It is currently 17 Oct 2017, 05:02

### 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

Math Expert
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [0], given: 12180

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

### Show Tags

14 Mar 2014, 03:18
Expert's post
14
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

85% (00:56) correct 15% (01:03) wrong based on 686 sessions

### HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

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

Problem Solving
Question: 164
Category: Algebra Properties of numbers
Page: 84
Difficulty: 600

GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________

Kudos [?]: 128527 [0], given: 12180

Math Expert
Joined: 02 Sep 2009
Posts: 41871

Kudos [?]: 128527 [0], given: 12180

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

### Show Tags

16 Mar 2014, 05:55
Expert's post
4
This post was
BOOKMARKED
SOLUTION

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

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.

_________________

Kudos [?]: 128527 [0], given: 12180

SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1853

Kudos [?]: 2615 [0], given: 193

Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: When 10 is divided by the positive integer n, the remainder [#permalink]

### Show Tags

27 Mar 2014, 21:08
Option A & B are ruled out as n>4

Plugged in 7 & got the answer

_________________

Kindly press "+1 Kudos" to appreciate

Kudos [?]: 2615 [0], given: 193

Manager
Joined: 26 Feb 2015
Posts: 125

Kudos [?]: 28 [0], given: 43

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

### Show Tags

14 Mar 2015, 07:08
Bunuel wrote:
SOLUTION

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

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.

I simply did it this way:

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

And then I just plugged in values for n. So:
$$10(0) + (0-4) = -4$$
$$10(1) + (1-4) = 7$$ <--my answer

Is this correct reasoning, or simply a lucky coincidence?

Kudos [?]: 28 [0], given: 43

Math Forum Moderator
Joined: 02 Aug 2009
Posts: 4962

Kudos [?]: 5449 [0], given: 112

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

### Show Tags

14 Mar 2015, 07:39
Expert's post
1
This post was
BOOKMARKED
erikvm wrote:
Bunuel wrote:
SOLUTION

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

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.

I simply did it this way:

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

And then I just plugged in values for n. So:
$$10(0) + (0-4) = -4$$
$$10(1) + (1-4) = 7$$ <--my answer

Is this correct reasoning, or simply a lucky coincidence?

hi erikvm,
here it is a lucky coincidence..
here you have found the value of y and not n...

$$10(1) + (1-4) = 7$$... here n=1 and y=7.... but the question asks us the value of n...
the equation that you have formed is wrong ..
it says when 10 is divided by the positive integer n, the remainder is n-4.. so the equation will be 10=xn+n-4..

what we have to find is that " when 10 is divided by n, the remainder is n-4"
now substitue the values
(A) 3.... 10/3 rem=1, which is not equal to n-4=3-4=-1.... not correct
(B) 4.... 10/4 rem=2, which is not equal to n-4=4-4=0.... not correct
(C) 7.... 10/7 rem=3, which is equal to n-4=7-4=3.... correct
(D) 8.... 10/8 rem=2, which is not equal to n-4=8-4=2.... not correct
(E) 12... 10/12 rem=10, which is not equal to n-4=10-4=6.... not correct

hope it is clear..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

Kudos [?]: 5449 [0], given: 112

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16765

Kudos [?]: 273 [1], given: 0

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

### Show Tags

02 Jun 2016, 11:38
1
KUDOS
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.
_________________

Kudos [?]: 273 [1], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16765

Kudos [?]: 273 [0], given: 0

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

### Show Tags

11 Jun 2017, 03:52
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.
_________________

Kudos [?]: 273 [0], given: 0

Re: When 10 is divided by the positive integer n, the remainder   [#permalink] 11 Jun 2017, 03:52
Display posts from previous: Sort by