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Math Expert V
Joined: 02 Sep 2009
Posts: 64174
For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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1
35 00:00

Difficulty:   15% (low)

Question Stats: 80% (01:54) correct 20% (02:08) wrong based on 900 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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Target Test Prep Representative V
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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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9
6
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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VP  D
Joined: 31 Oct 2013
Posts: 1489
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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5
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  B
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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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  D
Joined: 31 Oct 2013
Posts: 1489
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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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  B
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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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 V
Joined: 02 Sep 2009
Posts: 64174
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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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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e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3367
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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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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Intern  S
Joined: 19 Jan 2019
Posts: 46
Re: For positive integers a and b, the remainder when a is divided by b is  [#permalink]

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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

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