When the number 777 is divided by the integer N, the remaind : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 21 Feb 2017, 23:15

### 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 the number 777 is divided by the integer N, the remaind

Author Message
TAGS:

### Hide Tags

Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 690
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 15

Kudos [?]: 148 [1] , given: 15

When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

15 Sep 2010, 13:04
1
KUDOS
14
This post was
BOOKMARKED
00:00

Difficulty:

95% (hard)

Question Stats:

31% (02:45) correct 69% (01:32) wrong based on 220 sessions

### HideShow timer Statistics

When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

A. 2
B. 3
C. 4
D. 5
E. 6
[Reveal] Spoiler: OA

_________________

Consider kudos, they are good for health

Last edited by Engr2012 on 17 Jul 2015, 02:58, edited 1 time in total.
Edited the question, added the OA and tags
Math Expert
Joined: 02 Sep 2009
Posts: 37063
Followers: 7241

Kudos [?]: 96267 [6] , given: 10729

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

15 Sep 2010, 13:20
6
KUDOS
Expert's post
7
This post was
BOOKMARKED
mainhoon wrote:
When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

I think it should me mentioned that $$n$$ is a positive integer.

Positive integer $$a$$ divided by positive integer $$d$$ yields a reminder of $$r$$ can always be expressed as $$a=qd+r$$, where $$q$$ is called a quotient and $$r$$ is called a remainder, note here that $$0\leq{r}<d$$ (remainder is non-negative integer and always less than divisor).

So we'd have: $$777=qn+77$$, where $$remainder=77<n=divisor$$ --> $$qn=700=2^2*5^2*7$$ --> as $$n$$ must be more than 77 then $$n$$ could take only 5 values: 100, 140, 175, 350, and 700.

_________________
Director
Status: Apply - Last Chance
Affiliations: IIT, Purdue, PhD, TauBetaPi
Joined: 17 Jul 2010
Posts: 690
Schools: Wharton, Sloan, Chicago, Haas
WE 1: 8 years in Oil&Gas
Followers: 15

Kudos [?]: 148 [0], given: 15

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

15 Sep 2010, 13:39
Can N be allowed to be negative? Does GMAT allow that possibility and if so, how does one answer this then?
_________________

Consider kudos, they are good for health

Math Expert
Joined: 02 Sep 2009
Posts: 37063
Followers: 7241

Kudos [?]: 96267 [0], given: 10729

When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

15 Sep 2010, 13:42
mainhoon wrote:
Can N be allowed to be negative? Does GMAT allow that possibility and if so, how does one answer this then?

No, it cannot be the case, at least for GMAT. Every GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

_________________
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 108

Kudos [?]: 972 [0], given: 25

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

15 Sep 2010, 13:49
mainhoon wrote:
Can N be allowed to be negative? Does GMAT allow that possibility and if so, how does one answer this then?

the problem with negative numbers is that there is no unique definition of remainder

the only condition is that abs(remainder)<abs(divisor)

But even if we follow that, it is enough to tell us that the possible divisors is just double. All the positive ones listed above as well as -1*those numbers
hence, 10
_________________
Retired Moderator
Joined: 03 Aug 2010
Posts: 246
Followers: 2

Kudos [?]: 37 [0], given: 41

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

18 Oct 2010, 10:29
Bunuel wrote:
mainhoon wrote:
When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

I think it should me mentioned that $$n$$ is a positive integer.

Positive integer $$a$$ divided by positive integer $$d$$ yields a reminder of $$r$$ can always be expressed as $$a=qd+r$$, where $$q$$ is called a quotient and $$r$$ is called a remainder, note here that $$0\leq{r}<d$$ (remainder is non-negative integer and always less than divisor).

So we'd have: $$777=qn+77$$, where $$remainder=77<n=divisor$$ --> $$qn=700=2^2*5^2*7$$ --> as $$n$$ must be more than 77 then $$n$$ could take only 5 values: 100, 140, 175, 350, and 700.

I couldn't understand how we arrived at 100,140,175,350 and 700... is it something that we did manually or erupted out of the calculation given here
_________________

http://www.gmatpill.com/gmat-practice-test/

Amazing Platform

Senior Manager
Status: Not afraid of failures, disappointments, and falls.
Joined: 20 Jan 2010
Posts: 294
Concentration: Technology, Entrepreneurship
WE: Operations (Telecommunications)
Followers: 18

Kudos [?]: 236 [0], given: 260

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

19 Oct 2010, 01:30
hirendhanak wrote:
Bunuel wrote:
mainhoon wrote:
When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

I think it should me mentioned that $$n$$ is a positive integer.

