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66% (02:10) correct
34%
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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
(1) The first P salespeople sold 1/9 of all knives sold
(2) 14,400 knives were sold in total
15 Feb 2012, 16:25
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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.
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.
15 Feb 2012, 18:06
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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?
