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 - 30i.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 SUFFICIENTStatement 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 SUFFICIENTCombining 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
SUFFICIENTAnswer: Option
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