Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Aug 2016, 20:46

### 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 10 is divided by the positive integer n, the remainder

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 10 Mar 2008
Posts: 371
Followers: 5

Kudos [?]: 214 [1] , given: 0

When 10 is divided by the positive integer n, the remainder [#permalink]

### Show Tags

15 Sep 2008, 14:33
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

89% (01:45) correct 11% (00:55) wrong based on 408 sessions

### HideShow timer Statistics

When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n ?

A) 3
B) 4
C) 7
D) 8
E) 12
[Reveal] Spoiler: OA
Manager
Joined: 11 Jan 2008
Posts: 54
Followers: 0

Kudos [?]: 27 [0], given: 0

### Show Tags

15 Sep 2008, 17:08
back solving is easier for this one.

10/7 gives a remainder of 3. n-4 = 7-4 = 3
Current Student
Joined: 28 Dec 2004
Posts: 3385
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 14

Kudos [?]: 257 [1] , given: 2

### Show Tags

16 Sep 2008, 07:18
1
KUDOS
1
This post was
BOOKMARKED
10=NK+N-4; assume K=1

10=2N-4

14=2N. N has to be a multiple of 7...

C it is..
SVP
Joined: 21 Jul 2006
Posts: 1538
Followers: 10

Kudos [?]: 633 [0], given: 1

### Show Tags

17 Sep 2008, 07:04
vksunder wrote:
fresinha12 - I did the same way as you had described. But is it safe to assume that K=1?

well, since we can never have the denominator to be zero, otherwise the fraction will be undefined. so it makes sense to start off with k=1. If that doesn't work, then you just have to keep increasing the value of k until you can match your answer with the correct answer choice.
SVP
Joined: 17 Jun 2008
Posts: 1570
Followers: 11

Kudos [?]: 233 [0], given: 0

### Show Tags

18 Sep 2008, 00:18
I approached as follows.

10 = nx + n-4 for x = 0,1,2,3,4......
or, n(x+1) = 14
or, n = 14/(x+1)

For x = 0, n = 14, for x = 1, n = 7, x cannot be 2,3,4,5.
For x = 6, n = 2. x cannot be greater than 6.

Hence, possible values of n are 14, 7, 2. Answer choice has 7. Hence, 7 is the answer.
Manager
Joined: 30 May 2010
Posts: 190
Followers: 3

Kudos [?]: 165 [0], given: 32

Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

18 Jun 2010, 00:12
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?
Manager
Joined: 07 Oct 2006
Posts: 71
Location: India
Followers: 1

Kudos [?]: 8 [0], given: 3

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

18 Jun 2010, 00:56
As per my approach, it is easy to reach the solution by going thorough each one of the options.
You can eliminate 12,8,4 and 3 at one look. Then you just need to check for 7. It took me less than 1 minute to get to the answer. So that should be fine I guess.
Math Expert
Joined: 02 Sep 2009
Posts: 34438
Followers: 6261

Kudos [?]: 79503 [4] , given: 10018

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

18 Jun 2010, 01:58
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
jpr200012 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?

Algebraic approach:

THEORY:
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).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so $$10=nq+(n-4)$$ and also $$n-4\geq{0}$$ or $$n\geq{4}$$ (remainder must be non-negative).

$$10=nq+n-4$$ --> $$14=n(q+1)$$ --> as $$14=1*14=2*7$$ and $$\geq{4}$$ then --> $$n$$ can be 7 or 14.

Hope it's clear.
_________________
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 439

Kudos [?]: 1886 [0], given: 210

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

18 Jun 2010, 06:29
It says that the remainder when you divide 10 by n is n-4

This basically can be translated into the following statement algebraically:

$$10 = kn + (n-4)$$

This is simplified as follows:

$$10 = kn + n -4 = n *(k+1) - 4$$

Further simplifying:

$$10 + 4 = n*(k+1) 14 = n*(k+1) 7*2 = n*(k+1)$$

So n can be 7 or 2.

