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When the positive integer n is divided by 45, the remainder [#permalink]
12 May 2016, 04:49
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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
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Re: When the positive integer n is divided by 45, the remainder [#permalink]
12 May 2016, 04:50
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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.
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Re: When the positive integer n is divided by 45, the remainder [#permalink]
17 May 2016, 16:15
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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
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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..



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Re: When the positive integer n is divided by 45, the remainder [#permalink]
17 May 2018, 15:52
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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
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Re: When the positive integer n is divided by 45, the remainder [#permalink]
20 May 2018, 23:05
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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.



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Re: When the positive integer n is divided by 45, the remainder [#permalink]
27 May 2018, 12:08
Good approach



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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



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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.
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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?



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Re: When the positive integer n is divided by 45, the remainder [#permalink]
01 May 2019, 11:07
Hi, what did you mean ??
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Re: When the positive integer n is divided by 45, the remainder [#permalink]
14 Sep 2019, 10:59
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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.



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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 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.




Re: When the positive integer n is divided by 45, the remainder
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14 Sep 2019, 12:03





