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Help with understanding a problem

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Junior | Next Rank: 30 Posts
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by lateraldeath » Sun Apr 20, 2008 9:51 pm
A business bought R typewriters at $100 per typewriter and S calculators at $50 per calculator. What is the total cost of the typewriters and calculators?

1 The S calculators cost $200
2 2R+S
=10







The answer in the official Kaplan book says B. I don't understand how two variables can be derived from one equation, it's answer explanation was very confusing to me.

-Thanks!
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Source: — Data Sufficiency |
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by Neo2000 » Sun Apr 20, 2008 10:03 pm
For 2R+S to be equal to 10, R has to be either Even or ODD number and S definitely has to be Even.

Why can R be either Even or odd?? You know that 2 x (Any Number) = Even

So now substitute values of R and S
R = 1 S = 8
R = 2 S = 6
R = 3 S = 4
R = 4 S = 2

Now calculate total costs for each condition
100 + 8x50 = 500
2x100 + 6x 50 = 500 and so on
As you can see, in each case the total is 500 Hence B is sufficient.

You can also observe that value of S = R/2 i.e. every 2 calculators = 1 Typewriter
So if your calculator decreases by 2 but the typewriter increases by 1, overall there is no change in your cost.
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Re: Help with understanding a problem

by tmmyc » Tue Apr 22, 2008 3:51 pm
First, you don't want to fall into the trap thinking a DS problem with two variables cannot be solved with only one equation. The GMAT will often hide the answer using this trick to fool you.

For this problem, the question asks for the total cost of typewriters and and calculators. Translating the english into algebra, we get:

100*R + 50*S = Total
Find the Total.

Statement 1:

Insufficient since we only know the value of S but not T

Statement 2:

2*R + S = 10

What happens when we multiply both sides by 50?
50*[2*R + S] = 50*10
100*R + 50S = 500

There you have it. By multiplying both sides by 50, we find that 100*R + 50*S, which is equal to the Total, is 500. Sufficient.
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by akshatsingh » Wed Apr 23, 2008 11:04 pm
A business bought R typewriters at $100 per typewriter and S calculators at $50 per calculator. What is the total cost of the typewriters and calculators?

1 The S calculators cost $200
2 2R+S =10



Answer will be B.

Given no. of typewriters as R and no. of calculators be S.
We want 100R+50S=?

from statement 2..
2R+S=10
Multiply both sides by 50
100R+50S=500
This is what we want to find.

Statement 1 tells only about S, so NOT SUFFICIENT

Cheers!
Aks
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by rosenjon » Sun Apr 27, 2008 8:45 pm
What others have said is correct. However, I prefer to look at it in the opposite way from how others derived the answer.

Instead of multiplying by 50 with the statement, do the opposite for the stem.

100(R) +50 (S) = Total Price

50(2R+S) = Total Price

You will notice that statement 2 gives you 2R+S

So you can clearly get an integer value for Total Price.
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