Author 
Message 
TAGS:

Hide Tags

Director
Joined: 10 Feb 2006
Posts: 657

A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
03 Nov 2007, 05:32
2
This post received KUDOS
6
This post was BOOKMARKED
Question Stats:
65% (02:21) correct
35% (01:29) wrong based on 385 sessions
HideShow timer Statistics
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 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
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
GMAT the final frontie!!!.



Director
Joined: 30 Nov 2006
Posts: 591
Location: Kuwait

1
This post received KUDOS
1
This post was BOOKMARKED
n = 4q + 1
n = 5q + 3
I'll start with the first equation: n = 5+k4 where k = 0,1,2,3, ... etc
also, n = 8+m5 where m = 0,1,2,3,.. etc
for first equation: 5,9,13,17,21,25,29,33,37,41,45
for second equation: 8,13,18,23,28,33,38,43,48,53
The sum of minimum n's = 13 + 33 = 46
B



VP
Joined: 28 Mar 2006
Posts: 1369

my eq is 4x+1 = 5y+3
so 4x = 5y + 2
if y=2 x=3
ify=6 x=8
is the smallest group 8*4 + 1 =33



SVP
Joined: 05 Jul 2006
Posts: 1747

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
4x+1 = 5y+3...........ie: 4x5y = 2
x,y must be >1 and y is even ie ( 2,4,6,..etc)
if y = 2 thus x = 3 and thus n = 13
if y = 4 thus x is a fraction ( not possible)
if y = 6 thus x = 8 and n= 33
13+33 = 46..... B



CEO
Joined: 29 Mar 2007
Posts: 2559

Re: Remainder [#permalink]
Show Tags
03 Nov 2007, 11:11
alimad wrote: 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.
so ya 13+33=46.



VP
Status: Been a long time guys...
Joined: 03 Feb 2011
Posts: 1381
Location: United States (NY)
Concentration: Finance, Marketing
GPA: 3.75

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
13 Sep 2012, 07:58
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.
_________________
Prepositional Phrases ClarifiedElimination of BEING Absolute Phrases Clarified Rules For Posting www.UnivScholarships.com



Math Expert
Joined: 02 Sep 2009
Posts: 39678

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
13 Sep 2012, 08:15
4
This post received KUDOS
Expert's post
8
This post was BOOKMARKED
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, ... General formula for \(n\) based on above two statements will be: \(n=20m+13\) (the divisor should be the least common multiple of above two divisors 4 and 5, so 20 and the remainder should be the first common integer in above two patterns, hence 13). For more about this concept see: manhattanremainderproblem93752.html#p721341, whenpositiveintegernisdividedby5theremainderis90442.html#p722552, whenthepositiveintegeraisdividedby5and125591.html#p1028654From, \(n=20m+13\) we have that the two smallest possible values of \(n\) are 13 (for \(m=0\)) and 33 (for \(m=1\)). 13+33=46. Answer: B. Hope it helps.
_________________
New to the Math Forum? Please read this: All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15977

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
11 Dec 2013, 03:12
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Manager
Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 159
Location: India
Concentration: Finance, General Management
GMAT 1: 540 Q50 V15 GMAT 2: 640 Q50 V27
GPA: 3.11
WE: Consulting (Computer Software)

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
11 Dec 2013, 05:52
1
This post was BOOKMARKED
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 Adding the 2 minimum values of n 13 + 33 = 46 So, the correct answer is B.
_________________
Sahil Chaudhary If you find this post helpful, please take a moment to click on the "+1 KUDOS" icon. My IELTS 7.5 Experience From 540 to 640...Done with GMAT!!! http://www.sahilchaudhary007.blogspot.com



Manager
Joined: 18 Oct 2013
Posts: 83
Location: India
Concentration: Technology, Finance
Schools: Duke '16, Johnson '16, Kelley '16, Tepper '16, Marshall '16, McDonough '16, Insead '14, HKUST '16, HSG '15, Schulich '15, Erasmus '16, IE April'15, Neeley '15
GMAT 1: 580 Q48 V21 GMAT 2: 530 Q49 V13 GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
11 Dec 2013, 12:28
1
This post received KUDOS
From question we get N= => 4K+1=5P+3 K=P+(P+2)/4
So for P=2 & 6 we get K an integer i.e. K=13 & 33
Sum=13+33=46. B is correct.



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15977

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
26 Oct 2015, 20:01
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up  doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Senior Manager
Status: DONE!
Joined: 05 Sep 2016
Posts: 409

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
16 Oct 2016, 11:07
B is correct. Here's why: Given the information in the question we can create the following two equations: n = 4x+1 (5,9, 13,17,21,25,29, 33) n = 5y+3 (8, 13,18,23,28, 33) The parentheses following the equations represent potential value of n given various values of x (i.e. 1+). We can see from these calculations that 13 and 33 line up with both equations. Therefore, we can add 13 and 33 and we are done



Manager
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 58

Re: A group of n students can be divided into equal groups of 4 [#permalink]
Show Tags
03 Nov 2016, 03:03
n=4q+1 n= 5k+3
The smallest numbers that satisfies the equations are 13 and 33...so Answer B
_________________
Cours particuliers de GMAT par webcam avec un prof spécialisé




Re: A group of n students can be divided into equal groups of 4
[#permalink]
03 Nov 2016, 03:03







