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A group of n students can be divided into equal groups of 4 [#permalink]
03 Nov 2007, 04:32
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Difficulty:
45% (medium)
Question Stats:
63% (02:30) correct
37% (01:34) wrong based on 232 sessions
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
Re: A group of n students can be divided into equal groups of 4 [#permalink]
13 Sep 2012, 07:15
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siddharthasingh wrote:
Isn't there any arithmetic solution to this question. I mean, just Hit n Trial method. Indeed there must be an arithmetic way out. Using this hit and trial method sometimes takes much longer time, henceforth I needed to go with a systematic approach.
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
A. 33 B. 46 C. 49 D. 53 E. 86
Given: \(n=4q+1\), so \(n\) could be: 1, 5, 9, 13, ... \(n=5p+3\), so \(n\) could be: 3, 8, 13, ...
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
A group of n students can be divided into equal groups of 4 with 1 student left over or equal groups of 5 with 3 students left over. What is the sum of the two smallest possible values of n?
33 46 49 53 86
I got this so far
n = 4q + 1 n = 5q + 3
4q+1 + 5q+3 = 9q+4
plugging in value for q
q=1 q=2 q=3 q=4 q=5 = 45+4 = 49 ? not sure please help
Man ughhhh haha, I couldnt figure this question out forever. Was wondering why everyone was getting 46. I was like comon its 33.
question is really asking what is the SUM of the two possible values of n.
Re: A group of n students can be divided into equal groups of 4 [#permalink]
13 Sep 2012, 06:58
Expert's post
Isn't there any arithmetic solution to this question. I mean, just Hit n Trial method. Indeed there must be an arithmetic way out. Using this hit and trial method sometimes takes much longer time, henceforth I needed to go with a systematic approach. _________________
Re: A group of n students can be divided into equal groups of 4 [#permalink]
11 Dec 2013, 02:12
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Re: A group of n students can be divided into equal groups of 4 [#permalink]
11 Dec 2013, 04:52
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4x + 1 = n (1) 5y + 3 = n (2)
Equating (1) and (2) 4x + 1 = 5y + 3 4x = 5y + 2 Put y=1,2,3,4,etc. Since (5y + 2) need to be a multiple of 4 to satisfy the equation on the left side. The 2 minimum values of y are 2 and 6.
So, n = 5y + 3 n = 5(2) + 3 = 13 and n = 5(6) + 3 = 33
Re: A group of n students can be divided into equal groups of 4 [#permalink]
26 Oct 2015, 19:01
Hello from the GMAT Club BumpBot!
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