If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?
A) 0
B) 1
C) 2
D) 3
E) 5
OA: B
OG2016 - If n is a prime number greater than 3
This topic has expert replies
-
- Senior | Next Rank: 100 Posts
- Posts: 93
- Joined: Mon Apr 25, 2016 2:22 pm
- Thanked: 1 times
- Followed by:1 members
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
A nice fast approach is to TEST a possible value of n. Since n must be a prime number that's greater than 3, let's TEST n = 5boomgoesthegmat wrote:If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?
A) 0
B) 1
C) 2
D) 3
E) 5
OA: B
If n = 5, then n² = 5² = 25, and when we divide 25 by 12, we get 2 with REMAINDER 1
Answer: B
Cheers,
Brent
- OptimusPrep
- Master | Next Rank: 500 Posts
- Posts: 410
- Joined: Fri Mar 13, 2015 3:36 am
- Location: Worldwide
- Thanked: 120 times
- Followed by:8 members
- GMAT Score:770
We can solve this problem by testing values easily.boomgoesthegmat wrote:If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?
A) 0
B) 1
C) 2
D) 3
E) 5
OA: B
Assume n = 7, n^2 = 49
Remainder of (49/12) = 1
Another approach: Always remember that any prime number apart from 2 is of the form (6k +- 1)
Assume n = 6k + 1, n^2 = 36k^2 + 12k + 1
Remainder of (n^2/12) = 1
Assume n = 6k - 1, n^2 = 36k^2 - 12k + 1
Remainder of (n^2/12) = 1
Correct option: B
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
Hi All,
We're told that N is a PRIME number GREATER than 3. We're asked for the remainder when N^2 is divided by 12. Many questions in the GMAT Quant section can be solved by TESTing VALUES - and this question can be too. In general, you want to choose the 'easiest' value(s) that fit the given situation. You might notice that two of the explanations to this question us N=5 and N=7 - and they both lead to the SAME correct answer. These patterns hold true even when you use a value that isn't the 'easiest' one available. For example...
IF... N=11, then N^2 = (11)^2 = 121
121/12 = 10 r 1
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
We're told that N is a PRIME number GREATER than 3. We're asked for the remainder when N^2 is divided by 12. Many questions in the GMAT Quant section can be solved by TESTing VALUES - and this question can be too. In general, you want to choose the 'easiest' value(s) that fit the given situation. You might notice that two of the explanations to this question us N=5 and N=7 - and they both lead to the SAME correct answer. These patterns hold true even when you use a value that isn't the 'easiest' one available. For example...
IF... N=11, then N^2 = (11)^2 = 121
121/12 = 10 r 1
Final Answer: B
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7223
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We can let n = 5. Thus n^2 = 25 and 25/12 = 2 R 1.boomgoesthegmat wrote:If n is a prime number greater than 3, what is the remainder when n^2 is divided by 12?
A) 0
B) 1
C) 2
D) 3
E) 5
(Note: Since the answer choices don't have a choice such as "Can't be determined." We can safely say the correct answer must be 1, though we only used one value for n. If we want to make sure further that the answer must be 1, we can use another value for n such as n = 7. We see that n^2 = 49 and 49/12 = 4 R 1. The remainder once again is 1.)
Answer: B
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews