It is currently 30 Oct 2020, 05:11

### 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

# When the positive integer n is divided by 45, the remainder

Author Message
TAGS:
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2977 [1] , given: 394

When the positive integer n is divided by 45, the remainder [#permalink]  12 May 2016, 04:49
1
KUDOS
Expert's post
00:00

Question Stats:

73% (01:05) correct 26% (01:00) wrong based on 163 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

Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2977 [1] , given: 394

Re: When the positive integer n is divided by 45, the remainder [#permalink]  12 May 2016, 04:50
1
KUDOS
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: 8

Kudos [?]: 199 [6] , given: 0

Re: When the positive integer n is divided by 45, the remainder [#permalink]  17 May 2016, 16:15
6
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
41 Reviews

5-star rated online GRE quant
self study course

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 [?]: 13 [0], given: 15

Re: When the positive integer n is divided by 45, the remainder [#permalink]  22 Jan 2018, 08:02
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: 8

Kudos [?]: 199 [3] , given: 0

Re: When the positive integer n is divided by 45, the remainder [#permalink]  17 May 2018, 15:52
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 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
41 Reviews

5-star rated online GRE quant
self study course

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 [?]: 7 [5] , given: 1

Re: When the positive integer n is divided by 45, the remainder [#permalink]  20 May 2018, 23:05
5
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 [?]: 7 [0], given: 2

Re: When the positive integer n is divided by 45, the remainder [#permalink]  27 May 2018, 12:08
Good approach
Intern
Joined: 22 Jul 2018
Posts: 39
Followers: 0

Kudos [?]: 19 [0], given: 5

Similar problem [#permalink]  14 Oct 2018, 01:07
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
Retired Moderator
Joined: 07 Jun 2014
Posts: 4803
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 173

Kudos [?]: 2977 [0], given: 394

Re: Similar problem [#permalink]  15 Oct 2018, 06:43
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: 19
Followers: 0

Kudos [?]: 2 [0], given: 5

Re: When the positive integer n is divided by 45, the remainder [#permalink]  30 Apr 2019, 04:55
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: 13719
GRE 1: Q160 V160
Followers: 305

Kudos [?]: 3553 [0], given: 12681

Re: When the positive integer n is divided by 45, the remainder [#permalink]  01 May 2019, 11:07
Expert's post
Hi,

what did you mean ??
_________________

- Do you want all the GRE Prep Club resources at a glance (sort of ) ?? Look at GRE Prep Club Official LinkTree page
- Do you want all the GRE Prep Club FREE resources in one spot ?? Look at Free GRE Materials - Where to get it!! (2020)
- Do you want all the FREE GRE tests on earth ?? Look at FREE GRE Practice Tests [Collection] - New Edition (2021)
- Do you want to know the GRE score in the Top 25 BS in 7 continents ?? Look at here The GRE average score at Top 25 Business Schools 2020 Ed.
- Need Practice 20 Free GRE Quant Tests available for free with 20 Kudos
- GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests.

Manager
Joined: 19 Nov 2018
Posts: 102
Followers: 0

Kudos [?]: 108 [2] , given: 53

Re: When the positive integer n is divided by 45, the remainder [#permalink]  14 Sep 2019, 10:59
2
KUDOS
This one didn't really click with me until I tried one of the wrong answers. Let's try 11.

N = 45Q + 18

N = $$\frac{45Q + 18}{11}$$

N = $$\frac{45Q}{11} + \frac{18}{11}$$

You can clearly see now that N can not be an integer after division, which is what we want when looking for a divisor of N, unless BOTH 45Q and 18 are divisible by the answer choice.

So, 11 wouldn't work.

We can then try 9. 9 works. N will still be an integer if it is divided by 9. So, 9 is our answer.

To illustrate:

N = $$\frac{45Q}{9} + \frac{18}{9}$$

N = 5Q + 2

. we can see N will be an integer if we divide by 9. So, 9 works.
Intern
Joined: 06 Sep 2019
Posts: 1
Followers: 0

Kudos [?]: 0 [0], given: 0

Re: When the positive integer n is divided by 45, the remainder [#permalink]  14 Sep 2019, 12:03
sandy wrote:
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.
Re: When the positive integer n is divided by 45, the remainder   [#permalink] 14 Sep 2019, 12:03
Display posts from previous: Sort by