[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 37: Undefined array key "last_recommended_questions_epoch"
[phpBB Debug] PHP Notice: in file /includes/check_new_recommended_questions.php on line 41: Undefined array key "last_recommended_questions_epoch"
If r is the remainder when the positive integer n is divided by 7 what : Data Sufficiency (DS)
 Last visit was: 20 Jul 2024, 03:52 It is currently 20 Jul 2024, 03:52
Toolkit
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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If r is the remainder when the positive integer n is divided by 7 what

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 23 Sep 2009
Posts: 71
Own Kudos [?]: 538 [41]
Given Kudos: 37
Math Expert
Joined: 02 Sep 2009
Posts: 94428
Own Kudos [?]: 642464 [10]
Given Kudos: 86627
Intern
Joined: 15 Oct 2014
Posts: 4
Own Kudos [?]: 13 [7]
Given Kudos: 0
General Discussion
Intern
Joined: 04 Mar 2014
Posts: 9
Own Kudos [?]: [0]
Given Kudos: 47
Concentration: Marketing, General Management
GMAT 1: 680 Q50 V32
GPA: 3.9
WE:Information Technology (Investment Banking)
Re: If r is the remainder when the positive integer n is divided by 7 what [#permalink]
Bunuel wrote:
If r is the remainder when the postive integer n is divided by 7, what is the value of r ?

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).

(1) when n is divided by 21 the remainder is an odd number --> $$n=21q+odd=7*3q+odd$$, now as $$21q$$ is itself divisible by 7 then if $$odd=1$$ then $$n$$ divided by 7 will yield the same reminder of 1 BUT if $$odd=3$$ then $$n$$ divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.

Or try two different numbers for $$n$$:
If $$n=22$$ then $$n$$ divided by 21 gives remainder of 1 and $$n$$ divded by 7 also gives remainder of 1;
If $$n=24$$ then $$n$$ divided by 21 gives remainder of 3 and $$n$$ divded by 7 also gives remainder of 3.
Two different answers, hence not sufficient.

(2) when n is divided by 28, the remainder is 3 --> $$n=28p+3=7*(4p)+3$$, now as $$28p$$ is itself divisible by 7, then $$n$$ divided by 7 will give remainder of 3. Sufficient.

Thanks Bunnel. Could you please explain the logic behind "when n is divided by 28, the remainder is 3 --> $$n=28p+3=7*(4p)+3$$, now as $$28p$$ is itself divisible by 7, then $$n$$ divided by 7 will give remainder of 3. Sufficient." ?
Math Expert
Joined: 02 Sep 2009
Posts: 94428
Own Kudos [?]: 642464 [0]
Given Kudos: 86627
Re: If r is the remainder when the positive integer n is divided by 7 what [#permalink]
Keysersoze10 wrote:
Bunuel wrote:
If r is the remainder when the postive integer n is divided by 7, what is the value of r ?

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).

(1) when n is divided by 21 the remainder is an odd number --> $$n=21q+odd=7*3q+odd$$, now as $$21q$$ is itself divisible by 7 then if $$odd=1$$ then $$n$$ divided by 7 will yield the same reminder of 1 BUT if $$odd=3$$ then $$n$$ divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.

Or try two different numbers for $$n$$:
If $$n=22$$ then $$n$$ divided by 21 gives remainder of 1 and $$n$$ divded by 7 also gives remainder of 1;
If $$n=24$$ then $$n$$ divided by 21 gives remainder of 3 and $$n$$ divded by 7 also gives remainder of 3.
Two different answers, hence not sufficient.

(2) when n is divided by 28, the remainder is 3 --> $$n=28p+3=7*(4p)+3$$, now as $$28p$$ is itself divisible by 7, then $$n$$ divided by 7 will give remainder of 3. Sufficient.

Thanks Bunnel. Could you please explain the logic behind "when n is divided by 28, the remainder is 3 --> $$n=28p+3=7*(4p)+3$$, now as $$28p$$ is itself divisible by 7, then $$n$$ divided by 7 will give remainder of 3. Sufficient." ?

28p gives the remainder of 0, when divided by 7 and 3 gives the remainder of 3 when divided by 7.
Intern
Joined: 24 Aug 2016
Posts: 49
Own Kudos [?]: 75 [3]
Given Kudos: 24
Location: India
WE:Information Technology (Computer Software)
Re: If r is the remainder when integer n is divided by 7, what is the valu [#permalink]
2
Kudos
1
Bookmarks
Quote:
If r is the remainder when integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3

$$\frac{n}{7} = q + r$$

(1) $$\frac{n}{21}$$ = quotient + Some odd value

Minimum value of n could be 22 , 24 , 26 -- Not sufficient

(2) $$\frac{n}{28}$$ = quotient + 3

Minimum value of n will be 31 that will satisfy above. So r = 3. --Sufficient

Ans. B
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6804
Own Kudos [?]: 30839 [5]
Given Kudos: 799
Re: If r is the remainder when integer n is divided by 7, what is the valu [#permalink]
1
Kudos
4
Bookmarks
Top Contributor
Bunuel wrote:

Tough and Tricky questions: Remainders.

