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

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

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New post 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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New post 02 Jan 2017, 05:24
12
1
2
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


Please clarify my doubt.


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.

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

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New post 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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New post 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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New post 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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New post 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

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

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New post 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.

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

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New post 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


Please clarify my doubt.


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.

Answer: D.


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

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New post 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


Please clarify my doubt.


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.

Answer: D.


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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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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

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New post 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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New post 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

Answer D
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Re: When 24 is divided by the positive integer n, the remainder is 4. Whic &nbs [#permalink] 18 Jun 2018, 09:05
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