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

Question

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)

ScottTargetTestPrep · Accepted Answer

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

KSBGC · Answer

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.

samlovebar · Answer

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

KSBGC · Answer

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.

ironsheep · Answer

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.

Bunuel · Answer

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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For other subjects:
 ALL YOU NEED FOR QUANT ! ! ! 
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EgmatQuantExpert · Answer

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

suganyam · Answer

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 ///

Pksri · Answer

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)

Ezio23 · Answer

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

100mitra · Answer

Only condition possible is a=b and both reminder must be same, can be acheived with number 6x6 =36 - Option B

nilsruge · Answer

a = 2b (or b = 2a) is also an option:

a/b = 2b/b = 1 R b and b/a = b/2b = 0 R b

24 = 2*2*2*3 -> not possible
30 = 2*3*5 -> not possible
36 = 2*2*3*3 -> not possible

Not the case with these numbers, but should be considered.

e.g. 72 = 2*2*2*3*3 = (2*6)*6 = 12*6 -> 12/6 = 1 R 6 and 6/12 = 0 R 6

bumpbot · Answer

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

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