If r is the remainder when integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3

We can use a variety of divisibility rules to solve this, or we can list possible values of n based on the statements. The rule for listing possible values of n is as follows:
If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

Target question: What is the value of r?

Statement 1: When n is divided by 21, the remainder is an odd number.
There are several possible values of n that satisfy this condition. Here are two:
Case a: n = 1 (since 1 divided by 21 leaves remainder 1, which is odd). Here, r = 1
Case b: n = 3 (since 3 divided by 21 leaves remainder 3, which is odd). Here, r = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 28, the remainder is 3
Possible values of n: 3, 31, 59, 87, . . .
We can see that for all possible values of n, the remainder is always 3 when n is divided by 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO FROM OUR COURSE
Intern
Joined: 09 Apr 2018
Posts: 26
Own Kudos [?]: 6 [0]
Given Kudos: 92
Location: India
Schools: IIMA PGPX"20
GPA: 3.5
Re: If r is the remainder when integer n is divided by 7, what is the valu [#permalink]
GMATPrepNow wrote:
Bunuel wrote:

Tough and Tricky questions: Remainders.

If r is the remainder when integer n is divided by 7, what is the value of r?

(1) When n is divided by 21, the remainder is an odd number
(2) When n is divided by 28, the remainder is 3

We can use a variety of divisibility rules to solve this, or we can list possible values of n based on the statements. The rule for listing possible values of n is as follows:
If, when N is divided by D, the remainder is R, then the possible values of N include: R, R+D, R+2D, R+3D,. . .

Target question: What is the value of r?

Statement 1: When n is divided by 21, the remainder is an odd number.
There are several possible values of n that satisfy this condition. Here are two:
Case a: n = 1 (since 1 divided by 21 leaves remainder 1, which is odd). Here, r = 1
Case b: n = 3 (since 3 divided by 21 leaves remainder 3, which is odd). Here, r = 3
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: When n is divided by 28, the remainder is 3
Possible values of n: 3, 31, 59, 87, . . .
We can see that for all possible values of n, the remainder is always 3 when n is divided by 7
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

RELATED VIDEO FROM OUR COURSE

how statement 2 is sufficient?

when 69/28 remainder is =3; when 69/7 remainder =6
when 87/28 r=3 ; when 87/7 r=3
GMAT Tutor
Joined: 24 Jun 2008
Posts: 4128
Own Kudos [?]: 9454 [0]
Given Kudos: 91
Q51  V47
Re: If r is the remainder when integer n is divided by 7, what is the valu [#permalink]
SUNILAA wrote:
how statement 2 is sufficient?

when 69/28 remainder is =3; when 69/7 remainder =6
when 87/28 r=3 ; when 87/7 r=3

You do not get a remainder of 3 when you divide 69 by 28.

If Statement 2 is true, then n is 3 larger than a multiple of 28. But every multiple of 28 is a multiple of 7 too, so that means n is 3 larger than a multiple of 7. That's another way of saying "the remainder is 3 when you divide n by 7", so Statement 2 is sufficient.
Intern
Joined: 04 Jul 2017
Posts: 9
Own Kudos [?]: 2 [0]
Given Kudos: 64
Re: If r is the remainder when the positive integer n is divided by 7 what [#permalink]
Bunuel wrote:
If r is the remainder when the postive integer n is divided by 7, what is the value of r ?

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).

(1) when n is divided by 21 the remainder is an odd number --> $$n=21q+odd=7*3q+odd$$, now as $$21q$$ is itself divisible by 7 then if $$odd=1$$ then $$n$$ divided by 7 will yield the same reminder of 1 BUT if $$odd=3$$ then $$n$$ divided by 7 will yield the same reminder of 3. Two different answers, hence not sufficient.

Or try two different numbers for $$n$$:
If $$n=22$$ then $$n$$ divided by 21 gives remainder of 1 and $$n$$ divded by 7 also gives remainder of 1;
If $$n=24$$ then $$n$$ divided by 21 gives remainder of 3 and $$n$$ divded by 7 also gives remainder of 3.
Two different answers, hence not sufficient.

(2) when n is divided by 28, the remainder is 3 --> $$n=28p+3=7*(4p)+3$$, now as $$28p$$ is itself divisible by 7, then $$n$$ divided by 7 will give remainder of 3. Sufficient.

Bunuel what would have been the case in (2) if the numbers were not divisible by 7. Eg: 36p + 3

Non-Human User
Joined: 09 Sep 2013
Posts: 34038
Own Kudos [?]: 853 [0]
Given Kudos: 0
Re: If r is the remainder when the positive integer n is divided by 7 what [#permalink]
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: If r is the remainder when the positive integer n is divided by 7 what [#permalink]
Moderator:
Math Expert
94427 posts