Work/Rate Problem

[aditiniyer]

Machine A can fill an order of widgets in a hours. Machine B can fill the same in b hours. Machine A & B begin to fill an order of widget at noon, working together at their respective rates. If a & b are even integers, is machine A's rate same as Machine B.

1) Machine A & B finish the order at exactly 4:48pm .
2) (a+b) ^2 = 400

[Jay@ManhattanReview]

Machine A can fill an order of widgets in a hours. Machine B can fill the same in b hours. Machine A & B begin to fill an order of widget at noon, working together at their respective rates. If a & b are even integers, is machine A's rate same as Machine B.

1) Machine A & B finish the order at exactly 4:48pm .
2) (a+b) ^2 = 400

We have to see whether a = b given that and b are even integers. We need not find out whether 'a' is greater than 'b' or vice-versa.

S1: total time, A and B worked = 4.48 pm - 12 pm = 4 hours and 24 minutes = 24/5 hours

Thus, 1/a + 1/b = 5/24

Say, a = b, then 2/a = 5/24

=> a = 48/5 hours, not an even integer. Answer is NO. Sufficient.

S2: (a+b)^2 = 400

=> a+b = 20

If a = b = 10 (both even), the answer is YES.

However, if a = 2 and b = 18 (both even), the answer is NO. No unique answer.

Answer: A

-Jay
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[Scott@TargetTestPrep]

Machine A can fill an order of widgets in a hours. Machine B can fill the same in b hours. Machine A & B begin to fill an order of widget at noon, working together at their respective rates. If a & b are even integers, is machine A's rate same as Machine B.

1) Machine A & B finish the order at exactly 4:48pm .
2) (a+b) ^2 = 400

We are given that machine A can fill an order of widgets in a hours and machine B can fill the same order in b hours. We are also given that a and b are even integers, and we need to determine whether machine A's rate is same as machine B's. Since rate = work/time, the rate of machine A is 1/a and the rate of machine B is 1/b. We need to determine if 1/a = 1/b. However, if 1/a = 1/b, then a = b. So we need to determine if a = b.

Statement One Alone:

Machines A & B finish the order at exactly 4:48 pm.

Since the machines started working at 12 pm and finished at 4:48, we see that it took the machines 4 hours and 48 minutes to complete the job.

4 hours and 48 minutes = 4 and 48/60 hours = 4 and 4/5 hours = 24/5 hours

Thus, the combined rate is 1/(24/5) = 5/24. Let's now determine whether a = b. Suppose it does and we can make the rates of machines A and B the same; say both rates are 1/a. Thus we have:

1/a + 1/a = 5/24

2/a = 5/24

5a = 48

a = 48/5 = 9.6

However, since we are given that a and b are EVEN INTEGERS, and if both rates were the same, we would NOT PRODUCE an even integer for a or b. Statement one is sufficient for us to say that the rates of machines A and B are NOT equal. We can eliminate answer choices B, C, and E.

Statement Two Alone:

(a+b)^2 = 400

We can take the square root of both sides of the given equation:

a + b = 20

Since a + b = 20, we see that both a and b could be 10, making the rates equal, or a = 8 and b = 12, making the rates NOT EQUAL. Statement two alone is not sufficient to answer the question.

Answer: A