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Mobile telephone

by FernandaFranca » Tue Mar 27, 2012 12:49 pm
Users of a mobile telephone plan M are allowed to make calls to a hired limit of minutes per month, after which they will have to pay $0.50 for each extra minute. How many minutes is the original cap of the plan M?

(1) The cost of exceeding the limit by 50 percent is $75.
(2) A client who exceeds plan M by $75 uses 3/4 as much telephone time as a client who exceeds plan M by $150.
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Source: — Data Sufficiency |

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by Mike@Magoosh » Tue Mar 27, 2012 1:56 pm
Hi, there. I'm happy to contribute to this problem. :)

Prompt: Users of a mobile telephone plan M are allowed to make calls to a hired limit of minutes per month, after which they will have to pay $0.50 for each extra minute. How many minutes is the original cap of the plan M?

Let M be the number of minute one can talk for free under plan M.

Statement #1: The cost of exceeding the limit by 50 percent is $75.

$75 dollars means using an extra 150 minutes. If 150 is 50% of M, then M = 300 minutes. Statement #1, by itself, is sufficient to answer the question.

Statement #2: A client who exceeds plan M by $75 uses 3/4 as much telephone time as a client who exceeds plan M by $150.

The person who pays $75 talks for an extra 150 minutes.

The person who pays $150 talks for an extra 300 minutes.

This statement says that:

(M + 150) = (3/4)*(M + 300)

M + 150 = (3/4)*M + 225

(1/4)*M + 150 = 225

(1/4)*M = 75

M = 4*75 = 300 minutes

Statement #2, by itself, is sufficient to answer the question.

Answer = D

Here's a DS question with some related ideas.
https://gmat.magoosh.com/questions/952
When you submit your answer to the question, they following page will have the video explanation.

Does all this make sense? Let me know if you have any questions.

Mike :)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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