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work rate

by vaibhav101 » Wed Aug 01, 2018 9:21 am

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machine A can fill an order of widgets in a hours. machine B can fill the same order in b hours. Working together they begin to fill the order at noon. If a & b are even integers, is machine A's rate the same as that of machine B?

1) machine A and B finish the order at exactly 4:48pm
2)( a+b)^2=400
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Source: — Data Sufficiency |
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by deloitte247 » Fri Aug 10, 2018 9:18 am

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Machine A can do the work in a hour, so in 1 hour
$$=\ \frac{1}{a}$$
$$Same\ thing\ is\ applicable\ to\ machine\ B\ =\ \frac{1}{b}\ in\ 1hour.$$
Question; If a and b are even integers, is machine A's rate the same as that of B ?

Statement 1; Machine A and B finish the order at exactly 4 : 48 pm
$$This\ is\ the\ same\ as\ 4\frac{4}{5}\ hours\ =\ \frac{24}{5}hours$$
$$=\ \frac{24}{5}\left(\frac{1}{a}\ +\frac{1}{b}\right)=\ 1$$
$$\frac{\left(a+b\right)}{ab}=\ \frac{5}{24}$$
$$24a\ +\ 24b\ =\ 5ab$$
If both rates are equal the b = a
$$24a\ +\ 24b\ =\ 5a^2$$
$$48a=\ 5a^{2\ }\ or\ 5a\ =\ 48\ =\ 9.6.$$
A and B are supposed to be even integers.
Hence, machine A and B do not work at the same rate, however, statement 1 is SUFFICIENT.

$$Statement\ 2;\ \left(a\ +\ b\right)^2\ =\ 400$$
a + b = 200
There are so many possible combinations for this equation.
a = 100, b = 100
a = 5 b= 150. It is not specific.
Hence, statement 2 is NOT SUFFICIENT.
Option A is CORRECT.
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