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 350,000 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 3, the remainder is 2; [#permalink]
27 Aug 2006, 01:18

1

This post received KUDOS

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

60% (02:00) correct
40% (02:04) wrong based on 64 sessions

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

[quote="yezz"]When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5

2) t is divisible by 3

How can we generalize this concept ????

Thanks[/quote]
I think C it is
(1) alone
we have n-2 is divisible by both 3 and 5 so n=15a+2
t=5b+3 so nt=(15a+2)*(5b+3)=75ab+45a+10b+6
This tells nothing
(2) alone
t=15c+3 so nt=(3d+2)*(15c+3)=45ab+30b+9a+6
This tells nothing also
(1)(2) together we have
nt= (15a+2)*(15c+3)=15N+6
This means the remainder when nt is divided by 15 is 6
C it is

When positive integer n is divided by 3, the remainder is 2; and when positive integer t is divided by 5, the remainder is 3. What is the remainder when the product nt is divided by 15?

1) n-2 is divisible by 5

2) t is divisible by 3

How can we generalize this concept ????

Thanks

From question, we know that n-2 is a multiple of 3 and t-3 is a multiple of 5.

(1) says that n-2 is a multiple of 5. We know that n-2 is a multiple of 3, so n-2 is a multiple of 15 and n is 2 higher than a multiple of 15. Thus when n is divided by 15, the remainder is 2. All we know about t is that its units digit is either 3 or 8. If t=3, the remainder when nk is divided by 15 will be 6. If t=8, the remainder when nk is divided by 15 will be 1. NOT SUFF

(2) t is a mulltiple of 3. If n is a multiple of 5, nk will be a multiple of 15. If n is not a multiple of 5, mk will not be a multiple of 15. So when nk is divided by 15, the remainder may or may not be 0 NOT SUFF Note that As t is 3 more than a multiple of 5, the remainder when t is divided by 15 is either 3,8,or 13. But t is a multiple of 3, so when t is divided by 15, the remainder is 3,6,9 or 12. Thus from (2), we know that t/15 yields a remainder of 3.

Combining (1) and (2) n=15x+2 and t=15y+3 for some non-negative integers x and y. nt= 15^2xy+3(15x)+2(15y)+6. Each of the first three terms is a multiple of 15, so 6 is the remainder when nt is divided by 15

Kevin , I do understand why n when devided by 15 the remainder will always be 2.

But what if in the question stem , n

a) when it is devided by 3 remainder is 2
b) when divided by 5 remainder is 1

how can we know the remainder here?

and what if x is an intiger devisible by 4 and when divided by 5 yields a remainder of 3 ( is there a general formula for this number if we want to know the remainder when we divide it by 20 ie ( 5*4) am really confused wn i try to generalize the way you attacked the problem???

Kevin , I do understand why n when devided by 15 the remainder will always be 2.

But what if in the question stem , n

a) when it is devided by 3 remainder is 2 b) when divided by 5 remainder is 1 how can we know the remainder here?

and what if x is an intiger devisible by 4 and when divided by 5 yields a remainder of 3 ( is there a general formula for this number if we want to know the remainder when we divide it by 20 ie ( 5*4) am really confused wn i try to generalize the way you attacked the problem???

Thanks in advance

Think that between two multiples of 15, there are 4 multiples of 3
15k, 15k+3,15k+6,15k+9,15k+12, 15(k+1)

So if n yields a remainder of 2 when divided by 3, when divided by 15, n could yield a remainder of 5,8,11 or 14

Similarly, if when divided by 5, n yields a remainder of 1, when divided by 15, n will yield a remainder of 1,6,or 11

If both of these are true, n must yield a remainder of 11 when divided by 15.

and what if x is an intiger devisible by 4 and when divided by 5 yields a remainder of 3 ( is there a general formula for this number if we want to know the remainder when we divide it by 20 ie ( 5*4)

Since 4 is a factor of 20, if x is divisible by 4, x yields a remainder of 4k when divisible by 4 (here k is an integer from 0 to 4)

Since 5 is also a factor of 20, and when x is divided by 5, the remainder is 3, when x is divided by 20, the remainder is 5m+3, where m is from 0 to 3

So can 4k=5m+3 if k belongs to {0,1,2,3,4} and m belongs to {0,1,2,3}?

k=(5m+3)/4, so 5m+3 must be a multiple of 4- m must be 1 and the remainder when x is divided by 20 is 5(1)+3=8

Let n = 3x+2........EQ1
t = 5y+3..............EQ2
nt = 15xy + 10y + 9x+6
Remove 15xy because this is fully divisible by 15.
Now we have to find remainder when 10y + 9x+6 (.........EQ3) is divided by 15.

St1: n-2 is divisible by 5. From EQ1 we get n-2 = 3x for 3x to be divisible by 5 x must be a multiple of 5.
So EQ3 reduces to 10y+9*5z + 6
9*5z is divisible by 15. So removing this we get 10y+6. No conclusion: INSUFF

St2: t is divisible by 3. From EQ2, if t is to be divisible by 3 then y must be a multiple of 3. So EQ3 reduces to 10*3w+9x+6. 10*3w is divisible by 15. Removing this we get 10y+6. No conclusion: INSUFF

Together:
EQ3 reduces to 10*3w + 9*5z + 6. Both 10*3w and 9*5z are divisible by 15. Hence 6 will be remainder: SUFF _________________

Folks ( Dahiya and Kevin )you are great.... it takes me some time to grasp new concepts but you really helped a lot .

I merely spent the whole day with this issue in mind trying to blug in different combinations of numbers to find the concept ...but without your help i could ve never make it .

Re: When positive integer n is divided by 3, the remainder is 2; [#permalink]
09 Nov 2013, 06:51

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Type of Visa: You will be applying for a Non-Immigrant F-1 (Student) US Visa. Applying for a Visa: Create an account on: https://cgifederal.secure.force.com/?language=Englishcountry=India Complete...

I started running back in 2005. I finally conquered what seemed impossible. Not sure when I would be able to do full marathon, but this will do for now...