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Founder  Joined: 18 Apr 2015
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If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
Expert's post 00:00

Question Stats: 73% (01:37) correct 26% (02:44) wrong based on 97 sessions

If P > 0 and P % of 3P is P % less than P, then P equals:

A. 5

B. 25

C. 40

D. 50

E. 64
[Reveal] Spoiler: OA

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GRE Prep Club Members of the Month: Each member of the month will get three months free access of GRE Prep Club tests. Intern Joined: 08 Dec 2017
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Re: If P > o and P % of 3P is P % less than P, then P equal [#permalink]
1
KUDOS
(p/100)(3p)=p-(p^2/100)
or, 3p^2=(100P-p^2)
or, p =25 VP Joined: 20 Apr 2016
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WE: Engineering (Energy and Utilities)
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
3
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Carcass wrote:

If P > 0 and P % of 3P is P % less than P, then P equals:

A. 5

B. 25

C. 40

D. 50

E. 64

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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Manager Joined: 15 Feb 2018
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
The wording "P % less than P" was confusing for me. I thought it's P - P/100 on the left-hand-side.
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
P-(\frac{P}{100} * P)
how you figured out this RHS like that?
Founder  Joined: 18 Apr 2015
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
Expert's post
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
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
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
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
Expert's post
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.
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Intern Joined: 07 Jan 2019
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
thanks
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
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.
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
Expert's post
Quote:
If P > 0 and P % of 3P is P % less than P, then P equals:

A. 5

B. 25

C. 40

D. 50

E. 64

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.
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
Could someone explain why we multiply the (p/100*) with P?
I am having trouble grasping why that last multiplication is needed GRE Instructor Joined: 10 Apr 2015
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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
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Expert's post
bubidag wrote:
Could someone explain why we multiply the (p/100*) with P?
I am having trouble grasping why that last multiplication is needed

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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Re: If P >0 and P % of 3P is P % less than P, then P equal [#permalink]
1
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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

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_________ Re: If P >0 and P % of 3P is P % less than P, then P equal   [#permalink] 24 Jan 2020, 05:31
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