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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Problem Solving Question: 68 Category:Arithmetic Properties of numbers Page: 70 Difficulty: 650

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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

Positive 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 --> \(n+4=35k+31+4=35(k+1)\).

Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

30 Jan 2014, 02:07

1

This post received KUDOS

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 form

Possible 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.”

When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

31 Jan 2014, 09:06

3

This post received KUDOS

2

This post was BOOKMARKED

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

n is divided by 5, the remainder is 1 ---> \(n= 5x + 1\) or, n + k = 5x + (1 + k) So, n + k is divisible by 5, when (1+ k) is a multiple of 5. Or, Possible values of k are 4, 9, 14,19, 24, 29, 33,.....

n is divided by 7, the remainder is 3 ----> \(n=7y + 3\) Or, n + k = 7y +(3 + k) So, n + k is divisible by 7, when (3+ k) is a multiple of 7. Or, Possible values of k are 4, 11, 18, 25, 32, 39,.....

As the lowest common value is 4, the answer is (B).

Last edited by arunspanda on 29 Jan 2015, 21:26, edited 1 time in total.

Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

31 Jan 2014, 19:34

is there any other way, than number plugging? What if instead of 5 and 7, the question is changed to some scary numbers like 263 and 911?
_________________

“Confidence comes not from always being right but from not fearing to be wrong.”

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

Positive 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 --> \(n+4=35k+31+4=35(k+1)\).

When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

24 Jun 2014, 01:27

n+k is a multiple of 35 then n+k = 35x => n = 35x - k. When positive integer n is divided by 5, the remainder is 1 => when integer k is divided by 5, the remainder is 4 => B

[or When n is divided by 7, the remainder is 3 => when integer is divided by 7, the remainder is 4 => B or C, but we do not need to check this case]

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

Problem Solving Question: 68 Category:Arithmetic Properties of numbers Page: 70 Difficulty: 650

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project: 1. Please provide your solutions to the questions; 2. Please vote for the best solutions by pressing Kudos button; 3. Please vote for the questions themselves by pressing Kudos button; 4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!

Sol:

n=5a+1 => Remainder is 1 or -4 n=7b+3 => Remainder is 3 or -4

i.e. if I add +4 to the number the number will be perfect multiple of 35

Smaller value for K, if (K + N) is a multiple of 35?

This value is 4, because 4 + 31 = 35, and 35 is a multiple of 35.

Correct Answer b)

claudio hurtado GMAT GRE SAT math classes part
_________________

claudio hurtado maturana Private lessons GMAT QUANT GRE QUANT SAT QUANT Classes group of 6 students GMAT QUANT GRE QUANT SAT QUANT Distance learning courses GMAT QUANT GRE QUANT SAT QUANT

Website http://www.gmatchile.cl Whatsapp +56999410328 Email clasesgmatchile@gmail.com Skype: clasesgmatchile@gmail.com Address Avenida Hernando de Aguirre 128 Of 904, Tobalaba Metro Station, Santiago Chile.

Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

12 Jan 2015, 11:15

Sorry, I forgot to mention the reasoning behind k+31> 35.

I thought that since k + n is a multiple of 35, it cannot be smaller. It should actually have a larger or equal sign there. So, this is why it is k+31> 35.

I always do that to remember while solving the problem that a multiple is larger (in comparison to a factor which is smaller).

Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

24 Mar 2015, 12:24

The fastest way here is to realize that 35 is a factor of both 5 and 7. So you need to add a number to the remainder of both situations so that each number a factor of 5 and 7. By adding 4 to 1 it becomes a factor of 5, and by adding 4 to 3 it becomes a factor of 7. So B must be true

Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

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
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

01 Dec 2015, 13:44

1

This post received KUDOS

N+4 is multiple of both 5 and 7 so N+4 must be an LCM of 5 and 7 i.e. 35. So the smallest value needed to make it multiple of 35 is 4
_________________

Please contact me for super inexpensive quality private tutoring

My journey V46 and 750 -> http://gmatclub.com/forum/my-journey-to-46-on-verbal-750overall-171722.html#p1367876

When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

03 Aug 2016, 08:45

1

This post received KUDOS

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

6/7 = 1 remainder 4

16/7 = 2 remainder 2

21/7 = 3 remainder 0

26/7 = 3 remainder 5

31/7 = 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
_________________

Jeffrey Miller Jeffrey Miller Head of GMAT Instruction

gmatclubot

When positive integer n is divided by 5, the remainder is 1.
[#permalink]
03 Aug 2016, 08:45

Happy New Year everyone! Before I get started on this post, and well, restarted on this blog in general, I wanted to mention something. For the past several months...

It’s quickly approaching two years since I last wrote anything on this blog. A lot has happened since then. When I last posted, I had just gotten back from...

Happy 2017! Here is another update, 7 months later. With this pace I might add only one more post before the end of the GSB! However, I promised that...