GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 31 May 2020, 02:51

### 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

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

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

### Hide Tags

Manager
Joined: 29 Sep 2008
Posts: 82
When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

08 Nov 2010, 08:59
2
16
00:00

Difficulty:

15% (low)

Question Stats:

80% (02:09) correct 20% (02:40) wrong based on 254 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
##### Most Helpful Expert Reply
Math Expert
Joined: 02 Sep 2009
Posts: 64249
Re: number prop  [#permalink]

### Show Tags

08 Nov 2010, 09:17
2
12
mrinal2100 wrote:
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

i used the numbers and reached at two numbers 18 and 53 and 53-18 gives 35.is there any better way to solve this question

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.

Answer: C.

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

Hope it helps.
_________________
##### General Discussion
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10477
Location: Pune, India
Re: number prop  [#permalink]

### Show Tags

08 Nov 2010, 10:07
1
2
mrinal2100 wrote:
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

i used the numbers and reached at two numbers 18 and 53 and 53-18 gives 35.is there any better way to solve this question

If I have a number n which when divided by 5 gives a remainder 3 and when divided by 7 gives a remainder 4, the number is of the form:
n = 5a + 3
n = 7b + 4
I will need to check for the smallest such number.
I put b = 1. n = 11. Is it of the form 5a + 3? No.
Put b = 2. n = 18. Is it of the form 5a + 3? Yes.

When 18 is divided by 5, it gives a remainder of 3. When it is divided by 7, it gives a remainder if 4.

Next such number will be 35 + 18 because 35 will be divisible by 5 as well as 7 and whatever is the remainder from 18, will still be the remainder
Next will be 35*2 + 18
and so on...
Difference between such numbers will be a multiple of 35 so your answer is 35.
Note: Actually, because of this reasoning, you just had to take the LCM. You didn't even need to find the first such number!

I have discussed this topic a little more in detail here: http://gmatclub.com/forum/good-problem-90442-20.html#p814507
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Director
Joined: 17 Dec 2012
Posts: 619
Location: India
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

06 Oct 2013, 19:06
2
mrinal2100 wrote:
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

The easiest way to approach these problems is by taking an example

1. The first choice is 18. Take it as B
2. The next choice is 53. Take it as A
3. A-B=35

c is the only choice that is correct.
_________________
Srinivasan Vaidyaraman
Magical Logicians
https://magical-logicians-sat-gmat-gre.business.site

Holistic and Holy Approach
VP
Joined: 07 Dec 2014
Posts: 1252
When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

Updated on: 26 Jan 2018, 10:44
mrinal2100 wrote:
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

if A and B, when divided by the same divisors, leave the same remainders,
then the difference between them will always be a multiple of the product of those divisors
5*7=35
C

Originally posted by gracie on 05 Dec 2017, 16:38.
Last edited by gracie on 26 Jan 2018, 10:44, edited 1 time in total.
Manager
Joined: 06 Sep 2016
Posts: 122
Location: Italy
Schools: EDHEC (A\$)
GMAT 1: 650 Q43 V37
GPA: 3.2
WE: General Management (Human Resources)
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

26 Jan 2018, 08:45
SravnaTestPrep wrote:
mrinal2100 wrote:
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

The easiest way to approach these problems is by taking an example

1. The first choice is 18. Take it as B
2. The next choice is 53. Take it as A
3. A-B=35

c is the only choice that is correct.

I chose the same approach but only a further tip to speed up:
When you found the value of A you can simply try to add every value from the answer choices: if the number obtained satisfy the initial divisibility conditions then you have found the correct answer
Intern
Joined: 28 Aug 2016
Posts: 22
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

01 Oct 2018, 00:07
VeritasKarishma

Mam, I did it this way, is this a correct way?

A=5Q+3 & A=7s+4
so equating we get

5Q=7s+1

Which is for both A&B so the numbers derived are 18 and 53 solving for the above, hence the factor of 53-18= 35

C
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10477
Location: Pune, India
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

02 Oct 2018, 03:55
BigUD94 wrote:
VeritasKarishma

Mam, I did it this way, is this a correct way?

A=5Q+3 & A=7s+4
so equating we get

5Q=7s+1

Which is for both A&B so the numbers derived are 18 and 53 solving for the above, hence the factor of 53-18= 35

C

It seems that basically you have found 2 numbers which satisfy both conditions and taken their difference (which would need to be a multiple of at least one of the choices). It is correct. I hope you understand why it is correct. It you are not sure, check out the link I have given above in my post.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Non-Human User
Joined: 09 Sep 2013
Posts: 15024
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

29 Feb 2020, 05:21
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: When the positive integer A is divided by 5 and 7, the   [#permalink] 29 Feb 2020, 05:21

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

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

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