Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 29 May 2017, 19:32

### 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

# If N, C, and D are positive integers, what is the remainder

Author Message
TAGS:

### Hide Tags

Manager
Joined: 24 Aug 2012
Posts: 130
Followers: 2

Kudos [?]: 250 [2] , given: 2

If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

06 Nov 2012, 18:35
2
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

58% (02:37) correct 42% (01:54) wrong based on 270 sessions

### HideShow timer Statistics

If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.
[Reveal] Spoiler: OA

_________________

Push +1 kudos button please, if you like my post

Intern
Status: wants to beat the gmat
Joined: 18 Jul 2012
Posts: 20
Location: United States
Followers: 0

Kudos [?]: 9 [0], given: 1

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

06 Nov 2012, 18:54
1. insufficient b/c D and C can be any number. adding +1 can change remainder completely.
ex: D =2 , C = 3 R = 2 ... D = 2+1 , C = 3+1 R = 3
2: sufficient b/c (ND + NC)/CN => ND/CN + NC/CN => ND/CN =>D/C + 1 => R5

Intern
Joined: 20 Jun 2013
Posts: 8
Followers: 0

Kudos [?]: 0 [0], given: 5

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

11 Sep 2013, 04:20
Can someone please help with a detailed explanation? Was able to get the answer right but don't really know how I arrived at it.

Thanks
Intern
Joined: 20 Nov 2013
Posts: 31
Schools: LBS '17
Followers: 0

Kudos [?]: 14 [1] , given: 189

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

14 Oct 2014, 13:11
1
KUDOS
1) insufficient
2) ND+NC/CN gives a remainder of 5.

ND + NC / CN = (D+C)/C

So we know that (D+C)/C gives a remainder of 5.

The idea here is that if you add any multiple of C to C then you will definitely get a multiple of C. For eg. 4 is a multiple of 2. So (4+2)/2 will give R=0.
In this case though we have a number added to C leaving a remainder of 5. This means that D is not divisible by C and that D must leave a remainder of 5. Eg. (5+0)/10 leaves a remainder of 5 . (5+10)/10 will leave a remainder of 5 also. So the remainder will always be in D in the equation (D+C). This means that D/C will also give us a remainder of 5. Sufficient.
Manager
Joined: 14 Feb 2012
Posts: 55
Location: United States
WE: Project Management (Consulting)
Followers: 1

Kudos [?]: 18 [0], given: 0

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

28 Oct 2014, 12:10
Well, I am confused here and need some help.

I chose D.

Reason is as follows:
For statement A:
take D+1=12 and C+1=7 so 12/7 => remainder 5
if we take 11/6 => remainder is still 5

In the explanation above for D=CK + (K + 4), for different values of K, we are actually changing the value of D while keeping the value of C same. If the algebra calculations are correct and logic is correct, there must be some example to support this explanation.

We all agree to sufficiency of statement B.

Manager
Joined: 31 Jul 2014
Posts: 149
GMAT 1: 630 Q48 V29
Followers: 0

Kudos [?]: 51 [0], given: 373

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

04 Nov 2014, 02:55
VeritasPrepKarishma wrote:
kingb wrote:
If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.

Stmnt 1: If D+1 is divided by C+1, the remainder is 5.

D+1 = (C+1)k + 5
D = Ck + (k + 4)
When D is divided by C, the remainder will vary with k.
If k = 0, remainder will be 4 (C is greater than 4)
If k = 1, remainder will be 5 (C is greater than 5)
If k = 2, remainder will be 6 (C is greater than 6)
etc

2) If ND+NC is divided by CN, the remainder is 5.
ND + NC = CN*k + 5
DN = CN*(k-1) + 5
D = C*(k-1) + 5/N
Now, N is a positive integer and remainder must be a positive integer too. The only value that N can take such that 5/N is a positive integer is 1. So N must be 1.
D = C*(k -1) + 5
When D is divided by C, remainder is 5.

