GMAT Challenge Series (700+): Q14

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Question:

A customer using a certain telephone calling plan pays a fee of $25 per month, and then receives a discount of 40% on the regular charge for all calls made to country A. If calls to country A are regularly charged at $1.60 per minute for the first 3 minutes, and $0.80 per minute for each minute thereafter, what is the maximum the customer could have saved over regular prices if he was charged for 1 hour of calls made to country A in a certain month?

A. $8.75

B. $12.00

C. $13.40

D. $17.40

E. $24.40

MBA Wisdom's Answer:

$$\text{The maximum saving occurs when the bill is the highest}$$ $$\text{The bill is the highest when every minute is charged at \$1.60}$$ $$$$ $$\textit{max cost without plan} = \left(\textit{minutes}\right) \left(\textit{rate}\right)$$ $$\textit{max cost without plan} = {\left({60}\right) \left({1.6}\right)} = {96}$$ $$$$ $$\textit{max cost with plan} = \textit{plan fee} + \left(\textit{minutes}\right) \left(\textit{rate}\right) \left(\textit{1 - discount}\right)$$ $$\textit{max cost with plan} = {25} + {\left({60}\right) \left({1.6}\right) \left({0.6}\right)} = {25} + {57.6} = {82.6}$$ $$$$ $$\textit{max saving} = \textit{max cost without plan} - \textit{max cost with plan}$$ $$\textit{max saving} = {96} - {82.6}$$ $$\textit{max saving} = {13.4}$$

C. $13.40