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• $450 Tuition Credit & Official CAT Packs FREE February 15, 2019 February 15, 2019 10:00 PM EST 11:00 PM PST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) 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: 92 When the positive integer A is divided by 5 and 7, the [#permalink] Show Tags 08 Nov 2010, 08:59 1 15 00:00 Difficulty: 25% (medium) Question Stats: 80% (02:08) correct 20% (02:42) wrong based on 298 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: 52905 Re: number prop [#permalink] Show Tags 08 Nov 2010, 09:17 2 10 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: 8880 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: 624 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 Sravna Holistic Solutions http://www.sravnatestprep.com Holistic and Systematic Approach VP Joined: 07 Dec 2014 Posts: 1157 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. Current Student Joined: 06 Sep 2016 Posts: 132 Location: Italy Schools: EDHEC (A$)
GMAT 1: 650 Q43 V37
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Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

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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: 23
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

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01 Oct 2018, 00:07

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: 8880
Location: Pune, India
Re: When the positive integer A is divided by 5 and 7, the  [#permalink]

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02 Oct 2018, 03:55
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

Re: When the positive integer A is divided by 5 and 7, the   [#permalink] 02 Oct 2018, 03:55
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