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.
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