A pumpkin patch contains x pumpkins that weigh 10 pounds each and y pu

800score Official Solution:

The original statement says the average weight of a pumpkin is 12 pounds. Since x pumpkins weigh 10 pounds each, the y pumpkins must be heavier. If the y pumpkins weighed less than 12, then the average weight of all the pumpkins would be less than 12 as well, because all the pumpkins would simply weigh less than 12.

The equation for the average weight of the pumpkins is (10x + ry) / (x + y) = 12. Solve for r.
10x + ry = 12x + 12y
r = (2x + 12y) / y
r = 12 + 2x/y

Statement (1) tells us y = x + 6 . Plug it in the formula for r:
r = 12 + 2x/(x + 6)
Different values of x yield different values of r. For example the two following situations are possible: x = 2, y = 8, r = 12.5 and x = 6, y = 12, r = 13. Thus statement (1) is not sufficient.

Statement (2) tells us x = y/4 . Rewrite it as y = 4x and plug into the formula for r.
r = 12 + 2x/4x
r = 12.5
The value of r is definite, so statement (2) is sufficient.

The correct answer is B.

From the question-
10x + ry = 12(x+y).....Equation 1
The equation has 4 variables. So 3 equations are needed for solving.

From statement 1: y = x+ 6....Equation 2
Cannot be solved for r.

From statement 2: 4y = x....Equation 3
Cannot be solved for r.

Combining:
We have 3 equations and 3 variables. Can be solved.

C is my answer.