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Tom corrects 30% of a batch of 210 letters in 2 hours. He

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by BTGmoderatorLU » Fri Dec 27, 2019 4:37 pm
Source: Economist GMAT

Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes his pace, so the remaining letters take him five additional hours to finish. Tom's rate during the first two hours is how many times his rate during the following five hours?

A. 10/21
B. 7/12
C. 14/15
D. 15/14
E. 12/7

The OA is D
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by deloitte247 » Sat Dec 28, 2019 1:16 pm
In the first 2 hours, he completed 30% of the job
In the next 5 hours, he completed 70% of the job
Work = Rate x Time
Workdone in the first 2 hours = $$\frac{30}{100}\cdot210=63\ letters$$
$$Tom's\ rate\ in\ the\ first\ 2\ hours\ =\ \frac{63}{2}$$
$$Workdone\ in\ the\ next\ 5\ hours=\frac{70}{100}\cdot210=147\ letters$$
$$Tom's\ rate\ in\ the\ first\ 2\ hours\ =\ \frac{147}{2}$$
Rate of work for 2 hours : Rate of work for 5 hours
$$\frac{63}{2}:\frac{147}{5}$$
$$\frac{Rate\ for\ 2\ hours}{Rate\ for\ 5\ hours}=\frac{\frac{63}{2}}{\frac{147}{5}}=\frac{63}{2}\cdot\frac{5}{147}=\frac{315}{294}$$
$$=\frac{15}{14}\ \ \ \ \ \ \ \ \ \ Answer\ =\ option\ D$$
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by Scott@TargetTestPrep » Fri Jan 10, 2020 8:39 am
BTGmoderatorLU wrote:Source: Economist GMAT

Tom corrects 30% of a batch of 210 letters in 2 hours. He then changes his pace, so the remaining letters take him five additional hours to finish. Tom's rate during the first two hours is how many times his rate during the following five hours?

A. 10/21
B. 7/12
C. 14/15
D. 15/14
E. 12/7

The OA is D
Tom's rate during the first two hours is (210 x 0.3)/2 = 63/2 = 31.5.

His rate for the remaining letters in the next 5 hours is:

(210 x 0.7)/5 = 29.4.

Thus, his rate during the first two hours is 31.5/29.4 = 315/294 = 105/98 = 15/14 times his rate in the following five hours.

Answer: D

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