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

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Math Expert
Joined: 02 Sep 2009
Posts: 57298
If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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08 May 2018, 01:23
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Question Stats:

62% (01:45) correct 38% (02:32) wrong based on 82 sessions

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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

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e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3018
Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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08 May 2018, 02:57

Solution

Given:
• P > 0
• P% of 3P is P% less than P

To find:
• The value of P

Approach and Working:
• P% of 3P = $$\frac{P}{100} * 3P = \frac{{3P^2}}{100}$$
o Now this less than P by (P – $$\frac{{3P^2}}{100}$$)
o In terms of percentage, it is equal to [(P – 3P^2/100)/P] * 100 = P
Solving, we can get P = 25

Hence, the correct answer is option B.

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Joined: 02 Oct 2017
Posts: 726
Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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23 May 2018, 20:57
2
As per P % of 3P is P % less than P,

P*3P/100=P(1-(P/100))

Solve P we get P=25

Give kudos if it helps

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Manager
Joined: 29 May 2016
Posts: 72
Location: Czech Republic
Concentration: Finance, Strategy
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Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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01 Aug 2019, 12:11
I am not entirely sure whether I correctly converted the second half of the equation. I did the following:

$$\frac{P}{100}$$*3P=$$\frac{1-P}{100}$$*P

From there:

$$3P^2$$=(1-P)*P
$$3P^2$$=P-$$P^2$$
$$4P^2$$=P
P=$$\frac{1}{4}$$
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Re: If P > 0 and P % of 3P is P % less than P, then P equals:  [#permalink]

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06 Aug 2019, 17:45
Bunuel 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

Just as we can express 5% as 5/100, we can express P% as P/100. Doing so, we can create the equation:

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

3P^2/100=(100P - P^2)/100

3P^2 = 100P - P^2

4P^2 - 100P = 0

4P(P - 25) = 0

P = 0 or P = 25

Since we are given that P > 0, then P must be 25.

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Re: If P > 0 and P % of 3P is P % less than P, then P equals:   [#permalink] 06 Aug 2019, 17:45
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