(p/100)(3p)=p-(p^2/100)
or, 3p^2=(100P-p^2)
or, p =25

So, the answer is B.

Here it is given P% of 3P is P% less than P,

i.e we have \(\frac{P}{100} * 3P =\) \(P-(\frac{P}{100} * P)\)

or \(3P^2 =\) \(100P - P^2\)

OR \(4P = 100\)

OR \(P =25\) i.e option B
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The wording "P % less than P" was confusing for me. I thought it's P - P/100 on the left-hand-side.

P-(\frac{P}{100} * P)
how you figured out this RHS like that?

These are basic rules of % GRE problems, however.

If you do nor re-brush your math skills then is difficult to attack more difficult questions.

Translating math into words

P % of 3P is P % less than P

P% means \(\frac{P}{100}\)

of 3P means * 3P

is means =

P% less than p means a certain quantity such as 100 less a certain % we could say 10% which is equal to 90%

As such, P - (P/100*P). If you wanna from 100 to arrive directly to 90 you multiply 100* 0.9 and the result is 90.

Hope this helps.

Regards
_________________

If P% less than P meant.

P - (p/100)* p

What does P% more than P mean??
would that equal to P + (P/100)*P

Exactly.

Simpler, if you do have 100 or 80 or 75 you have to multiply for 100+15% (if the % change is 15 for instance)

100 * 1.15 = 115 or 80*1.15 you do have 100 or 80 plus 15% directly.

if you wanna take out the % you do 80 * 0.85% (100-15).

Hope this helps.
_________________

thanks

I was quite bogged down in the confusing p%p and so on. But I got it this way:
p-p%*3p=p%p [Since P%*3P <P by P%*P]
p=25.

An alternative approach to the problem should the direct translation prove difficult is to use the choices and backsolve. When backsolving always attempt to logically eliminate any impossible choices. In this case, it might be possible to eliminate the largest two choices since, 50% of 3 x 50 would be a value larger than P itself and thus not satisfy the conditions of the problem.

Then we can take the middle remaining choice, in this case choice B 25 and walk through the steps to see if it matches the conditions of the problem. So, use the provided calculator to determine that 25% of 75 = 18.75. Now, check to see if 18.75 is 25% less than 25 by using the percent change formula which is (difference/original) x 100. In this case the difference is 6.25 and the original would be our plugged in value of p which is 25. 6.25 ÷ 25 = 0.25 x 100 = 25%, therefore choice B 25 matches all conditions of the problem and is the correct choice.

Could someone explain why we multiply the (p/100*) with P?
I am having trouble grasping why that last multiplication is needed
Thank you for your answers

Key concept #1: p percent = p/100
For example, 17% = 17/100

Key concept #2: p percent of N is the same as p/100 of N
So, for example, 29% of 53 = 29/100 of 53 = (29/100)(53)

Key concept #3: p percent less than N is the same as N - (p percent of N)
For example, 10% less than 8 = 8 - (10% of 8) = 8 - 0.8 = 7.2


So....p percent less than p = p - (p% of p)
= p - (p/100 of p)
= p - (p/100)(p)
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Solution:

P % of 3P is P % less than P

Note:
P% of something means P/100 * (that thing) ... (i)

Another point: How to interpret P% less than P:

Note that P represents 100% of P (since 100% of P = 100/100 * P = P ---- from (i) above)
Thus, x% less than P would mean that from 100%, we reduce x% and get (100 - x)% of P

Thus: P% less than P means (100 - P)% of P = (100 - P)/100 * P

Thus, we have:

P % of 3P is P % less than P

=> (P/100) * 3P = (100 - P)/100 * P

Cancelling P from both sides:

(P/100) * 3 = (100 - P)/100

=> 3P = 100 - P
=> P = 25

Answer B
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