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At a refreshment stand, each can of soda sells for the same price and

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At a refreshment stand, each can of soda sells for the same price and  [#permalink]

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New post Updated on: 25 Jan 2015, 02:22
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At a refreshment stand, each can of soda sells for the same price and each sandwich sells for the same price. What is the total price for 2 sandwiches and 3 cans of soda at the stand?

(1) At the stand the total price for 1 sandwich and 1 can of soda if $3
(2) At the stand the total price for 3 sandwiches and 2 cans of soda is $8

Originally posted by ajca on 24 Jan 2015, 20:44.
Last edited by Bunuel on 25 Jan 2015, 02:22, edited 1 time in total.
Renamed the topic and edited the question.
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Re: At a refreshment stand, each can of soda sells for the same price and  [#permalink]

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New post 24 Jan 2015, 22:24
1
2
here we go...

Let price of Soda = p
Let price of sandwich = m

2m + 3p = ??

St1: m + p = 3

m = 2, p = 1 -----> holds true
m = 1.5, p = 1.5 -----> holds true

Clearly not sufficient


St2: 3m + 2p = 8

m = 2, p = 1----> holds true
m = 1.5, p = 1.75 -----> holds true


Clearly not sufficient

Combining St1 and St2

m + p = 3
3m + 2p = 8

Solve---
m = 2, p = 1

Hence C is the winner here.
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Re: At a refreshment stand, each can of soda sells for the same price and  [#permalink]

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New post 24 Jan 2015, 23:34
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1
Hi ajca,

This DS question is built on "system" Algebra, without any of the factors/multiples shortcuts that are common on DS versions of these questions.

We're asked for the total price of 2 sandwiches and 3 cans of soda.

**Note: When translating the Facts into Algebra, I'm going to use....

W = # of sandwiches
C = # of cans of soda

The question asks us for 2W + 3C

Fact 1: 1 sandwich and 1 can of soda = $3

W + C = 3

This is 1 equation with 2 variables, so there's no way to figure out the answer to the question. Here's the proof:

IF....
W = 1
C = 2
Then the answer to the question is 2(1) + 3(2) = 8

IF.....
W = 2
C = 1
Then the answer to the question is 2(2) + 3(1) = 7
Fact 1 is INSUFFICIENT

Fact 2: 3 sandwiches and 2 cans of soda = $8

We have a similar situation to what we have in Fact 1: 1 equation and 2 variables.....

3W + 2C = 8

IF....
W = 2
C = 1
Then the answer to the question is 2(2) + 3(1) = 7

IF....
W = 1
C = 2.5
Then the answer to the question is 2(1) + 3(2.5) = 9.5
Fact 2 is INSUFFICIENT

Combined, we have...
W + C = 3
3W + 2C = 8

This is a "system" - 2 variables and 2 unique equations, which means that we CAN solve for the values of W and C (and then answer the question.
Combined, SUFFICIENT

Final Answer:

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Re: At a refreshment stand, each can of soda sells for the same price and  [#permalink]

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New post 08 Oct 2018, 15:33
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Re: At a refreshment stand, each can of soda sells for the same price and   [#permalink] 08 Oct 2018, 15:33
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