TariqOmar wrote: ↑Wed May 09, 2018 3:26 am
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.
Correct answer:
C.
Solution:
Statement One Alone:
the Model P televisions sold for $30 less than the Model Q televisions
Suppose 20 Model P televisions were sold for $126 each and suppose 20 Model Q televisions were sold for $156 each. Then, the average selling price of 40 televisions is (20*126 + 20*156)/40 = (2,520 + 3,120)/40 = 5,640/40 = $141. In this scenario, 20 of the 40 televisions were Model P.
Suppose, on the other hand, that 28 Model P televisions were sold for $132 and 12 Model Q televisions were sold for $162. Then, the average selling price of the 40 televisions is (28*132 + 12*162)/40 = (3,696 + 1,944)/40 = 5,640/40 = $141. In this scenario, 28 of the 40 televisions were Model P.
Statement one alone is not sufficient. Eliminate answer choices A and D.
Statement Two Alone:
Either p=120 or q=120
Suppose 10 model P televisions were sold for $120 and 30 model Q televisions were sold for $148. Then, the average selling price of a television was (10*120 + 30*148)/40 = (1,200 + 4,440)/40 = 5,640/40 = $141. In this scenario, 10 model P televisions were sold.
Suppose, on the other hand, that 30 model P televisions were sold for $120 and 10 model Q televisions were sold for $204. Then, the average selling price of a television was (30*120 + 10*204)/40 = (3,600 + 2,040)/40 = 5,640/40 = $141. In this scenario, 30 model P televisions were sold.
Statement two alone is not sufficient. Eliminate answer choice B.
Statements One and Two Together:
If Model Q television sells for $120, then a Model P television must sell for 120 - 30 = $90 since statement one tells us that a Model P television sells for $30 less than a Model Q television. Then, the average selling price of a television will be between 90 and 120, which is inconsistent with the given fact that the average selling price of a television is $141. Thus, it must be true that a Model P television sells for $120 and a Model Q television sells for 120 + 30 = $150.
If we let n be the number of Model P televisions sold, then the number of Model Q televisions sold must be 40 - n. We can create the following equation:
(120*n + 150*(40 - n))/40 = 141
120n + 6,000 - 150n = 141*40
-30n = 5,640 - 6,000
-30n = -360
n = 12
So, the number of Model P televisions sold was 12. Statements one and two together are sufficient.
Answer: C
