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GMAT Prep2 ?? (Sandwiches)

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GMAT Prep2 ?? (Sandwiches)

by dferm » Wed May 14, 2008 8:12 pm
At a certain stand, all soft drinks cost the same and alll sandwiches cost the same. How much does 1 sandwich cost at the stand?

(1) At the stand, 1 sandwich and 2 soft drinks cost a total of $3.15.
(2) At the stand, 3 sandwiches and 1 soft drink cost a total of $5.70

Please Help..

Thanks..

These questions are driving me up the wall...
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Source: — Data Sufficiency |
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by mwilliams » Wed May 14, 2008 8:29 pm
(1) At the stand, 1 sandwich and 2 soft drinks cost a total of $3.15.
(2) At the stand, 3 sandwiches and 1 soft drink cost a total of $5.70

s=sandwich and d=soft drink
(1) s+2d=3.15, therefore s=3.15-2d
(2) 3s+d=5.70

substitute 3.15-2d for s in equation 2 giving you 9.45-6d+d=5.70, then 3.75-5d=0, then 3.75=5d, so d=.75 then plug d into equation 1, so s=3.15-1.50, s=1.65

(1) and (2) are sufficient together, but insufficient alone

note: you don't need to actually solve the problem, just be able to know you can solve it.
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by VP_Jim » Wed May 14, 2008 8:30 pm
Hi dferm,

First, since this is data sufficiency, realize that you don't need to solve this. Recognize that each statement gives us an equation with two variables in it, so it can't be A, B, or D, since we can't solve an equation with two variables.

So, either they are going to be sufficient together (C) or not (E). To solve for two variables, we need two equations, so C is the answer.

Now, if you want to solve it, we can set up the two equations:

x+2y=3.15
3x+y=5.70

Then, you can use equation 2 to set y in terms of x .... y=5.70-3x
Then, plug in 5.70-3x for y in the first equation, and you can solve for x.
x = 1.65

Since you know that x=1.65, then you can easily solve for y, which is .75. So, sandwiches cost $1.65, and sodas cost $.75.
Jim S. | GMAT Instructor | Veritas Prep
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