Alain and Brenda were each given 50 envelopes to address as part of a charity drive. How much time did it take Alain to

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Thu Apr 09, 2020 4:41 pm

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Alain and Brenda were each given 50 envelopes to address as part of a charity drive. How much time did it take Alain to address the envelopes he was given?

(1) Alain addressed his envelopes in 1.2 times the amount of time it took Brenda to address her envelopes.
(2) If Alain and Brenda had addressed 50 envelopes together, each working at the same rate as when they worked separately, it would have taken them 1 hour
and 50 minutes to address all the envelopes.

OA C

Source: EMPOWERgmat

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Source: Beat The GMAT — Data Sufficiency | Thu Apr 09, 2020 4:41 pm

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

Re: Alain and Brenda were each given 50 envelopes to address as part of a charity drive. How much time did it take Alain

by deloitte247 » Sat Apr 18, 2020 12:21 pm

Alain was given 50 envelopes
Brenda was also given 50 envelopes
Let the time taken by Alain to address 50 envelopes = a minutes
Let the time taken by Brenda to address 50 envelopes = b minutes
Question => how much time did it take Alian to address the envelopes he was given?
Statement 1 => Alian addressed his envelopes in 1.2 times the amount of time it took Brenda to address her envelopes.
a = 1.2b minutes, the exact value of b is unknown. Statement 1 is NOT SUFFICIENT

Statement 2 => if Alian and Brenda had addressed 50 envelopes together, each working at the same rate as when they worked separately, it would have taken them 1 hour and 50 minutes to address all the envelopes.
$$work rate=\frac{workdone}{time}$$
$$For\ Alian\ work rate\ for\ 50\ envelopes=\frac{50}{a}$$
$$Therefore,\ work\ rate\ for\ 1\ envelope=\frac{1}{a}and\ Brenda=\frac{1}{b}$$
1 hour 50 minutes = 60 minutes + 50 minutes = 110 minutes
For Brenda and Alian to work today in 50 envelopes with their present work rate,
$$._.^.\ \frac{1}{a}+\frac{1}{b}=\frac{1}{110}$$ but the value of b is still unknown. So, statement 2 is NOT SUFFICIENT

Combining both statements together =>
a = 1.2b
$$\frac{1}{a}+\frac{1}{b}=\frac{1}{110\ }\ \ where\ a\ =\ 1.2b$$
$$Therefore,\ \frac{1}{1.2b}+\frac{1}{b}=\frac{1}{110}$$
$$\frac{1+1.2}{1.2b}=\frac{1}{110}$$
$$\left(2.2\right)\cdot110=1.2b$$
$$\frac{242}{1.2}=\frac{1.2b}{1.2}$$
$$b=201.7\approx202\min utes$$
Back to a = 1.2b where b = 201.7
a = 1.2 * 201.7
a = 242 minutes

Both statements together ARE SUFFICIENT
Answer = C

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