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
