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When 24 is divided by the positive integer n, the remainder
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24 Aug 2020, 09:50
24 Aug 2020, 09:50
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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
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
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24 Aug 2020, 09:50
24 Aug 2020, 09:50
Expert Reply
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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
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Re: When 24 is divided by the positive integer n, the remainder
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24 Aug 2020, 16:27
24 Aug 2020, 16:27
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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.
