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

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Math Expert
Joined: 02 Sep 2009
Posts: 56272
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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55% (hard)

Question Stats:

59% (01:38) correct 41% (01:36) wrong based on 1770 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
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Posts: 56272
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
12
1
10
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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Joined: 20 Jan 2016
Posts: 43
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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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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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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: 56272
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: 36
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.
Re: When 24 is divided by the positive integer n, the remainder is 4. Whic   [#permalink] 12 Jan 2019, 01:04
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