Only 7 is listed as an option here, so the answer is C. Hope this helps!

jpr200012 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?
Math Expert
Joined: 02 Sep 2009
Posts: 34438
Followers: 6261

Kudos [?]: 79503 [0], given: 10018

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

18 Jun 2010, 06:46
whiplash2411 wrote:
It says that the remainder when you divide 10 by n is n-4

This basically can be translated into the following statement algebraically:

$$10 = kn + (n-4)$$

This is simplified as follows:

$$10 = kn + n -4 = n *(k+1) - 4$$

Further simplifying:

$$10 + 4 = n*(k+1) 14 = n*(k+1) 7*2 = n*(k+1)$$

So n can be 7 or 2.

Only 7 is listed as an option here, so the answer is C. Hope this helps!

$$n$$ cannot be 2 as in this case $$remainder =n-4=-2<0$$ and remainder is always non-negative (also notice that 10/2 has no remainder and n-4=-2, though n can also be 14 --> 10=14*0+(14-4)).

Hope it helps.
_________________
Ms. Big Fat Panda
Status: Three Down.
Joined: 09 Jun 2010
Posts: 1922
Concentration: General Management, Nonprofit
Followers: 439

Kudos [?]: 1886 [0], given: 210

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

18 Jun 2010, 06:52
Oh, yeah, that's right. I just saw the 7 and 2, and looked at the answer choices and chose 7.

Thanks, Bunuel. Your explanation will come in handy in case both 2 and 7 were listed as answer choices!
Director
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 63 [0], given: 7

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

16 Jul 2010, 04:22
Quote:
remainder is always non-negative

Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder
Math Expert
Joined: 02 Sep 2009
Posts: 34438
Followers: 6261

Kudos [?]: 79503 [1] , given: 10018

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

16 Jul 2010, 07:14
1
KUDOS
Expert's post
nonameee wrote:
Quote:
remainder is always non-negative

Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder

This has nothing to do with GMAT.

GMAT Prep definition of the remainder:

If $$a$$ and $$d$$ are positive integers, there exists unique integers $$q$$ and $$r$$, such that $$a = qd + r$$ and $$0\leq{r}<d$$. $$q$$ is called a quotient and $$r$$ is called a remainder.

Also EVERY GMAT divisibility question will tell you in advance that any unknowns represent positive integers.

So trust me: remainder is always non-negative and less than divisor for GMAT - $$0\leq{r}<d$$.
_________________
Director
Joined: 23 Apr 2010
Posts: 584
Followers: 2

Kudos [?]: 63 [0], given: 7

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

16 Jul 2010, 14:00
Thanks for clarification. But you can use that property (negative remainder) to solve remainder problems (as it has been done in several posts).
Director
Status: Impossible is not a fact. It's an opinion. It's a dare. Impossible is nothing.
Affiliations: University of Chicago Booth School of Business
Joined: 03 Feb 2011
Posts: 920
Followers: 13

Kudos [?]: 313 [0], given: 123

### Show Tags

05 Mar 2011, 01:24
If division by n leaves reminder. Then
i.e. Dividend - Remainder is a multiple of divider.
Here 10 -(n-4) must be a multiple of n.

Or Is [10 - (n-4)] / n = integer?

Now plug in the values of n from the options.

A - n-4 will give negative remainder. Illogical
B - (10-0)/4 is not integer
C - (10-3)/7 is integer
D - (10-4)/8 is not integer
E - (10-8)/12 is not integer

Baten80 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n ?

A) 3
B) 4
C) 7
D) 8
E) 12
Math Forum Moderator
Joined: 20 Dec 2010
Posts: 2021
Followers: 157

Kudos [?]: 1558 [0], given: 376

### Show Tags

05 Mar 2011, 01:44
$$10=nQ+n-4$$ where Q is the quotient

$$n(Q+1)=14$$, where n and Q are both integers.

