P is a positive integer. Cutting Edge Knife Company original : GMAT Data Sufficiency (DS)
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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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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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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.

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

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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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15 Feb 2012, 21:51
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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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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16 Feb 2012, 10:42
Thank You everyone
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink]

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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

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

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24 Mar 2015, 16:03
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Re: P is a positive integer. Cutting Edge Knife Company original [#permalink]

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24 Mar 2015, 21:26
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] 24 Mar 2015, 21:26
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