Sorry to bother , I just want to ask ... N can't be 5 ? 5/N will still be integer i.e. 1
Could you please explain why only value N can take is 1?
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7380
Location: Pune, India
Followers: 2292

Kudos [?]: 15168 [0], given: 224

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

04 Nov 2014, 21:03
Expert's post
1
This post was
BOOKMARKED
VeritasPrepKarishma wrote:
kingb wrote:
If N, C, and D are positive integers, what is the remainder when D is divided by C?

1) If D+1 is divided by C+1, the remainder is 5.
2) If ND+NC is divided by CN, the remainder is 5.

Stmnt 1: If D+1 is divided by C+1, the remainder is 5.

D+1 = (C+1)k + 5
D = Ck + (k + 4)
When D is divided by C, the remainder will vary with k.
If k = 0, remainder will be 4 (C is greater than 4)
If k = 1, remainder will be 5 (C is greater than 5)
If k = 2, remainder will be 6 (C is greater than 6)
etc

2) If ND+NC is divided by CN, the remainder is 5.
ND + NC = CN*k + 5
DN = CN*(k-1) + 5
D = C*(k-1) + 5/N
Now, N is a positive integer and remainder must be a positive integer too. The only value that N can take such that 5/N is a positive integer is 1. So N must be 1.
D = C*(k -1) + 5
When D is divided by C, remainder is 5.

Sorry to bother , I just want to ask ... N can't be 5 ? 5/N will still be integer i.e. 1
Could you please explain why only value N can take is 1?

Actually it can take value 5 too. I will rewrite the solution given above soon.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7380 Location: Pune, India Followers: 2292 Kudos [?]: 15168 [0], given: 224 Re: If N, C, and D are positive integers, what is the remainder [#permalink] ### Show Tags 04 Nov 2014, 21:15 nnitingarg wrote: Well, I am confused here and need some help. I chose D. Reason is as follows: For statement A: take D+1=12 and C+1=7 so 12/7 => remainder 5 if we take 11/6 => remainder is still 5 In the explanation above for D=CK + (K + 4), for different values of K, we are actually changing the value of D while keeping the value of C same. If the algebra calculations are correct and logic is correct, there must be some example to support this explanation. We all agree to sufficiency of statement B. Please advise. In statement 1, say if C+1 = 8 and D+1 = 21, remainder is 5. C = 7 and D = 20, remainder is 6. Not sufficient alone. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

Manager
Joined: 07 Dec 2009
Posts: 108
GMAT Date: 12-03-2014
Followers: 0

Kudos [?]: 31 [1] , given: 375

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

13 Aug 2015, 09:53
1
KUDOS
1) is clearly insufficient

2) (ND+NC)/CN = Q + 5

==> (D/C)+1 = Q + 5
(D/C) = Q + 4

Hence Sufficient . Is the above approach correct ? Don't quite understand the Solutions given above.
Many Thanks
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7380
Location: Pune, India
Followers: 2292

Kudos [?]: 15168 [0], given: 224

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

13 Aug 2015, 21:09
bhatiavai wrote:
1) is clearly insufficient

2) (ND+NC)/CN = Q + 5

==> (D/C)+1 = Q + 5
(D/C) = Q + 4

Hence Sufficient . Is the above approach correct ? Don't quite understand the Solutions given above.
Many Thanks

No, it is not.

Take some simple numbers: 11 divided by 5 gives quotient as 2 and remainder as 1.

$$\frac{11}{5} \neq 2 + 1$$

So $$\frac{(ND+NC)}{CN} \neq Q + 5$$

Actually, ND + NC = Q*CN + 5
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 02 Mar 2015 Posts: 32 Followers: 0 Kudos [?]: 5 [0], given: 8 Re: If N, C, and D are positive integers, what is the remainder [#permalink] ### Show Tags 28 Aug 2015, 02:03 1- Statement 1 insuf, C and D could be lot of number possibilities 2- N(D+C)/CN = D+C/C = D/C +1 = Q + 5/C => D = QC +4 is this good ? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7380 Location: Pune, India Followers: 2292 Kudos [?]: 15168 [0], given: 224 Re: If N, C, and D are positive integers, what is the remainder [#permalink] ### Show Tags 28 Aug 2015, 20:54 jimwild wrote: 1- Statement 1 insuf, C and D could be lot of number possibilities 2- N(D+C)/CN = D+C/C = D/C +1 = Q + 5/C => D = QC +4 is this good ? I don't understand how you got Q + 5/C from Q*CN + 5. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

