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

 It is currently 22 Sep 2019, 17:56 ### 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. ### Request Expert Reply # 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: 87
When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

1
15 00:00

Difficulty:   25% (medium)

Question Stats: 80% (02:10) correct 20% (02:44) wrong based on 311 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
Math Expert V
Joined: 02 Sep 2009
Posts: 58098
Re: number prop  [#permalink]

### Show Tags

2
11
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.

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

Hope it helps.
_________________
##### General Discussion
Veritas Prep GMAT Instructor D
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: number prop  [#permalink]

### Show Tags

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  S
Joined: 17 Dec 2012
Posts: 628
Location: India
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

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
Sravna Test Prep
http://www.sravnatestprep.com

Holistic and Systematic Approach
VP  P
Joined: 07 Dec 2014
Posts: 1230
When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

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, 17:38.
Last edited by gracie on 26 Jan 2018, 11:44, edited 1 time in total.
Current Student B
Joined: 06 Sep 2016
Posts: 126
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

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  B
Joined: 28 Aug 2016
Posts: 23
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

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 D
Joined: 16 Oct 2010
Posts: 9644
Location: Pune, India
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

### Show Tags

BigUD94 wrote:

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 > Re: When the positive integer A is divided by 5 and 7, the   [#permalink] 02 Oct 2018, 04:55
Display posts from previous: Sort by

# 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  