Positive integer $$a$$ divided by positive integer $$d$$ yields a reminder of $$r$$ can always be expressed as $$a=qd+r$$, where $$q$$ is called a quotient and $$r$$ is called a remainder, note here that $$0\leq{r}<d$$ (remainder is non-negative integer and always less than divisor).

So we'd have: $$777=qn+77$$, where $$remainder=77<n=divisor$$ --> $$qn=700=2^2*5^2*7$$ --> as $$n$$ must be more than 77 then $$n$$ could take only 5 values: 100, 140, 175, 350, and 700.

I couldn't understand how we arrived at 100,140,175,350 and 700... is it something that we did manually or erupted out of the calculation given here

by multiplying the factors of $$700$$ with each other and selecting only those numbers which result in $$\geq 77$$ till $$700$$.
_________________

"I choose to rise after every fall"
Target=770
http://challengemba.blogspot.com
Kudos??

Senior Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 326
Followers: 1

Kudos [?]: 447 [0], given: 193

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

22 May 2011, 22:25
AtifS wrote:

I couldn't understand how we arrived at 100,140,175,350 and 700... is it something that we did manually or erupted out of the calculation given here

by multiplying the factors of $$700$$ with each other and selecting only those numbers which result in $$\geq 77$$ till $$700$$.[/quote]

whats the fastest way of finding factors of 700
_________________

I'm the Dumbest of All !!

SVP
Joined: 16 Nov 2010
Posts: 1672
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 33

Kudos [?]: 520 [0], given: 36

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

23 May 2011, 06:20
Just break 700 into prime factors, take 5 and 2 as there is a 0 at end. Take 7 also, as the number is 700.

700 = 2^2 * 5^2 * 7
Then the number of factors will be (2+1) * (2+1) * (1+1)

Also, you can refer to Math Book for more details on prime factorization and number of factors.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Manager
Joined: 04 Apr 2010
Posts: 162
Followers: 1

Kudos [?]: 180 [0], given: 31

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

23 May 2011, 17:35
700 = 2^2 * 5^2 * 7
How to come quickly with divisors greater than 77 from above expression? It took almost two minutes to me.
_________________

Consider me giving KUDOS, if you find my post helpful.
If at first you don't succeed, you're running about average. ~Anonymous

VP
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 1353
Followers: 17

Kudos [?]: 243 [0], given: 10

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

23 May 2011, 20:49
good concept of number > 77 here.

777-77 = nQ
2^2 * 5^2 * 7 = 700

gives 100,140,175,350 and 700 .
_________________

Visit -- http://www.sustainable-sphere.com/
Promote Green Business,Sustainable Living and Green Earth !!

Intern
Joined: 11 Jan 2013
Posts: 16
Location: United States
Followers: 0

Kudos [?]: 31 [5] , given: 12

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

29 Jun 2013, 11:09
5
KUDOS
hirendhanak wrote:
Bunuel wrote:
mainhoon wrote:
When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

I think it should me mentioned that $$n$$ is a positive integer.

Positive integer $$a$$ divided by positive integer $$d$$ yields a reminder of $$r$$ can always be expressed as $$a=qd+r$$, where $$q$$ is called a quotient and $$r$$ is called a remainder, note here that $$0\leq{r}<d$$ (remainder is non-negative integer and always less than divisor).

So we'd have: $$777=qn+77$$, where $$remainder=77<n=divisor$$ --> $$qn=700=2^2*5^2*7$$ --> as $$n$$ must be more than 77 then $$n$$ could take only 5 values: 100, 140, 175, 350, and 700.

I couldn't understand how we arrived at 100,140,175,350 and 700... is it something that we did manually or erupted out of the calculation given here

You know that the feasible factors of 700 must be in a range above 77. Thus start breaking down 700 "from the top":

700 x 1
350 x 2
175 x 4
140 x 5
100 x 7

The next one, 70 x 10, is already out of range. That gives you 5 factors.
Current Student
Joined: 06 Sep 2013
Posts: 2035
Concentration: Finance
GMAT 1: 770 Q0 V
Followers: 63

Kudos [?]: 604 [0], given: 355

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

17 Oct 2013, 17:38
mainhoon wrote:
When the number 777 is divided by the integer N, the remainder is 77. How many integer possibilities are there for N?

Hey there, are there at least some answer choices for this question?
Much appreciated

Cheers
J
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13905
Followers: 589

Kudos [?]: 167 [0], given: 0

Re: When the number 777 is divided by the integer N, the remaind [#permalink]

### Show Tags

13 Nov 2014, 15:08
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.
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 37063
Followers: 7241

Kudos [?]: 96267 [0], given: 10729

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

### Show Tags

17 Jul 2015, 00:11
Expert's post
1
This post was
BOOKMARKED
When the number 777 is divided by the positive integer n, the remainder is 77. How many integer possibilities are there for n?