Veritas Prep Reviews

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15524
Followers: 651

Kudos [?]: 211 [0], given: 0

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

15 Sep 2016, 00:19
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.
_________________
Intern
Joined: 19 Aug 2016
Posts: 7
Location: India
GMAT 1: 760 Q50 V42
GPA: 2.74
WE: Engineering (Health Care)
Followers: 0

Kudos [?]: 5 [0], given: 83

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

19 Sep 2016, 09:39
OA is definitely wrong. Should be E.
you cannot write remainder(ND/NC) = remainder(D/C)

eg remainder(20/15) = 5, remainder(4/3) = 1
Manhattan GMAT Instructor
Joined: 04 Dec 2015
Posts: 302
GMAT 1: 790 Q51 V49
GRE 1: 340 Q170 V170
Followers: 40

Kudos [?]: 157 [1] , given: 31

Re: If N, C, and D are positive integers, what is the remainder [#permalink]

### Show Tags

19 Sep 2016, 15:35
1
KUDOS
Expert's post
lifetantrik wrote:
OA is definitely wrong. Should be E.
you cannot write remainder(ND/NC) = remainder(D/C)

eg remainder(20/15) = 5, remainder(4/3) = 1

I agree. Let me expand this out to show the actual cases that prove insufficiency.

(1)
case 1: D = 19, C = 14. Obeys the statement, because when 20 is divided by 15, the remainder is 5. The answer to the question is also 5.
case 2: D = 28, C = 5. Obeys, the statement, because when 29 is divided by 6, the remainder is 5. The answer to the question, though, is 3. That's because when you divide 28 by 5, the remainder is 3.

(2)
case 1: D = 4, C = 3, N = 5. Obeys the statement, because when 20 + 15 is divided by 15, the remainder is 5. The answer to the question is 1.
case 2: D = 20, C = 15, N = 1. Obeys the statement, because when 20+15 is divided by 15, the remainder is 5. The answer to the question, however, is 5.

We have two different possible answers to the question for statement 1, and two different possible answers for statement 2. Now let's put them together.

(1+2)
case 1: D = 19, C = 14, N = 1.
- Obeys statement 1 (we already tested it).
- It also obeys statement 2, because when 19 + 14 is divided by 14, the remainder is 5.
- The answer to the question is 5.

case 2: D = 25, C = 6, N = 5.
- Obeys statement 1: 26 divided by 7 has a remainder of 5.
- Obeys statement 2: 125 divided by 30 has a remainder of 5.
- The answer to the question is 1.

That said, on the test, I would work on this one for about 90 seconds and then guess either C or E.
_________________

Chelsey Cooley | Manhattan Prep Instructor | Seattle and Online

Did you like this post? Check out my upcoming GMAT classes and private tutoring!

Manhattan Prep GMAT Discount | Manhattan Prep GMAT Reviews

Re: If N, C, and D are positive integers, what is the remainder   [#permalink] 19 Sep 2016, 15:35
Similar topics Replies Last post
Similar
Topics:
5 If a, b, and c are positive integers, what is the remainder 4 06 Apr 2016, 06:52
13 If a, b, and c are positive integers, what is the remainder 7 02 Oct 2016, 07:06
28 What is the remainder when the positive integer n is divided 11 04 Jul 2013, 20:07
3 What is the remainder when the positive integer n is divided 4 03 Feb 2016, 12:36
27 What is the remainder when the positive integer n is divided 12 11 Feb 2017, 10:32
Display posts from previous: Sort by

# If N, C, and D are positive integers, what is the remainder

 Powered by phpBB © phpBB Group and phpBB SEO 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®.