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

Question

For positive integers a and b, when a is divided by b the remainder is 12. If a/b = 32.16, what is the value of b?

A. 25
B. 32
C. 64
D. 75
E. 96

pushpitkc · Accepted Answer

Since a/b = 32.16, the quotient is 32
Remainder is .16*x = 12
x = 12/.16 = 1200/16 = 300/4 = 75(Option D)

To check if our answer is correct, 75*32 + 12 = 2412.
This when divided by 75 gives us 32.16

JeffTargetTestPrep · Answer

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:
 
When positive integer a is divided by positive integer b, if integer Q is the quotient and r is the remainder, then a/b = Q + r/b.

In this problem, we are given that when positive integer a is divided by positive integer b, the remainder is 12. So, we can say:
 
a/b = Q + 12/b

We also are given that a/b = 32.16. Using the remainder formula, we can say:
 
a/b = 32.16
 
a/b = 32 + 0.16
 
a/b = 32 + 16/100
 
Because Q is always an integer, we see that Q must be 32, and thus the remainder 12/b must be 16/100. We can now equate 12/b to 16/100 and determine the value of b.
 
12/b = 16/100
 
12/b = 4/25

12 x 25 = 4b

3 x 25 = b

75 = b

Answer: D

gracie · Answer

16/100=12/b
b=75
D

matthewsmith_89 · Answer

I would do process elimination for this
 a/b = 32.16
a/b = 32 4/25

Answer B, C and E are incorrect because they are not multiple of 25.

Then I would do process elimination further

A 25 x 32 = 800 + 12 (Remainder) = 812

812/25 = 32.48. Not the answer

D 75 x 32 = 2400 + 12 (Remainder) = 2412

2412/75 = 32.16 Answer

Answer is D

praveenmittal95605 · Answer

Since a/b = 32.16, Rem is 0.16*b = 12; b = 12/.16 = 1200/16 = 300/4 = 75(Option D)

A_Nishith · Answer

CONCEPT :  Dividend = Divisor * Quotient + Remainder

Given,  a = b*quotient + 12 
Since a/b = 32.16, the quotient is 32
Remainder is  0.16*x = 12 
x = 12/.16 = 1200/16 = 300/4 =  75 
 Answer: D

Budhaditya_Saha · Answer

I solved it in an easier way without any calculation.

It is stated that a/b gives a remainder 12. Hence the min value of b is 13. Now since only option D (i.e. 75) is the only option which is a multiple of 13, hence the answer will be 75. In this way I was able to solve it within 30secs.

Correct me if I'm wrong.

BrushMyQuant · Answer

For positive integers a and b, when a is divided by b the remainder is 12. If a/b = 32.16

\frac{a}{b}  = 32.16
 => a = 32.16*b
=> a = 32b + 0.16b

Dividend = Quotient * Divisor + Remainder

=> a when divided by b gives 32 as quotient and 0.16b as remainder
=> 0.16b = 12
=> b =  \frac{12}{0.16}  = 75

So,  Answer will be D 
Hope it helps!

Watch the following video to MASTER Remainders

https://www.youtube.com/watch?v=P0S6j2uTaj4

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

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