OG - PS - #D13

[Carla]

Question:

s>0
t>0
s,t = int

s/t = 64.12

remainder = ?




I was able to come up with the equation for the remainder based on the given information as follows:

(1) r = s-64t --> s = 64t + r

From the solution:

We have to rearrange

s/t = 64.12

s = 64.12 t -->

(2) s = 64t + 0.12t


(1) and (2) together --> 64t + 0.12 t = 64t + r

--> 0.12t = r

Now it seems that we want a solution where t = integer... this is my question.. why do we need t to be an integer? It also would take me a long time to test out for values of t from every given answer choice..

The correct answer was t = 375 which is "E".

Any help on this would be great!

Thanks,
Carla

[Guest]

Carla -

The answer to the question "why does t have to be an integer" is that you are told that s,t are integers in the problem statement. You also know that the remainder is an integer. So you know from your equation .12t = r that .12t is an integer.

Note that .12 = 12/100 = 3/25. So any value of t that is not divisible by 25 can be ruled out as it would give you a non-integer value for the remainder, .12t. You didn't post the answer choices, so I'm not sure if that would be useful information or not.

Cheers,
Jeff

[dbernst]

So the forums can benefit future users or those who do not possess the Official Guide, please post the entire question with its answer choices. Once it is posted we will be glad to help explain the solution (though I think Jeff already has done a great job with this one!).

Thanks!