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

Kudos for a correct solution.
_________________
Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2651
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 120

Kudos [?]: 1370 [0], given: 789

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

### Show Tags

17 Jul 2015, 03:01
Bunuel wrote:
When the number 777 is divided by the positive integer n, the remainder is 77. How many integer possibilities are there for n?

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

Kudos for a correct solution.

The trick with this question is to realise that only numbers >77 will leave a remainder of 77 when dividing 777.

Given: 777=np+77 where n >77 ---> $$np =700 = 2^2*5^2*7$$

Now only numbers above 77 that will be factors of 700 are 100, 140, 175, 350 and 700. Thus 5 (D) is the correct answer.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Senior Manager
Joined: 27 Dec 2013
Posts: 315
Followers: 0

Kudos [?]: 23 [1] , given: 113

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

### Show Tags

17 Jul 2015, 05:13
1
KUDOS
Hi Engr2012.. 145 cannot be correct. Did u mean to type 140 instead.

Engr2012 wrote:
Bunuel wrote:
When the number 777 is divided by the positive integer n, the remainder is 77. How many integer possibilities are there for n?

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

Kudos for a correct solution.

The trick with this question is to realise that only numbers >77 will leave a remainder of 77 when dividing 777.

Given: 777=np+77 where n >77 ---> $$np =700 = 2^2*5^2*7$$

Now only numbers above 77 that will be factors of 700 are 100, 145, 175, 350 and 700. Thus 5 (D) is the correct answer.

_________________

Kudos to you, for helping me with some KUDOS.

Math Forum Moderator
Joined: 20 Mar 2014
Posts: 2651
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 120

Kudos [?]: 1370 [0], given: 789

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

### Show Tags

17 Jul 2015, 05:22
shriramvelamuri wrote:
Hi Engr2012.. 145 cannot be correct. Did u mean to type 140 instead.

Engr2012 wrote:
Bunuel wrote:
When the number 777 is divided by the positive integer n, the remainder is 77. How many integer possibilities are there for n?

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

Kudos for a correct solution.

The trick with this question is to realise that only numbers >77 will leave a remainder of 77 when dividing 777.

Given: 777=np+77 where n >77 ---> $$np =700 = 2^2*5^2*7$$

Now only numbers above 77 that will be factors of 700 are 100, 145, 175, 350 and 700. Thus 5 (D) is the correct answer.

Yes, I meant 140. It was a typo.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Senior Manager
Joined: 21 May 2013
Posts: 473
Followers: 1

Kudos [?]: 77 [1] , given: 437

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

### Show Tags

17 Jul 2015, 07:41
1
KUDOS
Bunuel wrote:
When the number 777 is divided by the positive integer n, the remainder is 77. How many integer possibilities are there for n?

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

Kudos for a correct solution.

There are only 5 such numbers = 100, 140, 175, 350 and 700
Intern
Joined: 04 Nov 2013
Posts: 43
Concentration: Finance, Strategy
GMAT 1: Q44 V38
GPA: 4
Followers: 0

Kudos [?]: 6 [1] , given: 10

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

### Show Tags

17 Jul 2015, 08:31
1
KUDOS
Bunuel wrote:
When the number 777 is divided by the positive integer n, the remainder is 77. How many integer possibilities are there for n?

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

Kudos for a correct solution.

777 = xn+77
700 = xn

Two numbers multiplied together must equal 700. To get a remainder above 77, each number must be above 77.
Prime factorization of 700 = 2^2*5^2*7

The answer choice are 100, 140, 175, 350, 700.

D
_________________

Please kudos if you found this post helpful. I am trying to unlock the tests

Re: When the number 777 is divided by the positive integer n, the   [#permalink] 17 Jul 2015, 08:31

Go to page    1   2    Next  [ 26 posts ]

Similar topics Replies Last post
Similar
Topics:
6 When 10 is divided by the positive integer n, the remainder 5 14 Mar 2014, 02:18
7 If the remainder is 13 when the integer n is divided by 26 7 20 Mar 2012, 23:05
44 If the remainder is 7 when positive integer n is divided by 14 06 Mar 2012, 22:28
15 When positive integer n is divided by 5, the remainder is 1. When n is 8 09 Apr 2011, 15:08
14 When 10 is divided by the positive integer n, the remainder 36 15 Sep 2008, 13:33
Display posts from previous: Sort by