Find all School-related info fast with the new School-Specific MBA Forum

It is currently 24 Oct 2014, 01:46

Close

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
Your Progress

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

When positive integer x is divided by 5, the remainder is 3;

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
VP
VP
avatar
Joined: 22 Nov 2007
Posts: 1102
Followers: 6

Kudos [?]: 135 [0], given: 0

When positive integer x is divided by 5, the remainder is 3; [#permalink] New post 12 Mar 2008, 12:16
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

80% (02:35) correct 20% (01:32) wrong based on 146 sessions
When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y?

(A) 12
(B) 15
(C) 20
(D) 28
(E) 35
[Reveal] Spoiler: OA
2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 15 Aug 2007
Posts: 255
Schools: Chicago Booth
Followers: 1

Kudos [?]: 53 [2] , given: 0

Re: gprep remainders [#permalink] New post 14 Mar 2008, 19:18
2
This post received
KUDOS
35

Interesting thing to note here is it doesn't matter what the reminders are, the only thing that matters is if the reminders are same for x and y when devided by the same number.

x can be written as 5a+3 or 7b+4
y can be written as 5c+3 or 7d+4
x-y=5(a-c) or 7(b-d)
take LCM of 5 and 7 = 35 (it's easy here bacause both are prime)
Senior Manager
Senior Manager
avatar
Joined: 20 Feb 2008
Posts: 296
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
Followers: 4

Kudos [?]: 28 [0], given: 0

Re: factor [#permalink] New post 11 May 2008, 09:19
Hi , I tried two ways of reaching the answer and I get E 35. Not sure if this is right though :? !

For x we have two equations:

x=3+5m
x=4+7n

Similarly for y:

y=3+5l
4= 4 +7j

x-y =3+5m - (3+5l)
=5(m-l)

x-y = 4+7n -(4+7j)
= 7(n-j)
7 and 5 are factors of x-y, therefore 7*5 =35 must be a factor of x-y.


Another way I tried to solve this is by using numbers, If x=3+5m, then c must be a number with units digit 8 or 3
since x=7 +5n , the values of x that satisfy these two equations are 18 and 53,

since y has similar rules and x>y; x=53 and y =18,
x-y= 53-18 =35, therefore 35 must be a factor of x-y.
Director
Director
User avatar
Joined: 14 Oct 2007
Posts: 759
Location: Oxford
Schools: Oxford'10
Followers: 13

Kudos [?]: 178 [0], given: 8

Re: factor [#permalink] New post 12 May 2008, 13:11
fresinha12 wrote:
x=5N+3 => 8,13,18,23,28,33,39
x=7N+4 => 11,18,25,32,39..

so if i pick x=23 y=11 then x-y=12..

A can be a factor of x-y..

if you pick x=39 y=11 then 28 can also be a factor..

so D can also be an answer..

not sure where this question is from?


Fresinha, the highlighted should be 38, hence ur error.

One way to look at this question is that the same reminders will be yielded every 5x7 times (common denominator offset by the same reminders).
1 KUDOS received
Director
Director
avatar
Joined: 23 Sep 2007
Posts: 798
Followers: 5

Kudos [?]: 82 [1] , given: 0

Re: factor [#permalink] New post 12 May 2008, 16:49
1
This post received
KUDOS
Agree with E

Remainder 3: x = 3 8 13 18 23 28 33 38 .... 53 58
Remainder 4: x = 4 11 18 25 ... 53

Remainder 3: y = 3 8 13 18 23 28 33 38 .... 53 58
Remainder 4: y = 4 11 18 25 ... 53

values of 18 and 53 are valid for x and y

x > y so x = 53, y = 18

x - y = 35
CEO
CEO
User avatar
Joined: 17 May 2007
Posts: 2995
Followers: 57

Kudos [?]: 443 [0], given: 210

Re: factor [#permalink] New post 12 May 2008, 16:55
I know you guys are doing this in a systematic manner but the only 2 numbers I could come up with - without doing any math - just running through the multiplication tables of 7 were 18 and 53. and 53-18 = 35. Hence answer is E.
SVP
SVP
User avatar
Joined: 05 Jul 2006
Posts: 1541
Followers: 5

Kudos [?]: 83 [0], given: 39

Re: GMAT Set - Q8 [#permalink] New post 17 Oct 2008, 15:04
pawan203 wrote:
Q8:
When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7,
the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when
y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of
x - y?

