¡¡¡¡2. What is the perimeter of triangle ABC above£¿
¡¡¡¡£¨1£© The ratio of DE to BF is 1£º 3.
¡¡¡¡£¨2£© D and E are midpoints of sides AB and CB£¬ respectively.
¡¡¡¡Since we do not even know whether BF is an altitude£¬ nothing can be determin
¡¡¡¡ed from £¨1£©¡£ More importantly£¬ there is no information telling us the absolu
¡¡¡¡te size of the triangle.
¡¡¡¡As to £¨2£©£¬ although from geometry we know that DE = AC/2£¬ this relationship
¡¡¡¡holds for any size triangle. Hence£¬ £¨2£© is also insufficient.
¡¡¡¡Together£¬ £¨1£© and £¨2£© are also insufficient since we still don't have inform
¡¡¡¡ation about the size of the triangle£¬ so we can't determine the perimeter. T
¡¡¡¡he answer is E.
¡¡¡¡3. A dress was initially listed at a price that would have given the store a
¡¡¡¡profit of 20 percent of the wholesale cost. What was the wholesale cost of
¡¡¡¡the dress£¿
¡¡¡¡£¨1£© After reducing the asking price by 10 percent£¬ the dress sold for a net
¡¡¡¡profit of 10 dollars.
¡¡¡¡£¨2£© The dress sold for 50 dollars.
¡¡¡¡Consider just the question setup. Since the store would have made a profit o
¡¡¡¡f 20 percent on the wholesale cost£¬ the original price P of the dress was 12
¡¡¡¡0 percent of the cost£º P = 1.2C. Now£¬ translating £¨1£©sintosan equation yield
¡¡¡¡s£º
¡¡¡¡P - .1P = C + 10
¡¡¡¡Simplifying gives
¡¡¡¡¡¡9P = C + 10
¡¡¡¡Solving for P yields
¡¡¡¡P = £¨C + 10£©/.9
¡¡¡¡Plugging this expression for PsintosP = 1.2C gives
¡¡¡¡£¨C + 10£©/.9 = 1.2C
¡¡¡¡Since we now have only one equation involving the cost£¬ we can determine the
¡¡¡¡cost by solving for C. Hence£¬ the answer is A or D.
¡¡¡¡£¨2£© is insufficient since it does not relate the selling price to any other
¡¡¡¡information. Note£¬ the phrase ¡°initially listed¡± implies that there was more
¡¡¡¡than one asking price. If it wasn't for that phrase£¬ £¨2£© would be sufficien
¡¡¡¡t. The answer is A.
