BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach 7 seats left
Chris Peckover
NEXT LIVE COHORT

Oct 13 to Jan 7, 2027

with Chris Peckover

Schedule
Tue, Thu · 8:00 to 10:00 PM ET
Included
40 live hours + 6 months of GMAT OnDemand
  • Live instruction and real-time questions
  • Class recordings and assigned practice
View class & enroll
Limited cohort · enrollment openTarget Test Prep
EALiveTeach 5 seats left
Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll
Limited cohort · enrollment openTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

Which is the divisor of n?

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Thu Dec 25, 2014 12:49 pm
by AndrewRivera7793 » Thu Dec 25, 2014 12:51 pm
When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

A) 11

B) 9

C) 7

D) 6

E) 4

Is there a formula of some sort to solve this problem? Any help is appreciated.

Thanks,

-Andy
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
GMAT Instructor
Posts: 15539
Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members
Location: New York, NY
Thanked: 13060 times
GMAT Score:790

by GMATGuruNY » Thu Dec 25, 2014 1:04 pm
AndrewRivera7793 wrote:When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

A) 11

B) 9

C) 7

D) 6

E) 4

Is there a formula of some sort to solve this problem? Any help is appreciated.

Thanks,

-Andy
When the positive integer n is divided by 45, the remainder is 18.
In other words, n is multiple of 45 plus 18:
n = 45a + 18, where a is a nonnegative integer.

Simplifying n = 45a + 18, we get:
n = 45a + 18 = 9(5a + 2).
Thus, n must be a multiple of 9.

The correct answer is B.

We can also TEST options for n.

If a=0, then n = 45a + 18 = 45*0 + 18 = 18.
Since 18 is not a multiple of 11, 7, or 4, eliminate A, C and E.
If a=1, then n = 45a + 18 = 45*1 + 18 = 63.
Since 63 is a not multiple of 6, eliminate D.

The correct answer is B.
Last edited by GMATGuruNY on Thu Dec 25, 2014 1:08 pm, edited 1 time in total.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.

As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.

For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

by Brent@GMATPrepNow » Thu Dec 25, 2014 1:05 pm
AndrewRivera7793 wrote:When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

A) 11
B) 9
C) 7
D) 6
E) 4
When it comes to remainders, we have a nice rule that says:

If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.

Here, we are told that n divided by 45 leaves a remainder of 18, so the possible values of n are: 18, 63, 108,... etc.

IMPORTANT: the question asks, "Which of the following must be a divisor of n?
So, let's test the smallest possible value of n, which is 18, and check the answer choices.

18 is NOT divisible by 11, 7 or 4, so we can ELIMINATE A, C and E.
So, the correct answer is either B or D

Now test the next possible value of n, which is 63.
63 is NOT divisible by 6, so we can ELIMINATE D

So, by the process of elimination, the correct answer is B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
Newbie | Next Rank: 10 Posts
Posts: 4
Joined: Thu Dec 25, 2014 12:49 pm

by AndrewRivera7793 » Thu Dec 25, 2014 1:12 pm
Wow, Thank you both for the excellent methods to solve this problem! I've "Thanked" you both. Merry Xmas :)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
User avatar
GMAT Instructor
Posts: 1462
Joined: Thu Apr 09, 2015 9:34 amFollowed by: 22 members
Location: New York, NY
Thanked: 39 times

by Jeff@TargetTestPrep » Thu May 17, 2018 5:11 pm
AndrewRivera7793 wrote:When the positive integer n is divided by 45, the remainder is 18. Which of the following must be a divisor of n?

A) 11

B) 9

C) 7

D) 6

E) 4
We can find all possible values of n by adding the remainder 18 to integer multiples of 45. Thus, we see that n can be values such as 18 or 63 or 108.

The only common factors of these three numbers are 1 and 9. Since 1 is not in the answer choices, the correct answer must be 9.

Answer: B

Jeffrey Miller
Head of GMAT Instruction
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1