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Alain and Brenda were each given 50 envelopes to address as

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by BTGmoderatorDC » Tue Nov 19, 2019 5:57 pm
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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by Jay@ManhattanReview » Tue Nov 19, 2019 10:41 pm
BTGmoderatorDC wrote: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
Say, working individually, Alian takes a minutes and Brenda takes b minutes to address 50 addresses.

We have to get the value of a.

Let's take each statement one by one.

(1) Alain addressed his envelopes in 1.2 times the amount of time it took Brenda to address her envelopes.

=> a = 1.2b. Can't get the value of a. Insufficient.

(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.

=> 1/a + 1/b = 1/110. Can't get the value of a. Insufficient.

(1) and (2) together

From (1), we have a = 1.2b and from (2), we have 1/a + 1/b = 1/110. We can get the unique value of a. Sufficient.

The correct answer: C

Hope this helps!

-Jay
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