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

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Math Expert
Joined: 02 Sep 2009
Posts: 62285
For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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29 Jul 2018, 23:21
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81% (01:54) correct 19% (02:09) wrong based on 825 sessions

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

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10 Aug 2018, 17:54
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5
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.

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Joined: 31 Oct 2013
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Concentration: Accounting, Finance
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For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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30 Jul 2018, 01:02
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2
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.

##### General Discussion
Intern
Joined: 09 Apr 2019
Posts: 2
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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15 Apr 2019, 10:17
KSBGC wrote:
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.

when b is divided by a , if b<a ,the result isn't a fraction but b!
VP
Joined: 31 Oct 2013
Posts: 1491
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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29 Jun 2019, 07:50
samlovebar wrote:
KSBGC wrote:
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.

when b is divided by a , if b<a ,the result isn't a fraction but b!

Read out the question properly. It is stated in the question that remainder is equal in both cases. Therefore a and b have to be equal.
Intern
Joined: 19 Jul 2019
Posts: 16
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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22 Jul 2019, 23:24
if a = 2, and b =4, then there wouldn't be any remainders, so the book should have 1 and 3 only as a answer choice. 2/4 equals .5 with no remainder and 4/2 equals 2 with no remainder, so the remainders are the same.
Math Expert
Joined: 02 Sep 2009
Posts: 62285
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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23 Jul 2019, 22:02
ironsheep wrote:
if a = 2, and b =4, then there wouldn't be any remainders, so the book should have 1 and 3 only as a answer choice. 2/4 equals .5 with no remainder and 4/2 equals 2 with no remainder, so the remainders are the same.

2 divided by 4 gives the remainder of 2.

When divisor (4 in our case) is more than dividend (2 in our case) then the reminder equals to the dividend. For example:
3 divided by 24 yields a reminder of 3 --> $$3=0*24+3$$;
or:
5 divided by 6 yields a reminder of 5 --> $$5=0*6+5$$,
2 divided by 5 yields a reminder of 2 --> $$2=0*5+2$$.

6. Remainders

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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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25 Jul 2019, 02:29

Solution

Given:
• a and b are positive integers.
• Remainder when a is divided by b = Remainder when b is divided by a

To find:
• The possible value of ab.

Approach and Working
The only case when the remainder of the division of a by b and b by a is equal when a=b.
Hence, ab =a^2
• So, ab can only be a perfect square.
• And, among the given option only 36 is a perfect square.

Hence, the correct answer is B.
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Posts: 49
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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08 Feb 2020, 10:32
I. 24
1*24 ,2*12,3*8,4*6 none have same rem
II. 30
1*3 ,2*15,3*10,5*6 none have same rem
III. 36
6*6 has the same rem ///
Re: For positive integers a and b, the remainder when a is divided by b is   [#permalink] 08 Feb 2020, 10:32
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