Math Expert Joined: 02 Sep 2009 Posts: 87818
When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] Updated on: 08 Aug 2022, 02:34
00:00
Difficulty: 15% (low)
Question Stats: 82% (02:00) correct 18% (02:21) wrong based on 2918 sessionsHide Show timer StatisticsWhen positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35 ?(A) 3(B) 4(C) 12(D) 32 (E) 35
Originally posted by Bunuel on 03 Jan 2010, 15:00.
Math Expert Joined: 02 Sep 2009 Posts: 87818
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 30 Jan 2014, 00:51
SOLUTION When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35 ? (A) 3(B) 4(C) 12(D) 32(E) 35Positive integer n is divided by 5, the remainder is 1 --> \(n=5q+1\), where \(q\) is the quotient --> 1, 6, 11, 16, 21, 26, 31, ... Positive integer n is divided by 7, the remainder is 3 --> \(n=7p+3\), where \(p\) is the quotient --> 3, 10, 17, 24, 31, .... There is a way to derive general formula for \(n\) (of a type \(n=mx+r\), where \(x\) is divisor and \(r\) is a remainder) based on above two statements: Divisor \(x\) would be the least common multiple of above two divisors 5 and 7, hence \(x=35\).Remainder \(r\) would be the first common integer in above two patterns, hence \(r=31\).Therefore general formula based on both statements is \(n=35m+31\). Thus the smallest positive integer k such that k+n is a multiple of 35 is 4 --> \(n+4=35k+31+4=35(k+1)\).Answer: B.More about deriving general formula for such problems at: https://gmatclub.com/forum/manhattan-rem ... ml#p721341 _________________
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] Updated on: 24 Aug 2020, 10:06
Bunuel wrote: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35 ?(A) 3(B) 4(C) 12(D) 32(E) 35 There's a nice rule that says, If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . . For example, if k divided by 6 leaves a remainder of 2, then the possible values of k are: 2, 2+6, 2+(2)(6), 2+(3)(6), 2+(4)(6), . . . etc.When n is divided by 5, the remainder is 1. So, possible values of n are 1, 6, 11, 16, 21, 26, 31, 36, 41, 46, 51, 56, 61, 66, 71, 76, etc. When n is divided by 7, the remainder is 3. So, possible values of n are 3, 10, 17, 24, 31, 38, 45, 52, 59, 66, 73, etc.So, we can see that n could equal 31, or 66, or an infinite number of other values. Important: Since the Least Common Multiple of 7 and 5 is 35, we can conclude that if we list the possible values of n, each value will be 35 greater than the last value. So, n could equal 31, 66, 101, 136, and so on. Check the answer choices....Answer choice A: If we add 3 to any of these possible n-values, the sum is NOT a multiple of 35. ELIMINATE AAnswer choice B: if we take ANY of these possible n-values, and add 4, the sum will be a multiple of 35. So, the smallest value of k is [spoiler]4[/spoiler] such that k+n is a multiple of 35.Answer = BRELATED VIDEO _________________
Brent Hanneson – Creator of gmatprepnow.comI’ve spent the last 20 years helping students overcome their difficulties with GMAT math, and the biggest thing I’ve learned is… Many students fail to maximize their quant score NOT because they lack the skills to solve certain questions but because they don’t understand what the GMAT is truly testing - Learn more
Tutor Joined: 17 Jul 2019 Posts: 1173 Location: Canada Schools: NYU Stern (WA) GMAT 1: 780 Q51 V45 GMAT 2: 780 Q50 V47 GMAT 3: 770 Q50 V45
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 25 Jan 2021, 09:51
Intern Joined: 20 Dec 2009 Posts: 9
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 05 Jan 2010, 04:31
kp1811 wrote: Pedros wrote: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+ n is a multiple of 35.A) 3B) 4C) 12D) 32E) 35Dont want to try numbers in any remainder problem , please hlep. OA here n is divided by 5 and 7 and remainders are 1 and 3. There is a rule wherein if the difference b/w and remainder is same then the number of obtained from LCM of 2 (here 2) numbers and the constant difference.Here constant difference is 5-1 = 4 and 7-3 = 4 so the required number if of the form A(LCM of 5 and 7) - constant difference = 35A - 4 So to obtain a multiple of 35 we would need to add 4 to 35A - 4.Hence B - 4 The rule is good to solve such problems but sometime we may just solve GMAT problems simply by observation. In this case we see that number n leaves a remainder 1 from 5 so if we add 4 to n, then the number will be divisible by 5.Similarly, the number n leaves remainder of 3 from 7, again adding 4 to n makes it divisible by 7. So in both the cases adding 4 makes the number n divisible by both 5 and 7 and hence it should also be divisible by LCM of 5,7 i.e.35. So 4 is the answer.It is better to remember the rule but just in case you don't then simply observe.Thanks!
