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

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Intern
Joined: 02 Jul 2013
Posts: 19
Schools: LBS MIF '15
Quick Sell Outlet sold a total of 40 televisions, each of  [#permalink]

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14 Oct 2013, 08:51
5
68
00:00

Difficulty:

75% (hard)

Question Stats:

62% (01:31) correct 38% (01:31) wrong based on 966 sessions

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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
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Joined: 02 Sep 2009
Posts: 47871
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. Intern Joined: 03 Feb 2015 Posts: 14 GMAT 1: 680 Q47 V36 GMAT 2: 720 Q49 V39 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
8
1
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

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GMAT 1: 700 Q48 V37
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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 ($141) which is not possible. hi bunuel, i don't understand this can you pls elaborate If you only score 70 and 80 on tests in a class, is it possible for you to get an average test score of 90 in the class? Intern Joined: 26 Feb 2017 Posts: 18 Re: Quick Sell Outlet sold a total of 40 televisions, each of [#permalink] ### Show Tags 18 Nov 2017, 05:07 Bunuel wrote: Quick Sell Outlet sold a total of 40 televisions, each of which was either a Model P television or a Model Q television. Each Model P television sold for$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?

(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.

HI,

Even here when q=120 and p=150, the average still comes out to be less than 141. Hence how can we take this as a solution?
Senior Manager
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Re: Quick Sell Outlet sold a total of 40 televisions, each of  [#permalink]

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18 Nov 2017, 05:56
1
bulletpoint 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

Let number of P televisions be m, and Q Televisions be n.

p*m + q*n/m+n = 141, m + n = 40
p*m + q*n = 5640
p = q - 30
q*(m+n) - 30*m = 5640. Now, when q = 120, m will be -ve which is not possible. So, only p = 120, q = 150
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Joined: 06 Jul 2016
Posts: 415
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Concentration: Strategy, Finance
Re: Quick Sell Outlet sold a total of 40 televisions, each of  [#permalink]

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18 Nov 2017, 06:11
bulletpoint 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? Average = $$\frac{{Total Sales}}{{No. of TVs sold}}$$ Let No. of Model P TVs be a => Model Q TVs = (40-a) We are given $$\frac{{ap + q(40-a)}}{40}$$ = 141 We need to find the value of a. Quote: 1) the Model P televisions sold for$30 less than the Model Q televisions

2) Either p=120 or q=120

S1) p = q-30
=> q(a+40) - a(30+q) = 5640
=> Not enough information to find the value of a.

Insufficient.

S2) p = $120 or q =$120
=> Clearly not enough information to find the value of a.

Insufficient.

Quote:
Combining S1+S1

p = q-30
if p = $120 then q =$150
if q = $120 then p =$90 => Not possible at the average is $141 [Ignore this case] Inputting values of p & q in $$\frac{{ap + q(40-a)}}{40}$$ = 141 => 120a + 150(40-a)=5640 => we can find the value of a. Sufficient. The answer is C _________________ Put in the work, and that dream score is yours! Senior Manager Joined: 06 Jul 2016 Posts: 415 Location: Singapore Concentration: Strategy, Finance Re: Quick Sell Outlet sold a total of 40 televisions, each of [#permalink] ### Show Tags 18 Nov 2017, 06:20 kartzcool wrote: Bunuel 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?

(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.

HI,

Even here when q=120 and p=150, the average still comes out to be less than 141. Hence how can we take this as a solution?

Hi mate,

You're assuming that 1 unit of both TVs was sold.
if p = 120 and q = 150 then, for the average to be \$141, more of model Q would need to be sold as the average is skewed towards 150.

Hope this helps.
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Re: Quick Sell Outlet sold a total of 40 televisions, each of &nbs [#permalink] 18 Nov 2017, 06:20
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