Question

Machine A can fill an order of widgets in a hours. Machine B can fill the same order of widgets in b hours. Machines A and B begin to fill an order of widgets at noon, working together at their respective rates. If a and b are even integers, is Machine A's rate the same as that of Machine B?(1) Machines A and B finish the order at exactly 4:48 p.m.(2) (a + b)^2 = 400

Answer 1

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.

Explanation:

Consider the provided information.

Machine A can fill an order of widgets in a hours. Machine B can fill the same order of widgets in b hours.

Thus, in 1 hr machine A's work is 1/a and machine B's work is 1/b.

We need to find whether the Machine A's rate the same as that of Machine B?

Statement 1: Machines A and B finish the order at exactly 4:48 p.m.

Total time, A and B worked = 4:48 = 4+
`(48)/(60)` hrs = 4+
`(4)/(5)` hrs=
`(24)/(5)` hours

Thus,
`(1)/(a)+(1)/(b) = (5)/(24)`

Let say Machine A's rate the same as that of Machine B

`(1)/(a)+(1)/(a) = (5)/(24)\\\\(2)/(a) = (5)/(24)\\\\a = (48)/(5)`

It is given that a and b are even integers, but
`(48)/(5)` is not an even integer.

Hence, Machine A's rate is not same as that of Machine B.

Therefore, statement (1) ALONE is sufficient.

Statement 2:
`(a + b)^2 = 400`

`(a+b)^2 = 400\\a+b=20`

There are many possible case in which a and b are even integer and there sum is 20.

If a = b = 10 (both even), then Machine A's rate is same as that of Machine B.

if a = 6 and b = 14 (both even), then Machine A's rate is not same as that of Machine B.

Therefore, No unique answer with statement 2.

Hence, statement 2 alone is not sufficient.