OG 13 PS # 95 -- Integer and remainder

richewalsh 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

There are a few ways to tackle this question.

One way is to examine a few other fractions.
7/2 = 3 with remainder 1.
7/2 = 3 1/2 = 3.5
Notice that 0.5 = 1/2

Another example:
11/4 = 2 with remainder 3.
11/4 = 2 3/4 = 2.75
Notice that 0.75 = 3/4

Now onto the question....

So, we know that x/y = some value with remainder 9
If x/y = 96.12, we can conclude that 0.12 = 9/y
Now solve for y.
0.12 = 9/y
12/100 = 9/y [rewrite 0.12 as 12/100]
Simplify to get: 3/25 = 9/y
At this point, we might already see that y = 75. If we don't spot this, we can always cross-multiply.
We get: 3y = (25)(9)
Solve to get y = 75

Cheers,
Brent

Hi richewalsh,

Both Mitch and Brent have provided similar algebra explanations. Here's a way to use Number Properties, the answer choices and "brute force" to find the solution.

In this prompt, we're told that X and Y are INTEGERS.

X/Y = 96.12 can be written as....

X = 96.12(Y)

The Y has to "multiply out" the .12 so that X becomes an integer. Since .12 is such a weird value, there can't be that many numbers that X and Y could be. Since none of the answers ends in 00, we need to find another way to multiply out the .12 - the only way to do it is with a multiple of 25. Eliminate A, C and E.

Between B and D, we just need to find the one that matches the rest of the info in the prompt (X/Y = 96.12 and X/Y has a remainder of 9)

Answer B: If Y = 75, then X = 7209

7209/75 gives a remainder of 9 THIS IS A MATCH

Final Answer: B

GMAT assassins aren't born, they're made,
Rich

richewalsh 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?

Thanks in advance, the explanation in the book wasn't of much help.

Solution:

This problem can be solved by using 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. Thus, we can say:

x/y = Q + 9/y

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

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, as shown here:

9/y = 3/25

3y = 9 x 25

y = 225/3 = 75

Answer: B