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For positive integers a and b, the remainder when a is divided by b is
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Bunuel
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For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  29 Jul 2018, 23:21
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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


(PS01466)
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ScottTargetTestPrep
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  10 Aug 2018, 17:54
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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 [#permalink] New post  30 Jul 2018, 01:02
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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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samlovebar
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  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.


The best answer is B.

when b is divided by a , if b<a ,the result isn't a fraction but b!
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KSBGC
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  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.


The best answer is B.

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.
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ironsheep
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  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.
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Bunuel
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  23 Jul 2019, 22:02
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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 --> \(5=0*6+5\),
or example from your post:
2 divided by 5 yields a reminder of 2 --> \(2=0*5+2\).

6. Remainders



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EgmatQuantExpert
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  25 Jul 2019, 02:29
Expert Reply

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.
Correct answer: Option B
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  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 ///
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  14 Jun 2020, 01:43
a and b are positive integers.

Equ 1: a/b = b.Quotient + remainder
Equ 2: b/a = a.Quotient + remainder

If both the values are same; a.Quotient + remainder = b.Quotient + remainder

It leaves with a = b.

From the given answers the only possibility is 36 (6*6)
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink] New post  20 Oct 2020, 23:01
Let R(a/b) = a - k*b
R(b/a) = b - m*a
where k and m are integers that satisfy the above two equations.

give that R(a/b) = R(b/a)
b can be represented as a*(1+m)/(1+k)

a*b = a^2 * some number

a*b is thus an integral multiple of a PSq
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Re: For positive integers a and b, the remainder when a is divided by b is [#permalink]
20 Oct 2020, 23:01
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