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Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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12 Dec 2012, 09:30

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

65% (02:25) correct
35% (01:10) wrong based on 80 sessions

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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.

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Last edited by Bunuel on 12 Dec 2012, 09:33, edited 1 time in total.

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.

Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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13 Dec 2012, 00:53

1

This post received KUDOS

Bunuel wrote:

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 ------- PRICE PER ITEM ------- # OF ITEMS PURCHASED 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.

Hi Bunuel. I am a bit confused over the usage of words in the questions. The question explicitly states that "a package of candy costs half as much as a bag of popcorn" then shouldn't a=b/2 rather than #of bags of candies=half of the #of bags of popcorn.
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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 ------- PRICE PER ITEM ------- # OF ITEMS PURCHASED 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.

Hi Bunuel. I am a bit confused over the usage of words in the questions. The question explicitly states that "a package of candy costs half as much as a bag of popcorn" then shouldn't a=b/2 rather than #of bags of candies=half of the #of bags of popcorn.

Columns had wrong labels (PRICE PER ITEM and # OF ITEMS PURCHASED should have been reversed). Edited.
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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13 Dec 2012, 06:07

The problem I found with the question is whether bag and package are same or not. In that case I marked E but when I re read the question I just got confused. though option 1 seems a bit way ward and unclear. answer would be C in case the the cost of bag of popcorn is equal to the cost of bag of pretzel. option 1 is not clear as such
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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