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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]

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14 Oct 2013, 08:51
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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? 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]

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14 Oct 2013, 09:13
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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) the Model P televisions sold for $30 less than the Model Q televisions 2) Either p=120 or q=120 _________________ Please Help with Kudos, if you like my post. [Reveal] Spoiler: Intern Joined: 03 Feb 2015 Posts: 14 GMAT 1: 680 Q47 V36 GMAT 2: 720 Q49 V39 Followers: 0 Kudos [?]: 8 [0], given: 9 Re: Quick Sell Outlet sold a total of 40 televisions, each of [#permalink] ### Show Tags 03 Jun 2015, 09:32 (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.

hi bunuel,
i don't understand this can you pls elaborate
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Re: Quick Sell Outlet sold a total of 40 televisions, each of [#permalink]

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03 Jun 2015, 09:51
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harDill wrote:
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

(1)+(2) If q=120, then p=90, so in this case both prices would be less than the average price ($141) which is not possible. hi bunuel, i don't understand this can you pls elaborate You need to understand the following first, (average price) = (total sales)/(Number of televisions sold) Because Total Televisions Sold = 40 So Let, Total models of P television sold = x Then, Total models of Q television sold = 40-x The Revenue earned by selling x television of type P =$p * x
The Revenue earned by selling (40-x) television of type Q = $q * (40-x) Total Revenue Earned = Average Price per television * No. of televisions sold =$141 * (40)

Hence,
141 * 40=px+q(40−x), where x is the number of Model P televisions sold.

$5640 = px+q(40−x) Unknown Variable to be calculated = x = ? Statement 1:$p = $q - 30 i.e.$5640 = px+q(40−x) can be Re-written as
$5640 = (q-30)x+q(40−x) But two unknown Variables q and x Hence, NOT SUFFICIENT Statement 2: Either p=120 or q=120 @p = 120, q and x are unknown hence not sufficient @q = 120, p and x are unknown hence not sufficient Hence, NOT SUFFICIENT Combining Statement 1 and Statement 2 together: Either p=120 or q=120 AND$p = $q - 30 AND$5640 = px+q(40−x)

i.e. If p = 120, then q = 150 and then x = 12, A Unique value
But if q = 120 then p = 90 and then x = -28 i.e. Negative Value which is IMPOSSIBLE

Hence SUFFICIENT

[Reveal] Spoiler:
C

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Re: Quick Sell Outlet sold a total of 40 televisions, each of [#permalink]

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21 Jun 2016, 23:50
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Quick Sell Outlet sold a total of 40 televisions, each of [#permalink]

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16 Sep 2016, 16:37
harDill wrote:
(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.

hi bunuel,
i don't understand this can you pls elaborate

If you only score 70 and 80 on tests in a class, is it possible for you to get an average test score of 90 in the class?
Quick Sell Outlet sold a total of 40 televisions, each of   [#permalink] 16 Sep 2016, 16:37
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