A. 12
B. 15
C. 20
D. 28
E. 35


x = 5a+3 , 7b+4

7b+4 = 5a+3 ie: 5a = 7b+1 ie b can be2 or 7 or 12..etc thus x can = (18or 53 or 88..etc)

y can be the same too such that x>y

53-18 = 35 , 88 - 53 = 35..etc

E
Director
Director
avatar
Joined: 23 May 2008
Posts: 840
Followers: 3

Kudos [?]: 31 [0], given: 0

Re: GMAT Set - Q8 [#permalink] New post 17 Oct 2008, 15:07
I got E

5n+3=x
7m+4=x

5n+3=y
7m+4=y

for x
5n+3=7m+4
5n=7m+1
5*10 = 7*7+1 (find numbers that fit)
x=50

for y
5n+3=7m+4
5n=7m+1
5*3=7*2+1
y=15

x-y=50-15=35, 35 is a factor of 35
Current Student
avatar
Joined: 28 Dec 2004
Posts: 3403
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 13

Kudos [?]: 164 [0], given: 2

Re: GMAT Set - Q8 [#permalink] New post 17 Oct 2008, 17:57
you have to realize that the smalled possible values for X=53 and y=18..the difference between is 35 and thus the largest factor possible here is 35..
1 KUDOS received
SVP
SVP
avatar
Joined: 17 Jun 2008
Posts: 1578
Followers: 12

Kudos [?]: 186 [1] , given: 0

Re: GMAT Set - Q8 [#permalink] New post 07 Nov 2008, 03:59
1
This post received
KUDOS
x = 5a + 3 = 7b + 4
y = 5c + 3 = 7d + 4
x-y = 5(a-c) = 7(b-d)

Since, 5 and 7 are prime number, hence 5*7 must be a factor of (x-y).
Manager
Manager
avatar
Affiliations: CFA Level 2 Candidate
Joined: 29 Jun 2009
Posts: 223
Schools: RD 2: Darden Class of 2012
Followers: 3

Kudos [?]: 60 [0], given: 2

Re: PS: When a number x is divided by 5 it leaves a reminder of [#permalink] New post 27 Aug 2009, 06:26
I am actually excited to see if there is an equation for this one.

I just used deduction.

If a number divided by 5 yields a remainder of 3. The last digit of the number Must be 3 or 8.

Since we know the remainder when divided by 7 is 4 I subtracted 4 from both 3 and 8

Therefore the last digit would be 9 (not -1 since we are dealing with unit digits) and 4.

Knowing the 7 multiplication table I took the known variables 49 and 14. Add back the 4 and we get two variables that meet the required premise

53 and 18

The difference between the two is 35.
2 KUDOS received
Manager
Manager
avatar
Joined: 10 Aug 2009
Posts: 130
Followers: 3

Kudos [?]: 55 [2] , given: 10

Re: PS: When a number x is divided by 5 it leaves a reminder of [#permalink] New post 27 Aug 2009, 06:55
2
This post received
KUDOS
The difference must be the multiple of 35, which is LCM of 5 and 7.
1) In order for x and y to leave the same remainder when divided by 5, the gap between two numbers should be a multiple of 5.
2)In order for x and y to leave the same remainder when divided by 7, the gap between two numbers should be a multiple of 7.
But x and y leave the same remainders when divided by both 5 and 7...so the gap between x and y should be a multiple of 5 AND a multiple of 7 or simply it should be a multiple of 35, which is LCM (5,7).

