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

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Math Expert
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When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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03 Jul 2016, 11:25
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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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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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02 Jan 2017, 05:24
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1
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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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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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03 Jul 2016, 12:03
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
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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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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

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

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

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

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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

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

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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.

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

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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: 60627
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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

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

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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

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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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12 Jan 2019, 01:04
take numbers that give 4 remainder when divided by 24. here we have only 5. Now validate with statement given.
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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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09 Oct 2019, 06:09
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.

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Posts: 362
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic  [#permalink]

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10 Oct 2019, 00:43
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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13 Oct 2019, 17:40
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.
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
181 Reviews

5-star rated online GMAT quant
self study course

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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