It is currently 19 Feb 2018, 00:04

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

When positive integer n is divided by 5, the remainder is 1.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Intern
Intern
avatar
B
Joined: 07 Jun 2015
Posts: 2
Re: When positive integer n is divided by 5, the remainder is 1. [#permalink]

Show Tags

New post 14 Jan 2018, 01:35
Bunuel wrote:
bingzhang wrote:
Bunuel wrote:
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) 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 --> \(n+4=35k+31+4=35(k+1)\).

Answer: B.


Hi Bunuel,

Would you please have a look at my solution? I've got the same answer yet a different path. Can you point it out what's wrong with my thought? Many thanks.

Question:
What is the smallest value of K, when N+K is the multiple of 35?

My solution process:
step 1. n+k=x(35), I was assuming that if x=1(because the hint is 'the smallest integer value'), then n+k=35, so k=35-n
step 2. how to get n? (the same process as you've stated above) n=31
step 3. k=35-n, and n=31, therefore k=4


Yes, the smallest value of n is 31, adding 4 gives a multiple of 35.


thank you! thank you, Bunuel. It's very nice of you.
Re: When positive integer n is divided by 5, the remainder is 1.   [#permalink] 14 Jan 2018, 01:35
Display posts from previous: Sort by

When positive integer n is divided by 5, the remainder is 1.

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.