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

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15 Feb 2012, 16:07

00:00

A

B

C

D

E

Difficulty:

55% (hard)

Question Stats:

58% (02:43) correct
42% (01:41) wrong based on 101 sessions

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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

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.

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

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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?

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]

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

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24 Mar 2015, 17:03

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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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