Data Sufficiency

In the first hour of a bake sale, students sold either chocolate chip cookies, which sold for $1.30 each, or brownies, which sold for $1.50 each. What was the ratio of chocolate chip cookies sold to brownies sold during that hour?

1) The average price for the items sold during that hour was $1.42
2) The total price for all items sold during that hour was $14.20

[spoiler]OA: D[/spoiler]

source: Veritas

Chip Cookies = 1.3C
Brownies = 1.5b

To find = c:b

Statement 1:
1.3c + 1.5b = 1.42 (c + b)
1.3c + 1.5b = 1.42c + 1.42b
-0.12c = -0.08 b
we can get the ratio..
SUFFICIENT

Statement 2:
1.3c + 1.5b = 14.20
13c + 15b = 142
we need to find a value of c so that the resultant has unit digit 0 or 5 so that it is divisible by 15
So lets consider
c = 4, then b = 90/15 = 6
c = 9, then b = (142-117)/15 = 25/15 NOT INT
So, 4:6
SUFFICIENT

[spoiler]{D}[/spoiler]

When the values of two groups are averaged, the result is a weighted average; it's called weighted average because instead of being exactly in the middle of the two groups, it is closer to the value of the larger group; there is a proportional relationship to the sizes of the groups: if group 1 is twice as big as group 2, the weighted average will be twice as close to group 1's value.

All this means that there are just 4 variables in a weighted avg question between 2 groups; the values of the individual groups, the relative weights of the groups (ratio of group sizes), and the weighted average. Knowing 3 of these unknowns is enough to discover the 4th.

Let's solve:

Statement 1:
The prompt gives us 2 values up front; the values of the individual groups (price of choc chip and price of brownies). Statement 1 gives us the weighted average, so we have 3 out of 4 unknowns; that's enough to find the 4th unknown, the ratio of group sizes.
SUFFICIENT

Statement 2:
If we call b and c the number of brownies and cookies, we can write the equation 1.3c + 1.5b = 14.2. Simplify to:
13c + 15b = 142

In general, when you have two variables and one equation you will not have enough data to solve. There is at least one important exception:

✔ If your equation is of the form Ax + By = C where A, B and C are known, and
✔ if your unknowns are positive integers, and
&#10004; if C < the least common multiple of A & B, then

the equation has only 1 solution! Since our equation (13c + 15b = 142) meets all three criteria I can tell at a glance that it is SUFFICIENT.

The answer is D.