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

 It is currently 27 Sep 2016, 12:59

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# When the positive integer A is divided by 5 and 7

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 13 May 2011
Posts: 317
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Followers: 21

Kudos [?]: 238 [1] , given: 11

When the positive integer A is divided by 5 and 7 [#permalink]

### Show Tags

06 Jan 2012, 12:09
1
KUDOS
9
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

82% (02:11) correct 18% (01:51) wrong based on 279 sessions

### HideShow timer Statistics

When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of A-B?

(A) 12
(B) 24
(C) 35
(D) 16
(E) 30
[Reveal] Spoiler: OA

Last edited by Bunuel on 06 Jun 2013, 06:22, edited 3 times in total.
Edited the question
Math Expert
Joined: 02 Sep 2009
Posts: 34871
Followers: 6491

Kudos [?]: 82839 [0], given: 10120

### Show Tags

13 Jan 2012, 06:55
Expert's post
5
This post was
BOOKMARKED
When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of A-B?

(A) 12
(B) 24
(C) 35
(D) 16
(E) 30

When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively: $$A=5q+3$$ (A could be 3, 8, 13, 18, 23, ...) and $$A=7p+4$$ (A 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 A must be of a type $$A=35m+18$$ (18, 53, 88, ...);

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

$$A-B=(35m+18)-(35n+18)=35(m-n)$$ --> thus A-B must be a multiple of 35.

manhattan-remainder-problem-93752.html?hilit=derive#p721341
good-problem-90442.html?hilit=derive#p722552

Hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11704
Followers: 527

Kudos [?]: 144 [0], given: 0

Re: When the positive integer A is divided by 5 and 7 [#permalink]

### Show Tags

04 Aug 2014, 08:01
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.
_________________
Manager
Joined: 11 Jun 2014
Posts: 57
Concentration: Technology, Marketing
GMAT 1: 770 Q50 V45
WE: Information Technology (Consulting)
Followers: 4

Kudos [?]: 32 [1] , given: 3

Re: When the positive integer A is divided by 5 and 7 [#permalink]

### Show Tags

04 Aug 2014, 21:27
1
KUDOS
Although there are methods.. this particular problem does not require any methods..

A divided by 5,7 gives 3 and 4
B divided by 5,7 gives 3 and 4.

means A and B are equidistant from the multiples of 5,7. the LCM of 5 and 7 is 35, so numbers like A & B repeat after every 35 numbers. so 35 is the answer.
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 39

Kudos [?]: 1711 [0], given: 193

Re: When the positive integer A is divided by 5 and 7 [#permalink]

### Show Tags

06 Aug 2014, 03:05
1
This post was
BOOKMARKED
With the remainders remaining same for both the required integers, it means there difference should be divisible by both 5 & 7

Out of all the five given options, only 35 stands out

_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11704
Followers: 527

Kudos [?]: 144 [0], given: 0

Re: When the positive integer A is divided by 5 and 7 [#permalink]

### Show Tags

13 Dec 2015, 21:39
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.
_________________
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 1792
GPA: 3.82
Followers: 129

Kudos [?]: 1062 [0], given: 0

Re: When the positive integer A is divided by 5 and 7 [#permalink]

### Show Tags

14 Dec 2015, 00:40
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

When the positive integer A is divided by 5 and 7, the remainder is 3 and 4, respectively. When the positive integer B is divided by 5 and 7, the remainder is 3 and 4, respectively. Which of the following is a factor of A-B?

(A) 12
(B) 24
(C) 35
(D) 16
(E) 30

By the conditions we may put A=5K+3 = 7L+4, B=5M+3 = 7N+4. So we have A-B= 5K+3-5M-3 = 5*(K-M)= 7L+4 - 7N-4=7*(L-N).

We may conclude that A-B is divisible by 5 and 7. That means 35 is a factor of A-B.

_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
Unlimited Access to over 120 free video lessons - try it yourself

Re: When the positive integer A is divided by 5 and 7   [#permalink] 14 Dec 2015, 00:40
Similar topics Replies Last post
Similar
Topics:
4 When both positive integers a and b are divided by 7 10 24 Apr 2016, 07:33
3 When a positive integer A is divided by 5 and 7, the remainders obtain 3 10 Mar 2016, 04:29
37 If the remainder is 7 when positive integer n is divided by 11 06 Mar 2012, 23:28
13 When positive integer n is divided by 5, the remainder is 1. When n is 8 09 Apr 2011, 16:08
18 When the positive integer A is divided by 5 and 7, the 6 08 Nov 2010, 09:59
Display posts from previous: Sort by