,0}
NOT SUFFICIENT

(1) + (2) 
1) n is divisible by 3.
n = 3k
n(n+1) = 3k(3k+1) = 9k^2 + 3k
The remainder when n(n+1) is divided by 12 = {0, 6}
2) n is divisible by 4.
n = 4k
n(n+1) = 4k(4k + 1) = 16k^2 + 4k 
The remainder when n(n+1) is divided by 12 = 4k(k+1) = {8,0}
Combining, we get
The remainder when n(n+1) is divided by 12 = 0
SUFFICIENT

IMO C

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

For a positive integer n, what is the remainder when n(n+1) is divided

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

For a positive integer n, what is the remainder when n(n+1) is divided

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards