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Users of a mobile telephone plan M

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Users of a mobile telephone plan M

by carlos.lara.7 » Thu Sep 15, 2016 4:21 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.

A - statement (1), BY ITSELF is sufficient to answer the question but statement (2) by itself is not sufficient to answer the question

B - statement (2), BY ITSELF is sufficient to answer the question but statement (1) by itself is not sufficient to answer the question

C - BOTH statement (1) and (2) TOGETHER are sufficient to answer the question, but NEITHER statement BY ITSELF is sufficient to answer the question

D - EACH statement BY ITSELF is sufficient to answer the question

E - the two statements, even when taken TOGETHER, are NOT sufficient to answer the question
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Source: — Data Sufficiency |

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by [email protected] » Thu Sep 15, 2016 4:34 pm
Hi carlos.lara.7,

This question is ultimately about translating words into 'math.' We're told that plan M allows users a certain number of minutes of phone calls. Any extra minutes beyond the plan 'limit' are charged at $0.50 for each additional minute. We're asked for the number of minutes allowed by plan M.

1) The cost of exceeding the limit by 50 percent is $75.

From the prompt, we know the price of each additional minute. Fact 1 tells us that $75 in extra fees will be added on IF the total number of minutes increase by 50%. That extra $75, at $0.50/minute, equals 150 minutes of extra calls. We're told that this is equal to a 50% increase over the plan, so....

150 minutes = (50%)(plan M)
300 minutes = plan M

We now know the answer to the question.
Fact 1 is SUFFICIENT

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.

From this Fact, and the information in the prompt, we know a few things:
$75 extra = 150 extra minutes
$150 extra = 300 extra minutes

(plan M + 150) = (3/4)(plan M + 300)
(plan M + 150) = (3/4)(plan M) + 225

(1/4)(plan M) = 225 - 150
(1/4)(plan M) = 75
plan M = 300 minutes

We now know the answer to the question.
Fact 2 is SUFFICIENT

Final Answer: D

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by Matt@VeritasPrep » Fri Sep 16, 2016 1:54 pm
I actually think the wording in S1 is ambiguous: "the cost of exceeding" doesn't necessarily mean "the extra cost incurred by exceeding", it could mean "the base cost + the extra cost".

But making the assumption that it only means the extra cost, S1 is sufficient. Is this a GMATPrep Q? Seems a little sloppy for them, but you never know.
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