 It is currently 16 Jun 2019, 20:50 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 the positive integer n is divided by 45, the remainder  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 , given: 397

When the positive integer n is divided by 45, the remainder [#permalink]
Expert's post 00:00

Question Stats: 66% (00:58) correct 33% (00:29) wrong based on 51 sessions
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

Practice Questions
Question: 10
Page: 62
[Reveal] Spoiler: OA

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 , given: 397

Re: When the positive integer n is divided by 45, the remainder [#permalink]
Expert's post
Explanation

The given information tells you that n can be expressed in the form n = 45k + 18, where k can be any non-negative integer. Consider how the divisors of 45 and 18 may be related to the divisors of n. Every common divisor of 45 and 18 is also a divisor of any sum of multiples of 45 and 18, like 45k + 18. So any common divisor of 45 and 18 is also a divisor of n. Of the answer choices given, only 9 is a common divisor of 45 and 18.
Thus the correct answer is Choice B.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Target Test Prep Representative Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 140  , given: 0

Re: When the positive integer n is divided by 45, the remainder [#permalink]
3
KUDOS
Expert's post
sandy 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 are given that when the positive integer n is divided by 45, the remainder is 18. We can express this in the remainder formula:

n/45 = Q + 18/45 (where Q = Quotient)

n = 45Q + 18

Any divisor of n must evenly divide into 45Q and 18. Thus, 9 is the correct answer.

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews

Intern Joined: 24 Oct 2017
Posts: 36
Followers: 0

Kudos [?]: 11 , given: 15

Re: When the positive integer n is divided by 45, the remainder [#permalink]
the 2nd explaination was more helpful then the first.. Target Test Prep Representative Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4

Kudos [?]: 140  , given: 0

Re: When the positive integer n is divided by 45, the remainder [#permalink]
2
KUDOS
Expert's post
sandy 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.

_________________

Jeffrey Miller

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GRE quant course on GRE Prep Club. Read Our Reviews Intern Joined: 20 May 2018
Posts: 6
Followers: 0

Kudos [?]: 4  , given: 1

Re: When the positive integer n is divided by 45, the remainder [#permalink]
2
KUDOS
Divisibility Rule:

DIVIDEND=(DIVISOR*QUOTIENT)+REMAINDER --(1)

Given:
1) Dividend = 'n'.
2)Divisor=45.
3)Remainder=18.
4)Quotient=?

Let's assume the Quotient to be 'a',

Putting the above values in the formula (1), we get

n=(45*a)+18.
n=45a+18.
n=9(5a+2).

Thus, n must be a multiple of 9.

(or)

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.
Intern Joined: 26 May 2018
Posts: 37
Followers: 0

Kudos [?]: 5 , given: 2

Re: When the positive integer n is divided by 45, the remainder [#permalink]
Good approach
Intern Joined: 22 Jul 2018
Posts: 41
Followers: 0

Kudos [?]: 11 , given: 5

Sid23 wrote:
Good approach

If k is the greatest positive integer such that 3^k is a divisor of 15! then k =

A. 3
B. 4
C. 5
D. 6
E. 7
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 , given: 397

Expert's post
ruposh6240 wrote:
Sid23 wrote:
Good approach

If k is the greatest positive integer such that 3^k is a divisor of 15! then k =

A. 3
B. 4
C. 5
D. 6
E. 7

Post this as a new question on the forum, please.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern Joined: 15 Mar 2019
Posts: 18
Followers: 0

Kudos [?]: 1 , given: 5

Re: When the positive integer n is divided by 45, the remainder [#permalink]
I think I'm being exceptionally stupid but I can't get my head around this as 63/ 9 = 7, there is no remainder? Surely a divisor of n shouldn't also be a divisor of 18 otherwise there would be no remainder?
Founder  Joined: 18 Apr 2015
Posts: 6874
Followers: 114

Kudos [?]: 1332 , given: 6293

Re: When the positive integer n is divided by 45, the remainder [#permalink]
Expert's post
Hi,

what did you mean ??
_________________ Re: When the positive integer n is divided by 45, the remainder   [#permalink] 01 May 2019, 11:07
Display posts from previous: Sort by

When the positive integer n is divided by 45, the remainder  Question banks Downloads My Bookmarks Reviews Important topics Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.