Remainder Problem

I think it's easier to think of this conceptually.

If we're working in the remainder system, there no such things as decimals. So if I've got 17 cookies and 4 friends, and I want to divide the cookies evenly, each friend gets 4 and the remainder is 1.

But in the decimal system, remainders are fine. So to go from the remainder system to the decimal system, I take the last cookie and cut into four parts, one for each friend. That gives me 1/4, or .25 additional cookies for everyone.

From this, I've got a useful relationship:

Remainder / Divisor = Decimal portion

Applied to our problem, we've got y friends and 9 cookies left, so

9 / y = .12

or y = 75

gmat009 wrote: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

This problem will be best solved using the remainder formula. Let’s first state the remainder formula:

When positive integer x is divided by positive integer y, if integer Q is the quotient and r is the remainder, then x/y = Q + r/y.

In this problem we are given that when positive integer x is divided by positive integer y, the remainder is 9. So we can say:

x/y = Q + 9/y

We also are given that x/y = 96.12. Using the remainder formula, we can say:

x/y = 96.12

x/y = 96 + 0.12

x/y = 96 + 12/100

Because Q is always an integer, we see that Q must be 96, and thus the remainder 9/y must be 12/100. We can now equate 9/y to 12/100 to determine the value of y.

9/y = 12/100

12y = 9 x 100

y = 900/12 = 75

Note: Had we simplified 12/100 to 3/25 first, we would have also obtained the same answer:

9/y = 3/25

3y = 9 x 25

y = 3 x 25 = 75

Answer: B

gmat009 wrote: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

We can create quotient/remainder equation, where the quotient Q is an integer:

x/y = Q + 9/y

We also are given that x/y = 96.12. Using the remainder formula we can say:

x/y = 96.12

x/y = 96 + 0.12

x/y = 96 + 12/100

Because Q is always an integer, we see that Q must be 96, and thus the remainder 9/y must be 12/100. We can now equate 9/y to 12/100 and determine the value of y.

9/y = 12/100

12y = 9 x 100

y = 900/12 = 75

Note: Had we simplified 12/100 to 3/25 first, we would have also obtained the same answer. See below.

9/y = 3/25

3y = 9 x 25

y = 3 x 25 = 75

Answer: B