Last visit was: 15 Jul 2024, 13:11 It is currently 15 Jul 2024, 13:11
Toolkit
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.

# If X is a positive integer, what is the remainder when X^2 is divided

SORT BY:
Tags:
Show Tags
Hide Tags
Current Student
Joined: 16 Jan 2019
Posts: 623
Own Kudos [?]: 1478 [5]
Given Kudos: 142
Location: India
Concentration: General Management
GMAT 1: 740 Q50 V40
WE:Sales (Other)
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9443 [0]
Given Kudos: 91
Q51  V47
VP
Joined: 20 Jul 2017
Posts: 1297
Own Kudos [?]: 3580 [2]
Given Kudos: 162
Location: India
Concentration: Entrepreneurship, Marketing
GMAT 1: 690 Q51 V30
WE:Education (Education)
Retired Moderator
Joined: 19 Oct 2018
Posts: 1868
Own Kudos [?]: 6636 [1]
Given Kudos: 705
Location: India
Re: If X is a positive integer, what is the remainder when X^2 is divided [#permalink]
1
Kudos
Statement 1 and 2 are clearly insufficient alone

Combining both equations
X is a prime number greater than or equal to 5

X=6k±1

$$X^2=36k^2±12k+1$$
Hence $$X^2=1 (mod 6)$$

firas92 wrote:
If $$X$$ is positive integer, what is the remainder when $$X^2$$ is divided by 6?

1. $$X≥5$$

2. $$X$$ has no factor P such that $$1<P<X$$
Non-Human User
Joined: 09 Sep 2013
Posts: 33980
Own Kudos [?]: 851 [0]
Given Kudos: 0
Re: If X is a positive integer, what is the remainder when X^2 is divided [#permalink]
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: If X is a positive integer, what is the remainder when X^2 is divided [#permalink]
Moderator:
Math Expert
94354 posts