When 777 is divided by a positive integer n, the remainder : Quant Question Archive [LOCKED]
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 18 Jan 2017, 21:05

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# When 777 is divided by a positive integer n, the remainder

Author Message
Intern
Joined: 29 Jun 2008
Posts: 37
Followers: 0

Kudos [?]: 30 [0], given: 0

When 777 is divided by a positive integer n, the remainder [#permalink]

### Show Tags

07 Jul 2008, 09:42
2
This post was
BOOKMARKED
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

When 777 is divided by a positive integer n, the remainder is 77. How many possibilites are there for n?

A. 2
B. 3
C. 4
D. 5
E. 6
Director
Joined: 13 Nov 2003
Posts: 790
Location: BULGARIA
Followers: 1

Kudos [?]: 47 [0], given: 0

Re: When 777 is divided by a positive integer n... [#permalink]

### Show Tags

07 Jul 2008, 09:55
Hi think that the ans is 5
n can be 100, 140,175, 350,700,
Intern
Joined: 29 Jun 2008
Posts: 37
Followers: 0

Kudos [?]: 30 [0], given: 0

Re: When 777 is divided by a positive integer n... [#permalink]

### Show Tags

07 Jul 2008, 09:56
BG wrote:
Hi think that the ans is 5
n can be 100, 140,175, 350,700,

Could you explain the way you did it?
Senior Manager
Joined: 09 Oct 2007
Posts: 466
Followers: 1

Kudos [?]: 42 [0], given: 1

Re: When 777 is divided by a positive integer n... [#permalink]

### Show Tags

07 Jul 2008, 10:02
Any factor of 700 greater than 100. If you do the prime factorization of 700, you'll get: 2, 2, 5, 5, 7. With those primes, you can only build the numbers BG said.
Director
Joined: 10 Sep 2007
Posts: 947
Followers: 8

Kudos [?]: 287 [0], given: 0

Re: When 777 is divided by a positive integer n... [#permalink]

### Show Tags

07 Jul 2008, 10:21
Start from the largest divisor.
Then check all the multiple of biggest divisor (700 in this case), which are greater than 77 but less than biggest divisors)

100,140,175,350,700

IMO D.

Last edited by abhijit_sen on 07 Jul 2008, 10:39, edited 1 time in total.
SVP
Joined: 30 Apr 2008
Posts: 1887
Location: Oklahoma City
Schools: Hard Knocks
Followers: 40

Kudos [?]: 570 [1] , given: 32

Re: When 777 is divided by a positive integer n... [#permalink]

### Show Tags

07 Jul 2008, 10:29
1
KUDOS
I wrote out all of the factors of 700 like 1..700, 2...350, 4...175, 5...140, 7...100, 10...70, STOP

I did this down to 10...70, because I realized at the point where you get blow the remainder in quesiton, you don't have a remainder of 77 anymore...so it's 100, 140, 175, 350, and 700...total of 5 in all.
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

GMAT Club Premium Membership - big benefits and savings

Director
Joined: 01 Jan 2008
Posts: 629
Followers: 4

Kudos [?]: 175 [0], given: 1

Re: When 777 is divided by a positive integer n... [#permalink]

### Show Tags

07 Jul 2008, 10:40
nirimblf wrote:
When 777 is divided by a positive integer n, the remainder is 77. How many possibilites are there for n?

A. 2
B. 3
C. 4
D. 5
E. 6

777 = k*n + 77 -> n > 77, k*n = 700 = 7*(2^2)*(5^2)

1) without 7 -> only (2^2)*(5^2) = 100 because otherwise below 77
2) with 7 -> 7*(2^x1)*(5^x2) > 77 -> 7*(2^2)*(5^2), 7^(2^2)*5 //with 2^2// 7^2*(5^2) //with 2^1 and 7^5^2 //with 2^0
1+4 = 5 -> D
Intern
Joined: 29 Jun 2008
Posts: 37
Followers: 0

Kudos [?]: 30 [0], given: 0

Re: When 777 is divided by a positive integer n... [#permalink]

### Show Tags

07 Jul 2008, 10:44
jallenmorris wrote:
I wrote out all of the factors of 700 like 1..700, 2...350, 4...175, 5...140, 7...100, 10...70, STOP

I did this down to 10...70, because I realized at the point where you get blow the remainder in quesiton, you don't have a remainder of 77 anymore...so it's 100, 140, 175, 350, and 700...total of 5 in all.

Thanks, that's an explanation I can easily understand. +1.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13441
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: When 777 is divided by a positive integer n, the remainder [#permalink]

### Show Tags

08 Jun 2016, 18:17
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.
_________________
Re: When 777 is divided by a positive integer n, the remainder   [#permalink] 08 Jun 2016, 18:17
Display posts from previous: Sort by