Question: c is What Percent of b?

Comment on c is What Percent of b?

Loving your lessons, but I've missed something along the way and now I'm totally confused – when/where you can just multiply each side by a chosen number and thus cancel parts out.

I'm confused because I don't think this "when you can do it" was addressed (my mistake if it was) but the one time I tried to apply it – here – by multiplying both by X, that was apparently wrong.

Confused as to when and why and how you can just multiply by chosen numbers (and when not).
greenlight-admin's picture

Good question. When dealing with EQUATIONS, you can multiply both sides of the equation by a variable as long as you are certain that the variable does not equal zero.

The question that you reference ( is a much different question because it is a Quantitative Comparison question, in which we do not have an equation. Instead we are comparing the values of two quantities.

In Quantitative Comparison questions, we must be very careful when multiplying both quantities by a variable. When doing so, we must be certain that the variable is POSITIVE. More here:

Thank you, I'm a lot clearer on this now.

So I just plugged in the answer (from the answer choices) 8 x 1.25 which gave me 10. So my fraction ended up looking like 10/8 = 1.25. Since 8 is 80% of 10 I was able to get the same answer.
greenlight-admin's picture


I do it like this:

If c is 100, b is 125.
100 is 80% of 125.
therefore, c is 80% of b
greenlight-admin's picture

Your "testing values" approach is perfect!


1.25 converting it to a fraction is 1+1/4, how then did you get 5/4, please?
greenlight-admin's picture

Glad to help!

1.25 = 1 + 1/4
= 4/4 + 1/4
= 5/4


I came up with an faster method.
I don't know if it can be applied in other situations as well but it did over here.

Since it is given that
b/c=1.25 which can be written as 1.25/1
So b=1.25 and c=1

We can further solve or guess the right answer as We can now see that c is clearly more than 50% and the only option in the choice more than 50% is option E. Hence the answer is E.

Please let me know if this process is right and can be used in similar cases where some variable fraction is = some fraction.

greenlight-admin's picture

Very nice!!!

is there any way to solve this with the first method that you showed us in the last video?
greenlight-admin's picture

You bet.

If b/c = 1.25, there are infinitely many pairs of values that satisfy this.
For example,
5/4 = 1.25
125/100 = 1.25
25/20 = 1.25
1250/1000 = 1.25

Let's choose b = 25 and c = 20 (although any pair above we'll also work)
So our question becomes: 20 is what percent of 25?
In other words: 20/25 = p/100

Does that help?

Yes, thank you

question: when you flipped c/b to b/c, is that rule applicable to any fraction? I didn't know that could be done. Is there a general rule that allows for that?
greenlight-admin's picture

You're referring to what happens at 1:15 in the above video, where I say that, since b/c = 5/4, we also know that c/b = 4/5

In general, we can say: If x/y = a/b, then y/x = b/a
Please note that the above property does not work if x = 0 or y = 0.

So, for example, if w/z = 7/2, then it is also true that z/w = 2/7

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Always Scan First!

Whenever you encounter a quantitative question with answer choices, be sure to SCAN the answer choices before performing any calculations. In many cases, the answer choices provide important clues regarding how to best solve the question. 

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