Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Aug 2710:00 AM EDT
-11:00 AM EDT
We’ve worked incredibly hard to build TTP into the best test prep experience possible, and it would mean a lot to us to win Newsweek’s 2026 Readers’ Choice Award for Best Test Prep. If TTP has helped you, we’d be incredibly grateful for your vote.
Sep 0410:00 AM PDT
-11:00 AM PDT
What does test anxiety really look like on the GMAT? For many test takers, it does not look like a panic attack. Instead, it shows up as brain fog, rereading, negative comparisons, mental noise....
Sep 0609:30 AM EDT
-12:30 PM EST
Top scores are possible when you enroll in a powerful EA course, taught live online + 6 months access to TTP OnDemand video courses included! Perfect class schedule and easy course access for working professionals. Class starts Sundays Sept. 6, 2026.- Sep 07
12:01 AM PDT
-11:59 PM PDT
On the 7th, GMAT Club Tests will be Free! Including all the Quizzes, Questions, and Tests. 12 AM - 11:59 PM PDT - Sep 09
07:00 AM PDT
-10:00 AM PDT
Meet AdComs and explore top Master’s programs - MiM, MiF, MSc, MSBA and more. - Application Fee Waivers - Free 1-Week of GMAT Club Tests: - Master's Application Toolkit - Grand Prize Giveaway 
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2108:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
25 May 2011, 11:18
Kudos
Bookmarks
1. Positive integer n leaves a remainder of 4 after division by 6 and a remainder of 3 after division by 5. If n is greater than 30, what is the remainder that n leaves after division by 30?
(A) 3
(B) 12
(C) 18
(D) 22
(E) 28
Solution:
Positive integer n leaves a remainder of 4 after division by 6 --> --> 4, 10, 16, 22, 28, ...
Positive integer n leaves a remainder of 3 after division by 5 --> --> 3, 8, 13, 18, 23, 28, ...
- we have 30 as lcm of 5 and 6 is 30 and we have 28 as the first common integer in the above patterns is 28.
Hence remainder when positive integer n is divided by 30 is 28.
Answer: E.
2. QR. 68. 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
Solution:
Positive integer n is divided by 5, the remainder is 1 --> , where is the quotient --> 1, 6, 11, 16, 21, 26, 31, ...
Positive integer n is divided by 7, the remainder is 3 --> , where is the quotient --> 3, 10, 17, 24, 31, ....
You can not use the same variable for quotients in both formulas, because quotient may not be the same upon division n by two different numbers.
For example 31/5, quotient q=6 but 31/7, quotient p=4.
Ans. B
What is the difference between the requirements of these two problems?
(A) 3
(B) 12
(C) 18
(D) 22
(E) 28
Solution:
Positive integer n leaves a remainder of 4 after division by 6 --> --> 4, 10, 16, 22, 28, ...
Positive integer n leaves a remainder of 3 after division by 5 --> --> 3, 8, 13, 18, 23, 28, ...
- we have 30 as lcm of 5 and 6 is 30 and we have 28 as the first common integer in the above patterns is 28.
Hence remainder when positive integer n is divided by 30 is 28.
Answer: E.
2. QR. 68. 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
Solution:
Positive integer n is divided by 5, the remainder is 1 --> , where is the quotient --> 1, 6, 11, 16, 21, 26, 31, ...
Positive integer n is divided by 7, the remainder is 3 --> , where is the quotient --> 3, 10, 17, 24, 31, ....
You can not use the same variable for quotients in both formulas, because quotient may not be the same upon division n by two different numbers.
For example 31/5, quotient q=6 but 31/7, quotient p=4.
Ans. B
What is the difference between the requirements of these two problems?
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
25 May 2011, 18:10
Kudos
Bookmarks
I am not sure I understand your question very well but I am assuming that what is troubling you is the quotient you get upon division. Well, quotient is not our worry in either of the questions. We only need to focus on the remainders.
Both the questions use the same concept. They just ask you for the answer in different formats.
Q1
Positive integer n leaves a remainder of 4 after division by 6 --> --> 4, 10, 16, 22, 28, ...
Positive integer n leaves a remainder of 3 after division by 5 --> --> 3, 8, 13, 18, 23, 28, ...
n satisfies both the conditions. The first such number is 28. So you get 28 as the smallest value of n. Next value of n will be 30+28 = 58 since 30 is the LCM of 6 and 5. Next will be 30+58 = 88 and so on
what is the remainder that n leaves after division by 30
When you divide 28/58/88... by 30, you get 28 as remainder.
Q2
Positive integer n is divided by 5, the remainder is 1 --> , where is the quotient --> 1, 6, 11, 16, 21, 26, 31, ...
Positive integer n is divided by 7, the remainder is 3 --> , where is the quotient --> 3, 10, 17, 24, 31, ....
n satisfies both the conditions. The first such number is 31. Hence smallest value of n is 31. Next value is 31+35 = 66 (35 is the LCM of 5 and 7) ... and so on
What is the smallest positive integer k such that k+n is a multiple of 35?
So n = 31/66... Is n a multiple of 35? No. 31 is not divisible by 35. What should you add to 31 to make it divisible by 35? The smallest number you could add is 4 because 31+4 = 35 which is divisible by 35.
So answer is 4.
I have been discussing Divisibility and Remainders for the past few weeks on my blog. The following posts might help you:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... unraveled/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... y-applied/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... emainders/
Both the questions use the same concept. They just ask you for the answer in different formats.
Q1
Positive integer n leaves a remainder of 4 after division by 6 --> --> 4, 10, 16, 22, 28, ...
Positive integer n leaves a remainder of 3 after division by 5 --> --> 3, 8, 13, 18, 23, 28, ...
n satisfies both the conditions. The first such number is 28. So you get 28 as the smallest value of n. Next value of n will be 30+28 = 58 since 30 is the LCM of 6 and 5. Next will be 30+58 = 88 and so on
what is the remainder that n leaves after division by 30
When you divide 28/58/88... by 30, you get 28 as remainder.
Q2
Positive integer n is divided by 5, the remainder is 1 --> , where is the quotient --> 1, 6, 11, 16, 21, 26, 31, ...
Positive integer n is divided by 7, the remainder is 3 --> , where is the quotient --> 3, 10, 17, 24, 31, ....
n satisfies both the conditions. The first such number is 31. Hence smallest value of n is 31. Next value is 31+35 = 66 (35 is the LCM of 5 and 7) ... and so on
What is the smallest positive integer k such that k+n is a multiple of 35?
So n = 31/66... Is n a multiple of 35? No. 31 is not divisible by 35. What should you add to 31 to make it divisible by 35? The smallest number you could add is 4 because 31+4 = 35 which is divisible by 35.
So answer is 4.
I have been discussing Divisibility and Remainders for the past few weeks on my blog. The following posts might help you:
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... unraveled/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... y-applied/
https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2011/0 ... emainders/
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
