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 Your Progress

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.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

27 Mar 2017, 06:55

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

Re: When a positive integer m^2 is divided by 4, what is the remainder?
[#permalink]

Show Tags

29 Mar 2017, 01:43

==> 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.

Therefore, the answer is B. Answer: B
_________________

Re: When a positive integer m^2 is divided by 4, what is the remainder?
[#permalink]

Show Tags

05 Jul 2018, 07:36

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.
_________________