Data Sufficiency

Hi aditiniyer,

When posting GMAT questions, you should make sure to include the correct answer.

In this prompt, we're told that $6 was spent buying a certain number of Ds and a certain number of Cs. We're asked for the number of Ds that were purchased.

1) The price of 2D was $0.10 less than the price of 3C.

This Fact tells us nothing about the actual price of the units nor the actual number of units that were purchased.
Fact 1 is INSUFFICIENT

2) The average price of 1D & 1C was $0.35.

This Fact also tells us nothing about the actual price of the units nor about the number of units that were purchased.
Fact 2 is INSUFFICIENT

Combined, we can create the following equations regarding the PRICES of the two items:

2D = 3C - .1
(D + C)/2 = .35

This is a 'system' of equations that you can solve...

D + C = .7
C = .7 - D

2D = 3C - .1
2D = 3(.7 - D) - .1
2D = 2.1 - 3D - .1
5D = 2.0
D = .4
C = .3

So each D costs $0.40 and each C costs $0.30. So how many ways are there to spend $6 on these two items at these prices....?

12 Cs and 6 Ds = $6 and the answer is 6
4 Cs and 12 Ds = $6 and the answer is 12
Combined, INSUFFICIENT

Final Answer: E

GMAT assassins aren't born, they're made,
Rich

Hi Mo2men,

This question isn't written in proper GMAT "style", but there's a broader lesson in how we're working through it. How you interpret a prompt is important, so if you find yourself unsure about the 'intent' of a question, you have to think about the other parts of the prompt and the design 'rules' that GMAT questions are built on.

Here, if you interpret the first sentence as "$6 was spent on 1D and 1C...", then what is the answer to the QUESTION ("How many D did he buy?")? Based on that interpretation of the first sentence, you would have to say that the answer to the question is 1. However, DS prompts NEVER given you enough information to answer the question until you consider what's in the two Facts underneath. Thus, there's no way that that interpretation can be correct.

GMAT assassins aren't born, they're made,
Rich

aditiniyer wrote:L spends $6 for one kind of D and one kind of C. How many D did he buy ?

1) The price of 2D was $0.10 less than the price of 3C.
2) The average price of 1D & 1C was $0.35.

We need to determine the number of Ds L bought given that he spent a total of $6 for one kind of D and one kind of C. If d = the price of one D, c = the price of one C, m = the number of Ds he bought and n = the number of Cs he bought, then md + nc = 6. We need to determine the value of m.

Statement One Alone:

The price of 2D was $0.10 less than the price of 3C.

Using the information in statement one we know that 2d = 3c - 0.1.

From the given we also know that md + nc = 6, however, this is not enough information to determine the value of m. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D.

Statement Two Alone:

The average price of 1D & 1C was $0.35.

Using the information from statement two, we know that:

(d + c)/2 = 0.35

d + c = 0.7

Even with the given equation, statement two is still not sufficient to determine a value of m.

Statements One and Two Together:

Using the information from the given, statement one, and statement two, we have the following 3 equations:

1) md + nc = 6

2) 2d = 3c - 0.1

3) d + c = 0.7

Notice that we could use equations 2 and 3 to determine that d = $0.40 and c = $0.30. We now can express equation 1) as:

md + nc = 6

0.40m + 0.30n = 6

4m + 3n = 60

We know that both m and n must be positive integers because they represent the number of items of D and C purchased.

However, the values of m and n are not unique. For example, if we let m = 6 and n = 12, the equation would be satisfied. But the equation would also be satisfied if we let m = 3 and n = 16.
Thus, statements one and two together are still not sufficient to answer the question.

Answer: E