Respuesta :
Answer:
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Step-by-step 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+[tex]\frac{48}{60}[/tex] hrs = 4+[tex]\frac{4}{5}[/tex] hrs= [tex]\frac{24}{5}[/tex] hours
Thus, [tex]\frac{1}{a}+\frac{1}{b} = \frac{5}{24}[/tex]
Let say Machine A's rate the same as that of Machine B
[tex]\frac{1}{a}+\frac{1}{a} = \frac{5}{24}\\\\\frac{2}{a} = \frac{5}{24}\\\\a = \frac{48}{5}[/tex]
It is given that a and b are even integers, but [tex]\frac{48}{5}[/tex] 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: [tex](a + b)^2 = 400[/tex]
[tex](a+b)^2 = 400\\a+b=20[/tex]
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.
