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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]

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New post 15 Feb 2012, 16:07
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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, 16:27, edited 1 time in total.
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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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New post 15 Feb 2012, 18:06
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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New post 15 Feb 2012, 22:51
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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New post 16 Feb 2012, 00:25
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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New post 16 Feb 2012, 11:42
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink]

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New post 02 Dec 2012, 00:01
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]

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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink]

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New post 24 Mar 2015, 22:26
Hi All,

This question is a "clone" of a question from the OG13/GMAT2015 book, from the DS section (question 71, page 281) - if you'd like to see how the Official GMAT writers would post such a question.

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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink]

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New post 08 Aug 2017, 02:15
arps wrote:
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



Given : P is a positive integer. Company had P salespeople, each of them sold 200 knives.
Each of the P salespeople hired P salespeople and these new people sold 200 knives each.

Old people sold total 200P knives
New people sold total 200 P^2 knives.

Statement 1: 200P/(200P+200P^2) = 1/9 ->1/(1+P) = 1/(1+8) -> P = 8
SUFFICIENT

Statement 2: 200P + 200P^2 = 14400
P^2+ P = 72
P^2 +9P -8P -72 =0
(P+9)(P-8) = 0
p=8
SUFFICIENT

Answer D
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Re: P is a positive integer. Cutting Edge Knife Company original   [#permalink] 08 Aug 2017, 02:15
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