Factors of 14;
n*(Q+1)
1*14; n=1, Q=13; Not possible because 1 won't leave any remainder with 10
2*7; n=2, Q=6; Not possible because 2 won't leave any remainder with 10
7*2; n=7, Q=1; Possible
14*1; n=14, Q=0; Possible

So; n can be 7 or 14.

Ans: "C"
_________________
Director
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 100 [0], given: 42

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

06 Mar 2011, 15:04
Nice explanation there Bunuel.

Bunuel wrote:
jpr200012 wrote:
When 10 is divided by the positive integer n, the remainder is n-4. Which of the following could be the value of n?

A. 3
B. 4
C. 7
D. 8
E. 12

My strategy was to create lists below:
n = 3, 4, 7, 8, 12
n-4 = -1(becomes 9), 0, 3, 4, 8
n/10 = R? = 3, 4, 7, 8, 4

There is no match between n-4 and n/10's R.

The solution uses 14 = ..., but I don't understand how they are using 14. Should the question have said a multiple of one of these numbers?

Algebraic approach:

THEORY:
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).

Original question says that when 10 is divided by the positive integer n, the remainder is n-4, so $$10=nq+(n-4)$$ and also $$n-4\geq{0}$$ or $$n\geq{4}$$ (remainder must be non-negative).

$$10=nq+n-4$$ --> $$14=n(q+1)$$ --> $$n$$ is an factor of 14 and $$\geq{4}$$ --> $$n$$ can be 7 or 14.

Hope it's clear.
Director
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 100 [0], given: 42

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

06 Mar 2011, 15:48
I thought of the same , why cant a remainder be negative?

I guess in some cases , as Bunel is suggesting we need to make an assumption that we are dealing with just positive integers.

nonameee wrote:
Quote:
remainder is always non-negative

Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder

Last edited by Spidy001 on 06 Mar 2011, 16:27, edited 1 time in total.
Math Expert
Joined: 02 Sep 2009
Posts: 34438
Followers: 6261

Kudos [?]: 79503 [0], given: 10018

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

06 Mar 2011, 15:55
Spidy001 wrote:
I thought of the same , why cant a remainder be negative?

I guess in some cases , as Bunel is suggesting we need an assumption that we are dealing with just positive integers.

nonameee wrote:
Quote:
remainder is always non-negative

Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder

It's not an assumption.

Remainder is a non-negative by definition (at least on the GMAT).
_________________
Director
Joined: 01 Feb 2011
Posts: 757
Followers: 14

Kudos [?]: 100 [0], given: 42

Re: Number properties question from QR 2nd edition PS 164 [#permalink]

### Show Tags

06 Mar 2011, 16:41
Bunuel,

I know in this case we don't have to make any assumption, because the question clearly states these are two positive integers.

i was referring more to scenarios like negative number division

-25 /7

-25 = 7(-3)+(-4)

Here remainder is -4 which is negative.

so lets say if question is like x,y are integers x/y . we cannot generalize and say remainder >=0 ,unless we assume that we are only talking about positive integers.

nonameee wrote:
Quote:
remainder is always non-negative

Bunuel, I have to disagree with you on that:

http://en.wikipedia.org/wiki/Remainder
[/quote]

It's not an assumption.

Remainder is a non-negative by definition (at least on the GMAT).[/quote]
Re: Number properties question from QR 2nd edition PS 164   [#permalink] 06 Mar 2011, 16:41

Go to page    1   2    Next  [ 36 posts ]

Similar topics Replies Last post
Similar
Topics:
20 When positive integer n is divided by 13, the remainder is 2. When n 14 02 Apr 2015, 06:09
39 When positive integer n is divided by 3, the remainder is 2. When n is 19 02 Apr 2015, 06:06
4 When 10 is divided by the positive integer n, the remainder 5 14 Mar 2014, 03:18
34 If the remainder is 7 when positive integer n is divided by 9 06 Mar 2012, 23:28
13 When positive integer n is divided by 5, the remainder is 1. When n is 8 09 Apr 2011, 16:08
Display posts from previous: Sort by