OG PS #106 12th edition - Properties of numbers

[barroblock]

I am struggling to understand this problem, the explanation in the book doesn't seem very clear for me. Anyone can provide a simpler explanation?

When positive integer x is divided by positive integer y, the remainder is 9. If x/y = 96.12, what is the value of y?

A) 96
B) 75
C) 48
D) 25
E) 12

OA = B

[Abdulla]

here you go..

x/y = Q + R
x/y = Q + 9 ------(1)

x/y = 96.12
x= y 96.12
x= y 96 + y 0.12 -------(2)

from (1) and (2) we know that y0.12 = 9 -----> y= 9/0.12.
Therefore, y = 75.

B is the answer.

[DarkKnight]

since x/y has 9 reminder and given x/y=96.12, we can say:

96y + 9=x ---------1)

Also from above, x=96.12y=(9612/100)y=(2403/25)y. Substituting value of x in 1) we get,

96y + 9 = (2403/25)y.....2)

Solve 2) for y and you get Y=75.

Answer y=75.

[tohellandback]

By reasoning
so remainder is 9 and x/y=96.12
after the division we are left with 9. when we put a decimal it become 90
check with the answer options
75 when divides into 90 , it gives 1 and remainder 15.
150 when divided by 75 leaves 0 as remainder
so 75 is the answer

[avanishjoshi]

Dividend = Divisor * Quotient + remainder
Therefore X = YQ + 9

Now given that X/Y = 96.12 , that means the when X is divide by Y the quotient is 96.12
Therefore X = Y(96.12) + 9

But the product of divisor and the quotient should always be a integer.

Thefore for Y(96.12) to be an integer, from the given options Y could be 75 or 25 .

Substitute 75 , 75*9612/100 = 3*9612/4 = 3*1403.
Substitute 25 , 25*9612/100 = 9612/4 =1403 which will definitely not leave a remainder 9(It leaves 3).

Therefore 75 is the answer.

[artistocrat]

Here is another approach: 9/x (remainder)=12/100 (or 0.12)

12x=900; x=75