During a sale, a clothing store sold each shirt at a price of $15 and each sweater at a price of $25. Did the store sell more sweaters than shirts during the sale?
(1) The average (arithmetic mean) of the prices of all the shirts and sweaters that the store sold during the sale was $21.
(2) The total of the prices of all the shirts and sweaters that the store sold during the sale was $420
Statement 1:
Just use common sense. If the store sold an equal number of shirts and sweaters, the average would be (15+25)/2 = 20. Since the average was greater than 20, the store must have sold a greater number of the more expensive item (the sweaters). Sufficient.
Statement 2:
Let x= shirts, y = sweaters.
15x + 25y = 420.
5(3x + 5y) = 420.
3x + 5y = 84.
x=3, y=15 works, because 3*3 + 5*15 = 84. In this case, x<y.
x=28, y=0 works, because 3*28 + 5*0 = 84. In this case, x>y.
Insufficient.
The correct answer is A.
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