Data Sufficiency

In what proportions should coffee of type A, type B and C be mixed to get coffee which costs $8 for every 100 ounces ??

1) the ratio in which coffee of type A and type C are mixed is 2:1

2) Coffee of type A, type B and type C cost $4, $10 and $6 respectively for 100 ounces..

Let:

A=fraction of mixture that is A
B=fraction of mixture that is B
C=fraction of mixture that is C

A,B, and C are the only kinds of coffee we want in the mixture, so it must be that A+B+C=1.

Statement 1. A=2C. Obviously insufficient as it tells us nothing about the cost.

Statement 2. With these prices, we can set up the following equation: 4A+10B+6C=8----dividing by 2----->2A+5B+3C=4. With A+B+C=1, we now have two equations and three variables. This is not enough information to solve for unique values of A,B, and C. For example, A=1/5, B=3/5, C=1/5 would be a solution as would A=1/4, B=1/8, C=5/8. INSUFFICIENT.

Statements 1&2: Adding A=2C to the two equations we got from statement 2 gives us three equations with three variables. Plugging A=2C into both equations yields:

5B+7C=4
B+3C=1

Solving this system gives us: B=5/8 C=1/8, which means A=1/4.

Hence the ratio A:B:C=2:5:1

Ans: C

Of course, you shouldn't necessarily solve it all the way out once you realize there is a unique solution.

I solved exactly the way it is given above...

It took some time for me to solve the question though: