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When the positive integer A is divided by 5 and 7, the
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08 Nov 2010, 08:59
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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 AB? (A) 12 (B) 24 (C) 35 (D) 16 (E) 30
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Re: number prop
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08 Nov 2010, 09:17
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 AB?
(A) 12 (B) 24 (C) 35 (D) 16 (E) 30
i used the numbers and reached at two numbers 18 and 53 and 5318 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): \(B=35n+18\); \(AB=(35m+18)(35n+18)=35(mn)\) > thus AB must be a multiple of 35. Answer: C. More about this concept: manhattanremainderproblem93752.html?hilit=derive#p721341goodproblem90442.html?hilit=derive#p722552Hope it helps.
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Re: number prop
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08 Nov 2010, 10:07
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 AB?
(A) 12 (B) 24 (C) 35 (D) 16 (E) 30
i used the numbers and reached at two numbers 18 and 53 and 5318 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/goodproblem9044220.html#p814507
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Re: When the positive integer A is divided by 5 and 7, the
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06 Oct 2013, 19:06
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 AB?
(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. AB=35 c is the only choice that is correct.
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When the positive integer A is divided by 5 and 7, the
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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 AB?
(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.



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Re: When the positive integer A is divided by 5 and 7, the
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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 AB?
(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. AB=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



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Re: When the positive integer A is divided by 5 and 7, the
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01 Oct 2018, 00:07
VeritasKarishmaMam, 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 5318= 35 C



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Re: When the positive integer A is divided by 5 and 7, the
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02 Oct 2018, 03:55
BigUD94 wrote: VeritasKarishmaMam, 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 5318= 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.
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Re: When the positive integer A is divided by 5 and 7, the
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