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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # When 24 is divided by the positive integer n, the remainder is 4. Whic

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Math Expert V
Joined: 02 Sep 2009
Posts: 60553
When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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7
79 00:00

Difficulty:   55% (hard)

Question Stats: 61% (01:38) correct 39% (01:40) wrong based on 1691 sessions

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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

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Math Expert V
Joined: 02 Sep 2009
Posts: 60553
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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16
1
13
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.

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Director  G
Joined: 20 Feb 2015
Posts: 734
Concentration: Strategy, General Management
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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3
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
Intern  Joined: 20 Jan 2016
Posts: 42
GMAT 1: 600 Q47 V26
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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

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Intern  Joined: 06 Oct 2015
Posts: 1
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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...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: 115
GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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  B
Joined: 12 Dec 2016
Posts: 1
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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

Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9072
Location: United States (CA)
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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.

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VP  D
Joined: 09 Mar 2016
Posts: 1225
When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 60553
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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).
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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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N can be either 5 or 20 or both, so only option 2 and 3 work
Manager  S
Joined: 07 Feb 2017
Posts: 173
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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

Intern  B
Joined: 01 May 2017
Posts: 34
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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take numbers that give 4 remainder when divided by 24. here we have only 5. Now validate with statement given.
Intern  Joined: 28 Sep 2019
Posts: 1
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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what about 15 - multiple of 5 which gives remainder = 9 . why no one is considering 15 integer.

ScottTargetTestPrep wrote:
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.

CrackVerbal Quant Expert G
Joined: 12 Apr 2019
Posts: 353
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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In this question, we are trying to find out which statement ‘Must be true’ or always true. If a statement has to always be true, it has to hold true whatever case you take. Even if it fails on one, it means that the statement is not always true.

This is the basis for our strategy for ‘Must be true’ questions. We always try to make a statement FALSE, by taking simple cases and eliminate options. Whatever option is left should be the answer. However, in this question, we can actually solve the entire question based on concepts and won’t have to take recourse to cases. Let’s see how we can do that.

When 24 is divided by the positive integer n, the remainder is 4. This means, we can write 24 in terms of n as follows:
24 = n*k + 4, where k is the quotient in the division process. Remember that when you have the remainder given, the quotient will always be an integral value. Therefore, k is an integer.

Re-arranging the terms of the equation above, we have n*k = 20. This means that n is a factor of the number 20. So, the possible values for n are 1, 2, 4, 5, 10 and 20.
But, when 24 was divided by n, the remainder was 4. This means that the value of n should be more than 4 since the remainder cannot be more than the divisor ever.
Therefore, n can only be 5 or 10 or 20. As you see, when you divide 24 by any of these three numbers, the remainder will be 4.

From this, we can say that statement I is not always true since 5 is not even. But, clearly, statement II is definitely true since all of 5, 10 and 20 are multiples of 5.

Coming to statement III, this is something we established during our analysis of the question stem, isn’t it. So, statement III has to be true.

The correct answer option is D.

Hope that helps!
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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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nit99 wrote:
what about 15 - multiple of 5 which gives remainder = 9 . why no one is considering 15 integer.

ScottTargetTestPrep wrote:
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.

24/15 = 1 remainder 9, not remainder 4. That is why we do not consider 15.
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# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: When 24 is divided by the positive integer n, the remainder is 4. Whic   [#permalink] 13 Oct 2019, 17:40
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