The only number that is a multiple of 35 is E, hence E is an answer.
2 KUDOS received
Manager
Manager
avatar
Joined: 25 Aug 2009
Posts: 177
Followers: 1

Kudos [?]: 61 [2] , given: 12

Re: PS: When a number x is divided by 5 it leaves a reminder of [#permalink] New post 27 Aug 2009, 08:39
2
This post received
KUDOS
Lets find out some numbers which leaves a reminder of 3 when divided by 5.

3,8,13,18,23,28,33,38,43,48,53,58,63,68,73,78,83,88

out of these numbers,

numbers which leaves a reminder of 4 when divided by 7 are

18,53,88....


as x is greater than y..

hence, if x = 18 , then y = 53
and if x = 53 , then y = 88 or if x = 18 , then y = 88

in all cases..

x-y is divisible by 35..

hence, answer is E..

Acc to me,in these kind of questions, plugging numbers is the best approach.
1 KUDOS received
Manager
Manager
avatar
Joined: 10 Aug 2009
Posts: 130
Followers: 3

Kudos [?]: 55 [1] , given: 10

Re: PS: When a number x is divided by 5 it leaves a reminder of [#permalink] New post 27 Aug 2009, 08:51
1
This post received
KUDOS
gmate2010 wrote:
Lets find out some numbers which leaves a reminder of 3 when divided by 5.

3,8,13,18,23,28,33,38,43,48,53,58,63,68,73,78,83,88

out of these numbers,

numbers which leaves a reminder of 4 when divided by 7 are

18,53,88....


as x is greater than y..

hence, if x = 18 , then y = 53
and if x = 53 , then y = 88 or if x = 18 , then y = 88

in all cases..

x-y is divisible by 35..

hence, answer is E..

Acc to me,in these kind of questions, plugging numbers is the best approach.


If you realize that the difference between the numbers is a multiple of 35, it takes about 30 sec to solve this one...plugging numbers you lose your time....but of course, people have different ways of solving...whatever works better for you
GMAT Instructor
avatar
Joined: 24 Jun 2008
Posts: 978
Location: Toronto
Followers: 261

Kudos [?]: 710 [0], given: 3

Re: NS Factor Combo!! [#permalink] New post 06 Sep 2011, 19:08
Here we are dealing with two numbers which give the same remainder by 5 and by 7. It's useful to know that if you were to list all such numbers, you would get an equally spaced list, where the numbers are separated by the LCM of 5 and 7, so by 35. So x-y must be divisible by 35 here.

Of course, you could come up with sample numbers if you weren't familiar with the underlying theory. We need two numbers which give a remainder of 3 when divided by 5, and a remainder of 4 when divided by 7. We can start by listing small numbers which give a remainder of 3 when divided by 5. This list is equally spaced, by 5, so it's straightforward to generate a long list quickly:

3, 8, 13, 18, 23, 28, 33, 38, 43, 48, 53, 58, 63, 68, ...

Now if you scan this list looking for numbers which give a remainder of 4 when divided by 7, you'll see that 18 and 53 both work. So it might be that x=53 and y=18, and their difference is 35, from which we also get answer E.
_________________

Nov 2011: After years of development, I am now making my advanced Quant books and high-level problem sets available for sale. Contact me at ianstewartgmat at gmail.com for details.

Private GMAT Tutor based in Toronto

Director
Director
User avatar
Status: GMAT Learner
Joined: 14 Jul 2010
Posts: 651
Followers: 34

Kudos [?]: 254 [0], given: 32

Re: When positive integer x is divided by 5, the remainder is 3; [#permalink] New post 13 Jan 2012, 08:32
Trial and error method is lengthy than the equation method provided by bigtreezl.
_________________

I am student of everyone-baten
Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23400
Followers: 3611

Kudos [?]: 28872 [3] , given: 2859

Re: When positive integer x is divided by 5, the remainder is 3; [#permalink] New post 13 Jan 2012, 09:31
3
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Baten80 wrote:
Trial and error method is lengthy than the equation method provided by bigtreezl.


