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Quick Sell Outlet sold a total of 40 televisions, each of

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Quick Sell Outlet sold a total of 40 televisions, each of [#permalink] New post 14 Oct 2013, 07:51
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56% (02:33) correct 44% (01:09) wrong based on 84 sessions
Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television. Each Model P television sold for $p and each Model Q sold for $q. The average (arithmetic mean) selling price of the 40 televisions was $141. How many of the 40 televisions were Model P televisions?

1) the Model P televisions sold for $30 less than the Model Q televisions

2) Either p=120 or q=120
[Reveal] Spoiler: OA
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Re: Quick Sell Outlet sold a total of 40 televisions, each of [#permalink] New post 14 Oct 2013, 08:13
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Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television. Each Model P television sold for $p and each Model Q sold for $q. The average (arithmetic mean) selling price of the 40 televisions was $141. How many of the 40 televisions were Model P televisions?

(average price) = (total sales)/(# of televisions sold)

141 = \frac{px+q(40-x)}{40}, where x is the number of Model P televisions sold.

(1) The Model P televisions sold for $30 less than the Model Q televisions --> p=q-30. Not sufficient to get x.

(2) Either p=120 or q=120. Not sufficient.

(1)+(2) If q=120, then p=90, so in this case both prices would be less than the average price ($141) which is not possible. Thus p=120 and q=150. When we substitute these values we'll have only one unknown x, so we can solve for it. Sufficient.

Answer: C.
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Re: Quick Sell Outlet sold a total of 40 televisions, each of   [#permalink] 14 Oct 2013, 08:13
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Quick Sell Outlet sold a total of 40 televisions, each of

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