Exam 5: The Power of Percents

[rishijmehta]

I'm having trouble seeing the leep where it says in the answer explanation, "Because a and b are positive integers and a < b, we know that the value of b must be greater than or equal to 2.".

Thanks for the help! Sorry looks like everything wont paste over.

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If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

We can rephrase the question as follows:

Is an integer?

Is an integer?

(1) INSUFFICIENT: We can simplify the given equation and substitute into our rephrased question:

Is an integer?

Is an integer?

Is an integer?

The variable c is an integer, but we have no idea whether c is a multiple of 100. c/100 might be an integer, but it also might not be.

(2) SUFFICIENT: We can substitute this value into our rephrased question:

Is an integer?

Is ab(100b-2) an integer?

Because a and b are positive integers and a < b, we know that the value of b must be greater than or equal to 2. Therefore, b−2 > 0. If this is the case, then the minimum possible value of 100b-2 is 1000 = 1 and every other possible value is also an integer (1001, 1002, and so on). As a result, the product of the integers a, b, and 100b-2 must also be an integer.

The correct answer is B.

[rishijmehta]

Ah, I am all set. I got it. Pretty straight forward, but I guess I needed time away from it!

Since a and b are positive integers and b>a, b must be 2 or greater since the lowest a could be is 1.

[tim]

Cool. Let us know if you have any further questions.

[drtfyghujd403]

I dont quite understand the reasoning behind Statement 2. Can anyone explain please? I do see how Statement 1 is not sufficient though.
Heres the full question:
If a, b, and c are positive integers such that a < b < c, is a% of b% of c an integer?

(1)b = (a/100)^-1

(2) c = 100^b

[RonPurewal]

as a starting hint, "a% of b% of c" can be rewritten as (a/100)(b/100)(c), or abc/10000.

beyond this point, you'll have to state specifically what you don't understand.
what have you tried?
which parts do you understand?
where are you getting stuck?
etc.

see, these problems already have answer keys. so, if you just say "i'm stuck" without any specifics, then the best course of action is simply to point you to the answer key.

[RonPurewal]

also—
if there's something in the answer key that you don't understand, please copy and paste that part of the answer key into your question.

thanks.