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number of doughnuts

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number of doughnuts

by Cheese12 » Sun Oct 09, 2011 7:55 am
At the bakery, Lew spent a total of $6.00 for one kind of cupcake and one kind of doughnut. How many doughnuts did he buy ?

1. The price of 2 doughnuts was $0.10 less than the price of 3 cupcakes.
2. The average price of 1 doughnut and 1 cupcake was $0.35



Hi All,

When I solved this question I reached till the point where I used both statements and could solve for price of doughnuts and price of cupcakes. Then I stopped and chose the answer as C, because I remembered that normally GMAT tests for questions where we know the total price and indivdual prices of the items and can still calculate the number of items bought. I know I should have worked out the problem till the end but the numbers were getting little dirty and I didnt have time. So can anyone tell me a quick or another method to do this one ?

Thanks !!!!!! :)
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by GmatMathPro » Sun Oct 09, 2011 10:43 am
By "dirty", do you mean a lot of the numbers were decimals? If you don't feel as comfortable working with decimals as you do with integers, one thing you can do is work the problem in terms of cents instead of dollars. That is, think of it as 600 cents instead of 6.00 dollars and 10 cents instead of 0.1 dollars.

C=number of cupcakes bought
x=Price of cupcake in cents
D=number of doughnuts bought
y=Price of doughnut in cents

Cx+Dy=600

Statement 1: 2y=3x-10. INSUFFICIENT.

Statement 2: x+y=70. INSUFFICIENT.

Statements 1&2:

3x-2y=10
x+y=70

Solving the system: x=30, y=40

PLugging in:

30C+40D=600

3C+4D=60

Any value of D that is a multiple of 3 works here.

D=3, C=16
D=6, C=12

are two examples.

Ans:
E

These types of problems can go either way. If the final equation had been 3C+4D=10, Then it would have to be D=1 and C=2. So I would abandon any ideas you have about how these things usually work out.

If there's a faster way to do it than just working it out completely, I don't see it.
Pete Ackley
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