Manager Joined: 30 Aug 2009 Posts: 153 Location: India Concentration: General Management
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 03 Jan 2010, 19:17
Pedros wrote: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k+ n is a multiple of 35.A) 3B) 4C) 12D) 32E) 35Dont want to try numbers in any remainder problem , please hlep. OA here n is divided by 5 and 7 and remainders are 1 and 3. There is a rule wherein if the difference b/w and remainder is same then the number of obtained from LCM of 2 (here 2) numbers and the constant difference.Here constant difference is 5-1 = 4 and 7-3 = 4 so the required number if of the form A(LCM of 5 and 7) - constant difference = 35A - 4 So to obtain a multiple of 35 we would need to add 4 to 35A - 4.Hence B - 4
GMAT Expert Joined: 16 Oct 2010 Posts: 13346 Location: Pune, India
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 07 Nov 2010, 19:24
First, let us say I have a number n which is divisible by 5 and by 7. We all agree that it will be divisible by 35, the LCM of 5 and 7.Now, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 1, we can say the number is of the formn = 5a + 1 e.g. 5 + 1, 10 + 1, 15 + 1, 20 + 1, 25 + 1, 30 + 1, 35 + 1 etcand n = 7b + 1 e.g. 7 + 1, 14 + 1, 21 + 1, 28 + 1, 35 + 1 etcSo when it is divided by the LCM, 35, it will give 1 as remainder (as is apparent above)Next, if I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 3, we can say the number is of the formn = 5a + 1andn = 7b + 3Now, the only thing you should try to understand here is that when n is divided by 5 and if I say the remainder is 1, it is the same as saying the remainder is -4. e.g. When 6 is divided by 5, remainder is 1 because it is 1 more than a multiple of 5. I can also say it is 4 less than the next multiple of 5, can't I? 6 is one more than 5, but 4 less than 10. Therefore, we can say n = 5x - 4 and n = 7y - 4 (A remainder of 3 when divided by 7 is the same as getting a remainder of -4)Now this question is exactly like the question above. So when you divide n by 35, remainder will be -4 i.e. n will be 4 less than a multiple of 35. So you must add 4 to n to make it a multiple of 35A trickier version is: If I have a number n which when divided by 5 gives a remainder 1 and when divided by 7 gives a remainder 5, what is the remainder when n is divided by 35?n = 5a + 1 = 5x - 4n = 7b + 5 = 7y -2Nothing common! Now, I will need to check for the smallest such number.I put b = 1. n = 12. Is it of the form 5a + 1? No.Put b = 2. n = 19. Is it of the form 5a + 1? No.Put b = 3. n = 26. Is it of the form 5a + 1? Yes.When 26 is divided by 5, it gives a remainder of 1. When it is divided by 7, it gives a remainder if 5.Next such number will be 35 + 26. Next will be 35*2 + 26and so on...The remainder when n is divided by 35 will be 26 (or we can say it will be -9). If we want to find the number that must be added to n to make it divisible by 35, that number will be 9. _________________
KarishmaOwner of Angles and Arguments Check out my Blog Posts here: Blog For Individual GMAT Study Modules, check Study Modules For Private Tutoring, check Private Tutoring
Director Joined: 25 Apr 2012 Posts: 565 Location: India GPA: 3.21 WE:Business Development (Other)
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 30 Jan 2014, 02:07
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35 ?(A) 3(B) 4(C) 12(D) 32 (E) 35 Sol: Given n=5a+1 where a is any non-negative integer and also n=7b+3 where b is any non-negative integer.....so n is of the formPossible values of n in case 1 : 1,6,11,16,21,26,31.... Possible value of n in case 2 : 3,10,17, 24,31...So, n=35C+ 31....Now for K+ n to be multiple of 35 K needs to be 4 so that k+n = 35C+31+4 or 35(c+1)Ans B.650 level is okay _________________
“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”
Manager Joined: 04 Oct 2013 Posts: 137 Location: India GMAT Date: 05-23-2015 GPA: 3.45
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] Updated on: 29 Jan 2015, 21:26
When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35 ?(A) 3(B) 4(C) 12(D) 32 (E) 35 Method 1 As the lowest common value is 4, the answer is (B).
