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?

Hi,
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!

Hi,
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?

Cheers
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.

Thanks
Aladdin
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?

Cheers,
Brent

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 - https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1101

Cheers,
Brent

Hi, I did this in this way
ab=100c
abc in this ab can be replaced by 100c
100c*c=2500
c^2=25
c=5
and 5% of 5 is .25
gmat-admin's picture

Perfect!

Hi Brent,

c% of c= c/100*c= c^2/100; can i write it as c/10= ?

I have evaluated statement-1 to c = 5 or -5. Sufficient

statement-2: c=b/a; since ab=100c, substituting c value here then ab=100*b/a, by evaluating it we get a=+/-10; so insufficient.

Ans: A. Is this correct?

gmat-admin's picture

I'm not sure I follow your logic.

You're correct to say that: c% of c = c/100*c = c^2/100
However, we can simplify this to be " What is the value of c/10 ?", since c^2/100 and c/10 are not equivalent.

Also, how did you conclude that c = 5 or -5?

Since you did arrive at the correct answer, it's quite possible your steps are mathematically sound. I'm just not following your solution.

Also, how did you conclude that c = 5 or -5?

a percent of b equal to c=> a/100*b=c => ab/100=c

so ab=100c; substituted the 100c in statement 1 i.e. abc=2500 then (100c)c=2500
100c^2=2500 dividing 100 on both sides=> c^2=25 => c=+/-5
gmat-admin's picture

Okay perfect.

Since we have two possible values of c, we need to use each value to determine the value of c percent of c (the target question).
If c = 5, then c percent of c = 5% of 5 = 0.25
If c = -5, then c percent of c = -5% of -5 = 0.25
Since we can be certain but the answer to the target question is 0.25, statement 1 is sufficient

Hi Brent, question is what is C% of C?

St.1 calculation result is abc = 1/4. Not quite follow how is that answer the question? What did I miss? Thanks
gmat-admin's picture

Don't forget that the question has some given information.
GIVEN: a percent of b is c

In the video solution above, I used the given information to help rephrase the target question as "What is the value of abc/10,000?"
So, when statement 1 tells us that abc = 2500, we can definitely answer the REPHRASED target question (the value of abc/10,000 = 2500/10,000 = 1/4).

Here's a video lesson on rephrasing the target question: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1100

Thanks Brent for your reply. Think I lost sight of the rephrased question.
To clarify as C was substituted to derive abc/10,000 = 2500/10,000 = 1/4, therefore C = 1/4 ? Is my understanding correct?
gmat-admin's picture

No, we aren't saying that C equals 1/4.
Since we rephrased the target question as "What is the value of abc/10,000?," all we are saying is that abc/10,000 = 1/4 when abc = 2500

OK think I get it now. C% of C is rephrased as abc/10,000 and the calculation is 1/4 when abc = 2500?
Whoop this just show how important it is to rephrase the target question. Thanks Brent
gmat-admin's picture

That's exactly how we need to interpret those results.

Great thanks Brent for your patience and preseverence all the way until we get it right. Very much appreciated.

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