ericaspoggi wrote:Hi there!

Could you help me out with this one?

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 paln M by $75 uses 3/4 as much telephone time as a client who exceeds plan M by $150.

Thanks

Let L = the limit.

Statement 1: The cost of exceeding the limit by 50 percent is $75.
For $75, the number of excess minutes purchased = (total charge)/(charge per minute) = 75/.5 = 150.
These 150 minutes constitute exceeding the value of L by 50%.
Since 150 is 50% of 300, L = 300 minutes.
SUFFICIENT.

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.
Here, the following constraint must be satisfied:
(total time with a $75 surcharge)/(total time with a $150 surcharge) = 3/4.

For $75, the number of excess minutes purchased = 150, as shown in statement 1.
For $150, the number of excess minutes doubles to 300.

Since the two statements cannot contradict each other, the value of L in statement 1 -- L=300 -- must also satisfy statement 2.
Case 1: L=300
(total time with a $75 surcharge)/(total time with a $150 surcharge) = (300+150)/(300+300) = 450/600 = 3/4.

Check whether a different value for L will also satisfy statement 2.
Case 2: L=200
(total time with a $75 surcharge)/(total time with a $150 surcharge) = (200+150)/(200+300) = 350/500 = 7/10.

In Case 2, (total time with a $75 surcharge)/(total time with a $150 surcharge) ≠ 3/4.
Implication:
Only the value in Case 1 -- L=300 -- will satisfy statement 2.
SUFFICIENT.

The correct answer is D.