GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 02 Jul 2020, 04:14 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # When a positive integer m^2 is divided by 4, what is the remainder?

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9133
GMAT 1: 760 Q51 V42
GPA: 3.82
When a positive integer m^2 is divided by 4, what is the remainder?  [#permalink]

### Show Tags

1
7 00:00

Difficulty:   55% (hard)

Question Stats: 65% (01:47) correct 35% (02:01) wrong based on 187 sessions

### HideShow timer Statistics

When a positive integer $$m^2$$ is divided by 4, what is the remainder?

1) When m is divided by 3, the remainder is 1
2) When m is divided by 2, the remainder is 1

_________________
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4947
GMAT 1: 770 Q49 V46
When a positive integer m^2 is divided by 4, what is the remainder?  [#permalink]

### Show Tags

Top Contributor
1
MathRevolution wrote:
When a positive integer m² is divided by 4, what is the remainder?

1) When m is divided by 3, the remainder is 1
2) When m is divided by 2, the remainder is 1

Target question: What is the remainder when m² is divided by 4?

Statement 1: When m is divided by 3, the remainder is 1
Let's TEST some values.
There are several values of m that satisfy statement 1. Here are two:
Case a: m = 4, which means m² =16. In this case, the remainder is 0 when m² is divided by 4
Case b: m = 7, which means m² =49. In this case, the remainder is 1 when m² is divided by 4
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When m is divided by 2, the remainder is 1
ASIDE: There's a nice rule that say, "If N divided by D equals Q with remainder R, then N = DQ + R"
For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2
Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3

So, in this case, we can write: m = 2k + 1 (where k is some integer)
If m = 2k + 1, then m² = (2k + 1)² = 4k² + 4k + 1 = 4(k² + k) + 1
In other words, m² = 4(some integer) + 1
Since m² is 1 GREATER THAN some multiple of 4, we can conclude that the remainder is 1 when m² is divided by 4
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO

_________________
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 9133
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: When a positive integer m^2 is divided by 4, what is the remainder?  [#permalink]

### Show Tags

==> In the original condition, there is 1 variable (m) and in order to match the number of variables to the number of equations, there must be 1 equation. Since there is 1 for con 1) and 1 for con 2), D is most likely to be the answer. For remainder questions, it is best to use direct substitution.

For con 1), if you substitute from m=3p+1=1,4,7…, from m=1, 1^2=1=4(0)+1, the remainder=1, and if m=4, from 4^2=16=4(4)+0, the remainder=0, hence it is not unique and not sufficient.
For con 2), from m=2q+1=1,3,5,7,…, you get m2=1,9,25,49.., and the remainder divided by 4 always becomes 1, hence it is unique and sufficient.

_________________
Non-Human User Joined: 09 Sep 2013
Posts: 15358
Re: When a positive integer m^2 is divided by 4, what is the remainder?  [#permalink]

### Show Tags

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________ Re: When a positive integer m^2 is divided by 4, what is the remainder?   [#permalink] 05 Jul 2018, 06:36

# When a positive integer m^2 is divided by 4, what is the remainder?  