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# Amanda and Todd purchase candy, popcorn, and pretzels at the

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

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12 Dec 2012, 08:30
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Question Stats:

63% (02:30) correct 37% (01:15) wrong based on 105 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.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 12 Dec 2012, 08:33, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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12 Dec 2012, 08:48
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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.

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

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12 Dec 2012, 23:33
this was a tricky question... I marked 'E' cuz I thought as prices have not been given so info is incomplete
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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12 Dec 2012, 23:53
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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.

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

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13 Dec 2012, 02:35
Marcab wrote:
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.

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, 05:07
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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14 Dec 2012, 07:16
Nice question n nice explaination too...thnks
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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16 Jun 2015, 04:57
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the [#permalink]

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17 Nov 2016, 09:56
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Re: Amanda and Todd purchase candy, popcorn, and pretzels at the   [#permalink] 17 Nov 2016, 09:56
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