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For positive integers a and b, the remainder when a is divided by b is

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For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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New post 30 Jul 2018, 00:21
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For positive integers a and b, the remainder when a is divided by b is equal to the remainder when b is divided by a. Which of the following could be a value of ab ?

I. 24
II. 30
III. 36

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III


NEW question from GMAT® Quantitative Review 2019


(PS01466)

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For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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New post 30 Jul 2018, 02:02
Bunuel wrote:
For positive integers a and b, the remainder when a is divided by b is equal to the remainder when b is divided by a. Which of the following could be a value of ab ?

I. 24
II. 30
III. 36

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III


NEW question from GMAT® Quantitative Review 2019


(PS01466)


In this question , both a and b has to be equal. If a is greater than b we will have reminder but when we are going to divide b by a we get fraction as a result. So , a and b are equal.

Only option III meets the condition.

36 = 6*6

a/b = 6/6 = 1 + 0

b / a = 6/6 = 1 +0

Match the condition stated in the question.


The best answer is B.
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Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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New post 10 Aug 2018, 18:54
Bunuel wrote:
For positive integers a and b, the remainder when a is divided by b is equal to the remainder when b is divided by a. Which of the following could be a value of ab ?

I. 24
II. 30
III. 36

A. II only
B. III only
C. I and II only
D. II and III only
E. I, II, and III


The only way the remainder when a is divided by b is equal to the remainder when b is divided by a is a = b since then the remainder in both cases is 0. That is, if a = b, a/b = 1 R 0 and b/a = 1 R 0.

Since a = b, we see that ab must be a perfect square. So only III could be a value of ab.

Answer: B
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Re: For positive integers a and b, the remainder when a is divided by b is &nbs [#permalink] 10 Aug 2018, 18:54
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