GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 20 Jun 2018, 17:54

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 24 is divided by the positive integer n, the remainder is 4. Whic

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 46207
When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

03 Jul 2016, 11:25
5
28
00:00

Difficulty:

55% (hard)

Question Stats:

59% (01:04) correct 41% (01:03) wrong based on 850 sessions

HideShow timer Statistics

When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true?

I. n is even
II. n is a multiple of 5
III. n is a factor of 20

A) III only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

_________________
Senior Manager
Joined: 20 Feb 2015
Posts: 386
Concentration: Strategy, General Management
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

03 Jul 2016, 12:03
2
1
When 24 is divided by the positive integer n, the remainder is 4

can be written as

24=nk+4
nk=20

n can take the following values
5,10,20

therefore D
Manager
Joined: 20 Jan 2016
Posts: 54
GMAT 1: 600 Q47 V26
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

03 Jul 2016, 12:04
1
24= m*n + 4

m*n=20
put values of m

m=1 n=20
m=2 n=10
m=4 n=5

I. not true
II. true
III. true

D. correct

Sent from my iPhone using GMAT Club Forum mobile app
Intern
Joined: 06 Oct 2015
Posts: 1
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

17 Aug 2016, 14:13
...because 1, 2, and 4 could have been cases but when divided by 24 do not produce a remainder of 4 correct?
Manager
Joined: 04 Jan 2014
Posts: 120
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

18 Aug 2016, 18:01
atmanb wrote:
...because 1, 2, and 4 could have been cases but when divided by 24 do not produce a remainder of 4 correct?

Please note that the question says number n divides 24 and not that number n is divided by 24.
Intern
Joined: 12 Dec 2016
Posts: 1
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

01 Jan 2017, 14:39
I am not clear with the solution.

nk+4 = 24
nk = 20

if k=1, n=20
if k=2, n=10
if k=4, n=05

But why are we not considering the following cases too:
if k=5, n=04
if k=10, n=02
if k=20, n=01

Math Expert
Joined: 02 Sep 2009
Posts: 46207
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

02 Jan 2017, 05:24
9
1
1
shankey_sehgal@yahoo.com wrote:
I am not clear with the solution.

nk+4 = 24
nk = 20

if k=1, n=20
if k=2, n=10
if k=4, n=05

But why are we not considering the following cases too:
if k=5, n=04
if k=10, n=02
if k=20, n=01

When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true?

I. n is even
II. n is a multiple of 5
III. n is a factor of 20

A) III only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

When 24 is divided by the positive integer n, the remainder is 4:

24 = qn + 4, where q is a quotient, n is a divisor and 4 is the remainder. Notice that the remainder is always less than the divisor, so n > 4.

qn = 20.

q = 1 and n = 20.

q = 2 and n = 10.

q = 4 and n = 5.

_________________
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2758
Location: United States (CA)
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

21 Jan 2018, 19:56
Bunuel wrote:
When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true?

I. n is even
II. n is a multiple of 5
III. n is a factor of 20

A) III only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

We are given that when 24 is divided by n, the remainder is 4. Thus, we see that n can be 5, 10, or 20.

Of the answer choices, we see that n must be a multiple of 5 or a factor of 20.

_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Director
Joined: 09 Mar 2016
Posts: 605
When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

06 May 2018, 04:45
Bunuel wrote:
shankey_sehgal@yahoo.com wrote:
I am not clear with the solution.

nk+4 = 24
nk = 20

if k=1, n=20
if k=2, n=10
if k=4, n=05

But why are we not considering the following cases too:
if k=5, n=04
if k=10, n=02
if k=20, n=01

When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true?

I. n is even
II. n is a multiple of 5
III. n is a factor of 20

A) III only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

When 24 is divided by the positive integer n, the remainder is 4:

24 = qn + 4, where q is a quotient, n is a divisor and 4 is the remainder. Notice that the remainder is always less than the divisor, so n > 4.

qn = 20.

q = 1 and n = 20.

q = 2 and n = 10.

q = 4 and n = 5.

Bunuel hello

one question, if $$q = 1$$ and $$n = 20$$, then it means that $$n$$ is even, why then first option (I. n is even ) is not correct we divide by even $$n$$ which is $$20$$ and remainder is $$4$$, so my question why to exclude option one in which $$n$$ is even

thank you and have a good day
Math Expert
Joined: 02 Sep 2009
Posts: 46207
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

06 May 2018, 05:48
1
dave13 wrote:
Bunuel wrote:
shankey_sehgal@yahoo.com wrote:
I am not clear with the solution.

nk+4 = 24
nk = 20

if k=1, n=20
if k=2, n=10
if k=4, n=05

But why are we not considering the following cases too:
if k=5, n=04
if k=10, n=02
if k=20, n=01

When 24 is divided by the positive integer n, the remainder is 4. Which of the following statements about n must be true?

I. n is even
II. n is a multiple of 5
III. n is a factor of 20

A) III only
B) I and II only
C) I and III only
D) II and III only
E) I, II, and III

When 24 is divided by the positive integer n, the remainder is 4:

24 = qn + 4, where q is a quotient, n is a divisor and 4 is the remainder. Notice that the remainder is always less than the divisor, so n > 4.

qn = 20.

q = 1 and n = 20.

q = 2 and n = 10.

q = 4 and n = 5.

Bunuel hello

one question, if $$q = 1$$ and $$n = 20$$, then it means that $$n$$ is even, why then first option (I. n is even ) is not correct we divide by even $$n$$ which is $$20$$ and remainder is $$4$$, so my question why to exclude option one in which $$n$$ is even

thank you and have a good day

The question asks which of the following MUST be true not COULD be true. n is not necessarily even, it could also be odd (n = 5).
_________________
Intern
Joined: 31 Jul 2017
Posts: 46
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

18 Jun 2018, 08:39
N can be either 5 or 20 or both, so only option 2 and 3 work
Manager
Joined: 07 Feb 2017
Posts: 91
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic [#permalink]

Show Tags

18 Jun 2018, 09:05
24 = nz + 4
n, z integers; n > 4

20 = nz
n = 5, 10, 20

I. n = 5; not true
II. must be true
III. must be true

Re: When 24 is divided by the positive integer n, the remainder is 4. Whic   [#permalink] 18 Jun 2018, 09:05
Display posts from previous: Sort by