The way to derive general formula is described in the solution below:

When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y?
(A) 12
(B) 15
(C) 20
(D) 28
(E) 35

When the positive integer x is divided by 5 and 7, the remainder is 3 and 4, respectively: x=5q+3 (x could be 3, 8, 13, 18, 23, ...) and x=7p+4 (x could be 4, 11, 18, 25, ...).

There is a way to derive general formula based on above two statements:

Divisor will be the least common multiple of above two divisors 5 and 7, hence 35.

Remainder will be the first common integer in above two patterns, hence 18 --> so, to satisfy both this conditions x must be of a type x=35m+18 (18, 53, 88, ...);

The same for y (as the same info is given about y): y=35n+18;

x-y=(35m+18)-(35n+18)=35(m-n) --> thus x-y must be a multiple of 35.

Answer: E.

More about this concept:
manhattan-remainder-problem-93752.html?hilit=derive#p721341
good-problem-90442.html?hilit=derive#p722552

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Status: K... M. G...
Joined: 22 Oct 2012
Posts: 51
Concentration: General Management, Leadership
GMAT Date: 08-27-2013
GPA: 3.8
Followers: 0

Kudos [?]: 6 [0], given: 118

Re: When positive integer x is divided by 5, the remainder is 3; [#permalink] New post 02 Nov 2012, 23:47
Bunuel wrote:
Baten80 wrote:
Trial and error method is lengthy than the equation method provided by bigtreezl.


The way to derive general formula is described in the solution below:

When positive integer x is divided by 5, the remainder is 3; and when x is divided by 7, the remainder is 4. When positive integer y is divided by 5, the remainder is 3; and when y is divided by 7, the remainder is 4. If x > y, which of the following must be a factor of x - y?
(A) 12
(B) 15
(C) 20
(D) 28
(E) 35

When the positive integer x is divided by 5 and 7, the remainder is 3 and 4, respectively: x=5q+3 (x could be 3, 8, 13, 18, 23, ...) and [m]x=7p+4[/m] (x could be 4, 11, 18, 25, ...).

There is a way to derive general formula based on above two statements:

Divisor will be the least common multiple of above two divisors 5 and 7, hence 35.

Remainder will be the first common integer in above two patterns, hence 18 --> so, to satisfy both this conditions x must be of a type x=35m+18 (18, 53, 88, ...);

The same for y (as the same info is given about y): y=35n+18;

x-y=(35m+18)-(35n+18)=35(m-n) --> thus x-y must be a multiple of 35.

Answer: E.

More about this concept:
manhattan-remainder-problem-93752.html?hilit=derive#p721341
good-problem-90442.html?hilit=derive#p722552

Hope it helps.


In the above colored statement, x could be 18 but how can assume that remainder will be the first common integer.. please explain this formula & also with example
CEO
CEO
User avatar
Joined: 09 Sep 2013
Posts: 2838
Followers: 207

Kudos [?]: 43 [0], given: 0

Premium Member
Re: When positive integer x is divided by 5, the remainder is 3; [#permalink] New post 03 Mar 2014, 10:58
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

Re: When positive integer x is divided by 5, the remainder is 3;   [#permalink] 03 Mar 2014, 10:58
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic When positive integer x is divided by 5, the remainder is 2. Critique 4 15 Jun 2014, 03:20
11 Experts publish their posts in the topic When positive integer x is divided by 5, the remainder is 3 shopaholic 7 02 Mar 2012, 09:39
1 when a positive integer x is divided by 3, the remainder is vd 19 12 Jun 2008, 23:00
When a positive integer n is divided by 3, the remainder is asaf 3 14 Jul 2007, 13:07
3 What is the remainder when positive integer x is divided by kjmath 2 15 Jan 2007, 14:36
Display posts from previous: Sort by

When positive integer x is divided by 5, the remainder is 3;

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.