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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!
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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
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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⋅Q+R where 0≤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≤R<|B|.
Since 24 is divided by a positive integer n and its remainder is 4, we have 24=n⋅q+4 for some integer q where 0≤4<n.
Thus we have n⋅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.
