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C
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Difficulty:
45%
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Question Stats:
66% (01:49) correct
34%
(01:54)
wrong
based on 544
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Amanda and Todd purchase candy, popcorn, and pretzels at the stadium. If a package of candy costs half as much as a bag of popcorn, how much more money did Amanda and Todd spend on the candy than on the popcorn and pretzels combined?
(1) The cost of a bag of popcorn is equal to the cost of a pretzel.
(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn.
(1) The cost of a bag of popcorn is equal to the cost of a pretzel.
(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn.
12 Dec 2012, 09:48
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Amanda and Todd purchase candy, popcorn, and pretzels at the stadium. If a package of candy costs half as much as a bag of popcorn, how much more money did Amanda and Todd spend on the candy than on the popcorn and pretzels combined?
ITEM ------- # OF ITEMS PURCHASED ------- PRICE PER ITEM
Candy ----------------------- a ---------------------------- x
Popcorn --------------------- b ---------------------------- 2x (since a package of candy costs half as much as a bag of popcorn)
Pretzels --------------------- c ---------------------------- z
Question: \(ax-(2bx+cz)=?\)
(1) The cost of a bag of popcorn is equal to the cost of a pretzel --> \(2x=z\) --> substitute in the question: \(ax-(2bx+2cx)=x(a-2b-2c)=?\). Not sufficient.
(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn --> \(a=24\) and \(b=c=6\). Not sufficient.
(1)+(2) Substitute the values from (2) into (1): \(x(a-2b-2c)=x(24-12-12)=0\), thus Amanda and Todd spent equal amount of money on the candy AND on the popcorn and pretzels combined. Sufficient.
Answer: C.
ITEM ------- # OF ITEMS PURCHASED ------- PRICE PER ITEM
Candy ----------------------- a ---------------------------- x
Popcorn --------------------- b ---------------------------- 2x (since a package of candy costs half as much as a bag of popcorn)
Pretzels --------------------- c ---------------------------- z
Question: \(ax-(2bx+cz)=?\)
(1) The cost of a bag of popcorn is equal to the cost of a pretzel --> \(2x=z\) --> substitute in the question: \(ax-(2bx+2cx)=x(a-2b-2c)=?\). Not sufficient.
(2) Amanda and Todd purchased 24 packages of candy, 6 pretzels, and 6 bags of popcorn --> \(a=24\) and \(b=c=6\). Not sufficient.
(1)+(2) Substitute the values from (2) into (1): \(x(a-2b-2c)=x(24-12-12)=0\), thus Amanda and Todd spent equal amount of money on the candy AND on the popcorn and pretzels combined. Sufficient.
Answer: C.
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