Originally posted by arunspanda on 31 Jan 2014, 09:06.
SVP Joined: 27 Dec 2012 Status:The Best Or Nothing Posts: 1587 Location: India Concentration: General Management, Technology WE:Information Technology (Computer Software)
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 02 Oct 2014, 02:10 Picked up 7 & added 3 = 1010 gives a remainder 3 when divided by 7 Wrote down similar numbers. We are looking for numbers which would either end by 1 or 6 (so they would provide a remainder 1 when divided by 5) 10172431 ........ stop 31 is the number when divided by 5, provides remainder 1 (Its already tested that it provides remainder 3 when divided by 7)First available multiple of 35 is 35, which is just 4 away from 31Answer = 4
Current Student Joined: 10 Mar 2013 Posts: 371 Location: Germany Concentration: Finance, Entrepreneurship Schools: WHU MBA"20 (A$) GPA: 3.7 WE:Marketing (Telecommunications)
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 26 Aug 2015, 13:41 Hi all, actually we don't need pluging all those values for x,y... n=5x+1 and n=7y+3 --> n+k=> (5x+1+k)/35 so 1+k must be a multiple of 5 if we want this expression to yield an integer so k=4 Use same logic here (7y+3+k)/35 -> 3+k must be a multiple of 7, so k=4
Target Test Prep Representative Joined: 04 Mar 2011 Status:Head GMAT Instructor Affiliations: Target Test Prep Posts: 2812
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 03 Aug 2016, 08:45
Quote: When positive integer n is divided by 5, the remainder is 1. When n is divided by 7, the remainder is 3. What is the smallest positive integer k such that k + n is a multiple of 35 ?(A) 3(B) 4(C) 12(D) 32 (E) 35 We can find the value of n first by just strategically find values that when divided by 5 have a reminder of 1. For example, since the remainder is 1 when n is divided by 5, n will be a [(multiple of 5) + 1] and thus must be one of the following numbers: 1, 6, 11, 16, 21, 26, 31, … Now we have to find out which of these numbers when divided by 7, have a remainder of 3.1/7 = 0 remainder 1 6/7 = 0 remainder 6 11/7 = 0 remainder 6 16/7 = 2 remainder 2 21/7 = 3 remainder 0 26/7 = 3 remainder 531/7 = 4 remainder 3 We can see that 31 is the smallest value of n that satisfies the requirement. So we must determine the value of k such that k + n is a multiple of 35. Obviously, since 4 + 31 = 35 and 35 is a multiple of 35, then the smallest positive integer value of k is 4. Answer: B _________________
CrackVerbal Representative Joined: 03 Oct 2013 Affiliations: CrackVerbal Posts: 4987 Location: India
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 21 Aug 2021, 21:23
When a number N is divided by X , the remainder is a and when N is divided by Y , the remainder is b.
Intern Joined: 23 Aug 2022 Posts: 13
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 26 Aug 2022, 05:48 Is this is sub 600 level question?
GMAT Tutor Joined: 05 Apr 2011 Status:Tutor - BrushMyQuant Posts: 1487 Location: India Concentration: Finance, Marketing Schools: XLRI (A) GPA: 3 WE:Information Technology (Computer Software)
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 19 Oct 2022, 10:40
When positive integer n is divided by 5, the remainder is 1 Theory: Dividend = Divisor*Quotient + Remainder n -> Dividend5 -> Divisora -> Quotient (Assume)1 -> Remainders=> n = 5*a + 1 = 5a + 1When n is divided by 7, the remainder is 3 Let quotient be b=> n = 7b + 3n = 7b + 3 = 5a + 1=> 5a = 7b + 2=> a = \(\frac{7b + 2}{5}\)Now, only those values of "b" which will give "a" also as an integer will give us the common values of n which satisfy both n = 7b + 3 = 5a + 1 the conditionsb=4 => a = \(\frac{7*4 + 2}{5}\) = 6 => Integer=> n = 7*4 + 3 = 28 + 3 = 31What is the smallest positive integer k such that k + n is a multiple of 35 31 + 4 = 35 => k = 4So, Answer will be B Hope it helps!Watch the following video to learn the Basics of Remainders _________________
Re: When positive integer n is divided by 5, the remainder is 1. When n is [#permalink] 19 Oct 2022, 10:40 |