there seems to me that there is something wrong with the solution here. i've bolded the part of the solution that I think misinterprets what the question is saying. pls help!
A certain shipment of identical cans of soup can be packed either into cartons that hold 15 cans each or into cartons that hold 25 cans each. If all cartons will be completely filled regardless of the size chosen, and there will be an equal number of small and large cartons used, how many of the larger cartons would be needed to for the entire shipment?
(1) Forty fewer cartons would be needed if the shipment were packed in the larger cartons than if it were packed in the smaller cartons.
(2) If the cans were packed into the smaller cartons, 100 cartons would be needed.
OA is D
PR Solution:
Yes. Remember that when you are dealing with unknown quantities on a Data Sufficiency problem, you should think of the information in terms of algebraic equations. The problem tells you that the total number of cans to be packed in 15-can cartons is equal to the number of cans to be packed in 25-can cartons. 15x = 25y. Statement 1 tells you that the difference in the number of cartons required is 40, or x - y = 40. Combined with the problem, this yields enough information to solve for each variable (two independent equations, two variables); eliminate BCE. Statement 2 specifies one of the variables (x = 100), and so is sufficient for the same reason. Eliminate A.
The question is saying, that NUMBER of large and small cartons will be the same....NOT the number of cans. Pls advise.
A certain shipment of identical cans of soup can be packed either into cartons that hold 15 cans each or into cartons that hold 25 cans each. If all cartons will be completely filled regardless of the size chosen, and there will be an equal number of small and large cartons used, how many of the larger cartons would be needed to for the entire shipment?
(1) Forty fewer cartons would be needed if the shipment were packed in the larger cartons than if it were packed in the smaller cartons.
(2) If the cans were packed into the smaller cartons, 100 cartons would be needed.
OA is D
PR Solution:
Yes. Remember that when you are dealing with unknown quantities on a Data Sufficiency problem, you should think of the information in terms of algebraic equations. The problem tells you that the total number of cans to be packed in 15-can cartons is equal to the number of cans to be packed in 25-can cartons. 15x = 25y. Statement 1 tells you that the difference in the number of cartons required is 40, or x - y = 40. Combined with the problem, this yields enough information to solve for each variable (two independent equations, two variables); eliminate BCE. Statement 2 specifies one of the variables (x = 100), and so is sufficient for the same reason. Eliminate A.
The question is saying, that NUMBER of large and small cartons will be the same....NOT the number of cans. Pls advise.
