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Joe, Bob and Dan worked in the ratio of 1:2:4 hours,

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by AAPL » Fri Sep 20, 2019 12:19 am

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Joe, Bob and Dan worked in the ratio of 1:2:4 hours, respectively. How many hours did Bob work?

1) Together, Joe, Bob and Dan worked a total of 49 hours.
2) Dan worked 21 hours more than Joe.

OA D
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Source: — Data Sufficiency |
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by deloitte247 » Sat Sep 21, 2019 7:56 pm
Ratio of work done by the three (Joe : Bob : Dan) = 1 : 2 : 4
So, how many hours did Bob work?
Statement 1: Together Joe, Bob and Dan worked a total of 49 hours.
Work done by the 3 = 49 hrs
The ratio can be written as 1x : 2x : 4x where x is a factor of each ratio.
The total hours worked now = 1x+2x+4x
Therefore, 7x/7 = 49hrs/7
x = 7hrs
Work done by Bob is in ratio 2x; therefore; 2x = 2*7 = 14 hours
Statement 1 is SUFFICIENT.

Statement 2: Dan work 21 hours more than Joe.
Respective ratio= 1 : 2 : 4
This can be written as 1x : 2x : 4x where x is a factor of each ratio, and with Dan working more than Joe, we have an expression below;
4x - 1x = 21 hrs
Dan=4x
Joe=1x
$$Therefore,\ \frac{3x}{3}=\frac{21}{3};\ \ \ \ \ x=7hrs$$
Now, work done by Bob is in ratio 2x = 2*7 = 14.
Statement 2 is also SUFFICIENT.

Since each statement alone is SUFFICIENT, then we have the correct answer to be Option D.
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