GRE Prep 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
Track
Your Progress
Practice
Pays
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
[#permalink]
24 Aug 2020, 09:50
24 Aug 2020, 09:50
1
Expert Reply
2
Bookmarks
00:00
Question Stats:
55% (01:13) correct
44% (01:07) wrong based on 58 sessions
Hide Show 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
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
Re: When 24 is divided by the positive integer n, the remainder
[#permalink]
24 Aug 2020, 09:50
24 Aug 2020, 09:50
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
For more theory and practice see our GRE - Math Book
Retired Moderator
Joined: 20 Aug 2020
Posts: 49
Given Kudos: 0
Re: When 24 is divided by the positive integer n, the remainder
[#permalink]
24 Aug 2020, 16:27
24 Aug 2020, 16:27
4
Carcass 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
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 have the following expression when an integer \(A\) is divided by an integer \(B\).
\(A = B \cdot Q + R\) where \(0 \le R < |B|\).
\(A, B, Q\) and \(R\) are called a dividend, a divisor, a quotient and a remainder, respectively.
Don't forget the restriction about the remainder \(0 \le R < |B|\).
Since 24 is divided by a positive integer \(n\) and its remainder is \(4\), we have \(24 = n \cdot q + 4\) for some integer \(q\) where \(0 \le 4 < n\).
Thus we have \(n \cdot q = 20\) where \(n > 4\).
It means \(n\) is a factor of \(20\), greater than \(4\). The possible values of \(n\) are \(5, 10\) and \(20\).
Thus, II and III only are true.
Therefore, D is the right answer.
