Question: c percent of c

Comment on c percent of c

Since ab/100=c, if we plug in the second statement (c=b/a), we get a^2=100 and thus a=10. Similarly, b=10. Therefore, we can calculate c% of C.
Could you please check?
gmat-admin's picture

How did you conclude that b = 10?

Apologies. I made a silly mistake. Anyway, I really like all your videos. They are amazing.
Thank you so much.
gmat-admin's picture

Glad you like them!

Is it necessary that the solution should have only numerical value or can there be variables as well?
gmat-admin's picture

Great question.
If a Data Sufficiency question asks us to determine the value of some variable, we must be able to provide a single numerical value in order to conclude that the statement is sufficient.

Here's an example:

What is the value of x?
(1) 5x = 2k
If we try to solve for x, we get x = 2k/5. Since we can't provide an actual numerical value for x, statement 1 is not sufficient.

Can we write question stem like:

C=0.01ab and we need to find 0.01c^2 -?

from statement 1:
ab=2500/c replace in question stem c=0.01 * 2500/c and hence c^2=25 ; from here we can replace 0.01C^2= 0.01*25=0.25 - Suff

from statement 2:
a=b/c replace in question stem c=0.01*b*(b/c) , multiply both sides with c and get c^2=0.01*b^2
and we need to find:
0.01c^2=0.01*(0.01*b^2 ) - Insuf
gmat-admin's picture

That's a valid solution - nice work.

Hi I have a question, would this be considered a difficult question on the GMAT? Is knowing how to master a question like this essential to a score over 650 on the gmat? (Also, please answer this one instead of the last one because I didn't check email notifications to the other comment so I might not get a notification.)
gmat-admin's picture

This is a very difficult question. I'd say the difficulty level of this question is above 700. On test day, you could still get this question incorrect and still score over 750. So, don't worry about it too much. That said, be sure you understand the solution, so that it may help you with similar questions.

Fshew! Great thank you!!

Hi Brent

At 2min into the video you simplify the (AB/100 /100) to (AB/100 * 1/100) I don't understand this step?

Wouldn't it be (AB/100 * 100/1) ?
Rules of dividing by a fraction?

gmat-admin's picture

To divide fractions, we multiply by the reciprocal of the divisor.

That is, a/b ÷ c/d = a/b x d/c
Likewise, (a/b)(c/d) = a/b x d/c

First, (AB/100)/(100) is the same as (AB/100)/(100/1)

So, (AB/100)/(100) = (AB/100)/(100/1)
= (AB/100) x (1/100)

Does that help?

Yes, thank you, I was manipulating the fraction incorrectly.

Hi Brent,
Is this a valid approach:
Question tells us that a/100 * b = c --> ab/100=c --> ab=100c
St1) abc = 2500 --> ab =2500/c
Substitute ab with 2500/c in ab=100c --> 2500/c = 100c
Cross multiply we get 2500 = 100c^2
Divide both sides by 100 to get 25 = c^2 --> c =5 --> St1 is Suff.
St2) is not Suff.

gmat-admin's picture

That's a perfectly valid solution.
Nice work!

Hi Brent,

I tried to solve it in some other way.
First I concluded that c/b = a/100, so c = ab/100.

The target question is to find c percent of c, which is c/100 = X/c, isn't it?
So, our target is to find X, which is equal to c²/100.
Using this approach, the answer is C, because we need both conditions to solve an equation.
gmat-admin's picture

Everything you've said is true.
The only thing is that we DON'T need both statements to determine the value of c²/100

Statement 1 says abc = 2500
IMPORTANT: On its own, statement 1 is not enough to determine the value of c²/100
However, we ALSO know that c = ab/100, which means ab = 100c

So, if we take statement 1 (abc = 2500), and replace ab with 100c, we get: (100c)c = 2500
Simplify 100c² = 2500, which means c² = 25

Now that we know c² = 25, we CAN determine the value of c²/100
c²/100 = 25/100 = 1/4

Does that help?


Will assigning values to a, b, and c work/not work for this question? Thanks.
gmat-admin's picture

The problem with testing values is that strategy only yields definitive results when we get conflicting answers to the target question.

For more on this, watch the following video starting from 5:55 -


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