Data Sufficiency

At the bakery, Lew spent a total of $6.00 per 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 (arithmetic mean) price of 1 doughnut and 1 cupcake was $0.35

OA: E

I was able to get it right, however, I couldn't find a way to develop the two statements to reach to a firm conclusion.

Thanks,
Fambrini

Hi fambrini.

Statement 1 and Statement 2 can be used together to determine that the price of one doughnut is .40 and the price of one cupcake is .30.

At that point, the question becomes "Is there more than one way to add multiples of .40 and .30 to get 6.00.

If there is only one way to do that, they you can determine how many of each he bought.

If there are multiple ways, then the information provided is not sufficient for determining how many he bought.

One way to determine whether there are multiple possible numbers of doughnuts is to start with 1 doughnut (1D) and see whether there is a multiple of .30, the price of cupcakes, that you could add to .40 to get 6.00. Then move to 2 doughnuts (2D) and so on.

1D: .40 5.60 is not a multiple of .30.

2D: .80 5.20 is not a multiple of .30.

3D: 1.20 4.80 is a multiple of .30. So 3 doughnuts works.

Now you are at a key moment, because if you notice that 1.20 and 4.80 are both multiples of both .40 and .30, then you realize that there are at least two numbers of doughnuts that would work, and so the statements combined are insufficient for determining how many doughnuts he purchased.

The correct answer is E.

(By the way, the way the question is worded, it seems possible that he bought either all doughnuts and 0 cupcakes or all cupcakes and 0 doughnuts, as 6.00 is divisible by both .40 and .30. So if that reading of the question is correct, then you don't even have to go through figuring out possible combinations to determine that there are multiple numbers of doughnuts that work. I am a little surprised actually that the wording of a GMAT Prep question would be ambiguous the way the wording of this one is. That having been said, you can read the question either way and still get it right.)