ExpertsGlobal5
An animation program, Squibble, renders 200 items per minute, another, Pencil Lab, renders 400 items per minute, and a third, Paint Lab, colors 3,600 items per minute. All items rendered are colored and no item not fully rendered is colored. In a particular minute, how many animation programs are running?
(1) A total of 10,800 items are rendered that minute.
(2) For that minute, there are 4 Pencil Lab programs running for every Paint Lab program running.
Explanation: Number of items rendered by one Squibble program in a minute = 200.
Number of items rendered by one Pencil Lab program in a minute = 400.
Number of items colored by one Paint Lab program in a minute = 3600.
Let the number of Squibble programs running be A.
Let the number of Pencil Lab programs running be B.
Let the number of Paint Lab programs running be C.
We need to find whether the value of A + B + C can be determined. Statement (1) Since 10800 items are rendered in a minute: 200A + 400B = 10800 (Equation I)
Also, since all rendered items are colored, it follows that 10800 items are also colored in a minute.
C = 10800/3600 = 3 (Equation II)
Equation I has
multiple solutions for A and B. Possibility 1: If A = 54, B = 0, and C = 3, then it satisfies the given condition and A + B + C = 57.
Possibility 2: If A = 0, B = 27, and C = 3, then it satisfies the given condition and A + B + C = 30.
It is NOT possible to determine the exact number of the animation programs running.
Hence, Statement (1) is insufficient. Statement (2) B = 4C (Equation III)
Equation III has
multiple solutions for B and C. Possibility 1: If A = 10, B = 4, and C = 1, then it satisfies the given condition and A + B + C = 15.
Possibility 2: If A = 20, B = 8, and C = 2, then it satisfies the given condition and A + B + C = 30.
As Statement (1) alone as well as Statement (2) alone is insufficient to answer the question, we need to now combine the two statements.
Statement (1) and Statement (2) combined From Equation I, Equation II and Equation III, we have 3 equations with 3 unknown variables which can be solved to determine the exact value of A, B and C.
Hence, Statement (1) and Statement (2) combined are sufficient. C is the correct answer choice.