Lesson: Conversions with Fractions and Decimals

Comment on Conversions with Fractions and Decimals

Can you please help me with an explanation of the answer to the following question:

If r and s are positive integers, is r/s a terminating decimal?
Statement 1: r is a factor of 100
Statement 2: s is a factor of 500
gmat-admin's picture

You bet!

I have provided a full solution here (2nd post): http://www.beatthegmat.com/if-r-and-s-are-positive-integers-is-r-s-a-ter...


Hi Brent
I couldn't understand where are thos r=1, s=4 or r=1 s=3 coming from. Couldn't get the relation, can you help about that?
gmat-admin's picture

Link: http://www.beatthegmat.com/if-r-and-s-are-positive-integers-is-r-s-a-ter...

Once I decided to test some values, I needed to come up with values that satisfy the given conditions.

For statement 1, this means that r must be a factor (aka divisor) of 100. For the s-value, there are no conditions in statement 1, but the given information tells us that s is a positive integer.

NOTE: When we test value like this, our goal is to determine whether there are certain values that will provide different answers to the target question (which means the statement is not sufficient.

So, I recognized that the values r = 1 and s = 4 yield a terminating decimal, and the values r = 1 and s = 3 yield a NON-terminating decimal.

For more on testing values, see this article: http://www.gmatprepnow.com/articles/data-sufficiency-when-plug-values


Hi Brent,

this question has the following statements on gmat club:

1) 1/r is a terminating decimal
2) 1/s is a terminating decimal

but it has the following statements on beat the gmat.

1) r is a factor of 100
2) s is a factor of 500

I was reviewing your answer on gmat club site but the statements in the answer are not the same as the original question. could you please let me know whether these statements relate or something else.


gmat-admin's picture

Thanks for the heads up!

There are actually two different questions at play here:

I must have assumed they were the same question and simply inserted my solution to one question to the other question.

I've now fixed the situation.

Is there a set of slides available that has all the recommended information to be memorized? For example, in this video, the 'base conversion table of fractions to decimals' is very useful.

I can take a screenshot, or take a note. But if a collections of slides of 'suggested items to memorize' is available, that would be wonderful.

gmat-admin's picture

In most cases, I think it's best that students take their own notes. The process of summarizing and condensing information is a tremendous learning activity and will help reinforce the concepts you've learned.

With that said, you can download my math flash cards here: https://www.gmatprepnow.com/content/free-content


I just downloaded the Math flash cards - total of 162 pages. I will review the slides and select which pages to print.

I assume the Math flash cards cover everything in all the Math videos? Thanks!
gmat-admin's picture

Yes, pretty much all of the key concepts are covered in the flashcards.

Perfect. The Math flashcards will be very useful to me. Thanks!
Yulia's picture

Hi Brent,

Could you please explain me why statenent 2 is insufficient? https://gmatclub.com/forum/if-a-and-b-are-positive-integers-is-a-b-207838.html

If a and b are positive integers, is a/b = 5/8 ?

(1) 1/2 < a/b < 2/3

(2) b = 8

Statement 2 I percieved as if b=8 then a/8=5/8 > a=5 so sufficient. Where I am wrong?
gmat-admin's picture

Question link: https://gmatclub.com/forum/if-a-and-b-are-positive-integers-is-a-b-20783...

This is a common error.
Our goal here is to determine whether or not a/b = 5/8.
That is, without any extra information, it could be the case that a/b = 5/8 or it could be the case that a/b ≠ 5/8.

While analyzing statement 2, you're assuming that the equation, a/b = 5/8, is true, when we don't yet know that (in fact, that's the goal of this question).

With statement 2, all we can be certain of is that b = 5.
So it COULD be the case that a = 1, in which case the answer to the target question is "NO, a/b does not equal 5/8"
Or it COULD be the case that a = 5, in which case the answer to the target question is "YES, a/b equals 5/8"

Does that help?

Hello, quick question.. how did you turn 1.15 to 23/20? Could you elaborate. Thanks
gmat-admin's picture

I'm not sure where I made that conversion, but here's how I'd typically do that:
1.15 = 115/100
= 23/20 (after dividing numerator and denominator by 5)

Here's another way...
1.15 = 115/100
= 230/200 (after multiplying numerator and denominator by 2)
= 23/20 (after dividing numerator and denominator by 10)

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