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P is a positive integer. Cutting Edge Knife Company original

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P is a positive integer. Cutting Edge Knife Company original [#permalink] New post 15 Feb 2012, 15:07
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P is a positive integer. Cutting Edge Knife Company originally had (P) salespeople, each of whom sold 200 knives. Each salesperson then hired several more (P) salespeople, each of whom sold 200 knives. What is the value of P?

(1) The first P salespeople sold 1/9 of all knives sold
(2) 14,400 knives were sold in total
[Reveal] Spoiler: OA

Last edited by Bunuel on 15 Feb 2012, 15:27, edited 1 time in total.
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink] New post 15 Feb 2012, 15:25
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P is a positive integer. Cutting Edge Knife Company originally had (P) salespeople, each of whom sold 200 knives. Each salesperson then hired several more (P) salespeople, each of whom sold 200 knives. What is the value of P?

Since each of P salespeople hired P salespeople, then there were P*P=P^2 new salespeople hired, which makes total # of salespeople equal to P+P^2. Now, as all of them sold 200 knives then total # of knives sold is 200*(P+P^2).

(1) The first P salespeople sold 1/9 of all knives sold --> 200*P=1/9*200*(P+P^2) --> 9P=P+P^2 --> P(8-P)=0 --> P=8 (since Given that P is a positive integer P=0 is not a valid solution). Sufficient.

(2) 14,400 knives were sold in total --> 200*(P+P^2)=14,000 --> P(P+1)=72 --> P=8 (since Given that P is a positive integer P=-9 is not a valid solution). Sufficient.

Answer: D.

Similar question to practice: mary-persuaded-n-friends-to-donate-500-each-to-her-election-10075.html

Hope it helps.
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink] New post 15 Feb 2012, 17:06
My doubt here is, it says: 'Each salesperson then hired several more (P) salespeople'. So how does several mean that each of the P salesperson employs P more salespeople?
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink] New post 15 Feb 2012, 21:51
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arps wrote:
My doubt here is, it says: 'Each salesperson then hired several more (P) salespeople'. So how does several mean that each of the P salesperson employs P more salespeople?


I agree with you that the wording could have been better. Anyway: "each salesperson hired several more (P) salespeople" means that "each salesperson hired P salespeople".
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink] New post 15 Feb 2012, 23:25
Here the correct answer is D as both are sufficient to answer the question. To find the ans either you need the total or information about the fraction of the total which each statement provides.
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink] New post 16 Feb 2012, 10:42
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink] New post 01 Dec 2012, 23:01
How many total sales people? P + P*P = P + P^2
How many total knives sold? 200P + 200p^2

Test Statements:
(1) 200P = \frac{1}{9}(200P + 200P^2)
SUFFICIENT

(2) 200P + 200P^2 = 14,400
SUFFICIENT

Answer: D
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Re: P is a positive integer. Cutting Edge Knife Company original   [#permalink] 01 Dec 2012, 23:01
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