Author 
Message 
TAGS:


GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4711
WE: Business Development (Energy and Utilities)
Followers: 91
Kudos [?]:
1615
[0], given: 376

When the positive integer n is divided by 45, the remainder [#permalink]
12 May 2016, 04:49
Question Stats:
59% (00:56) correct
40% (00:26) wrong based on 32 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
_________________
Sandy If you found this post useful, please let me know by pressing the Kudos Button
Try our free Online GRE Test




GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4711
WE: Business Development (Energy and Utilities)
Followers: 91
Kudos [?]:
1615
[0], given: 376

Re: When the positive integer n is divided by 45, the remainder [#permalink]
12 May 2016, 04:50
ExplanationThe given information tells you that n can be expressed in the form n = 45k + 18, where k can be any nonnegative 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
Status: Head GRE Instructor
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4
Kudos [?]:
114
[2]
, given: 0

Re: When the positive integer n is divided by 45, the remainder [#permalink]
17 May 2016, 16:15
2
This post received KUDOS
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. Answer: B
_________________
Jeffery Miller
Head of GRE Instruction
GRE Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 24 Oct 2017
Posts: 36
Followers: 0
Kudos [?]:
10
[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
Status: Head GRE Instructor
Affiliations: Target Test Prep
Joined: 09 May 2016
Posts: 161
Location: United States
Followers: 4
Kudos [?]:
114
[1]
, given: 0

Re: When the positive integer n is divided by 45, the remainder [#permalink]
17 May 2018, 15:52
1
This post received KUDOS
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. Answer: B
_________________
Jeffery Miller
Head of GRE Instruction
GRE Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Intern
Joined: 20 May 2018
Posts: 6
Followers: 0
Kudos [?]:
2
[1]
, given: 1

Re: When the positive integer n is divided by 45, the remainder [#permalink]
20 May 2018, 23:05
1
This post received 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: 31
Followers: 0
Kudos [?]:
5
[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: 41
Followers: 0
Kudos [?]:
7
[0], 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



GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4711
WE: Business Development (Energy and Utilities)
Followers: 91
Kudos [?]:
1615
[0], given: 376

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




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





