GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Oct 2019, 13:11 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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  A group of n students can be divided into equal groups of 4

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Director  Joined: 10 Feb 2006
Posts: 566
A group of n students can be divided into equal groups of 4  [#permalink]

Show Tags

6
13 00:00

Difficulty:   45% (medium)

Question Stats: 68% (02:01) correct 32% (02:08) wrong based on 346 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

_________________
GMAT the final frontie!!!.
Math Expert V
Joined: 02 Sep 2009
Posts: 58434
Re: A group of n students can be divided into equal groups of 4  [#permalink]

Show Tags

5
9
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: manhattan-remainder-problem-93752.html#p721341, when-positive-integer-n-is-divided-by-5-the-remainder-is-90442.html#p722552, when-the-positive-integer-a-is-divided-by-5-and-125591.html#p1028654

From, $$n=20m+13$$ we have that the two smallest possible values of $$n$$ are 13 (for $$m=0$$) and 33 (for $$m=1$$).

13+33=46.

Hope it helps.
_________________
General Discussion
Director  Joined: 30 Nov 2006
Posts: 504
Location: Kuwait

Show Tags

1
1
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: 1089

Show Tags

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
Retired Moderator B
Joined: 05 Jul 2006
Posts: 1408

Show Tags

1
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: 4x-5y = 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
SVP  Joined: 29 Mar 2007
Posts: 1989

Show Tags

1
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: 1007
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

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.
_________________
Manager  Status: Work hard in silence, let success make the noise
Joined: 25 Nov 2013
Posts: 126
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

2
1
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: 68
Location: India
Concentration: Technology, Finance
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

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.
Current Student B
Status: DONE!
Joined: 05 Sep 2016
Posts: 357
Re: A group of n students can be divided into equal groups of 4  [#permalink]

Show Tags

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  P
Status: Quant Expert Q51
Joined: 02 Aug 2014
Posts: 103
Re: A group of n students can be divided into equal groups of 4  [#permalink]

Show Tags

n=4q+1

n= 5k+3

The smallest numbers that satisfies the equations are 13 and 33...so Answer B
_________________
EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 15294
Location: United States (CA)
GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: A group of n students can be divided into equal groups of 4  [#permalink]

Show Tags

Hi All,

You would likely find it easiest to 'brute force' this question (simply write down enough of the possibilities until you either spot the pattern involved or have the exact answer on your pad).

Equal groups of 4 with 1 left over COULD be... 5, 9, 13, 17, 21, 25, 29, 33.....
Equal groups of 5 with 3 left over COULD be... 8, 13, 18, 23, 28, 33....

The two SMALLEST values that fit BOTH groups are 13 and 33. We're asked for the sum of those values...

GMAT assassins aren't born, they're made,
Rich
_________________
Non-Human User Joined: 09 Sep 2013
Posts: 13316
Re: A group of n students can be divided into equal groups of 4  [#permalink]

Show Tags

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.
_________________ Re: A group of n students can be divided into equal groups of 4   [#permalink] 10 Feb 2019, 19:01
Display posts from previous: Sort by

A group of n students can be divided into equal groups of 4

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  