If a Taxi Driver Charges x Cents for the First Quarter-Mile of a Trip GMAT Problem Solving

Question: If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trips whose distance in miles is the whole number y?

1. (x+xy)/125
2. (4x+4xy)/5
3. (4x+xy)/500
4. (4x+xy)/5
5. xy/25

“If a taxi driver charges x cents for the first quarter-mile of a trip and (x/5) cents for each additional quarter-mile, what is the charge, in cents, for a trips whose distance in miles is the whole number y?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

Answer:

Approach Solution (1):

Since 1 mile has 4 quarter-miles, a trip of y miles ahs 4y quarter-miles and after the first-quarter mile that charges x cents, there are 4y-1 additional quarter-miles that charges x/5 cents each. Thus, the total cost is:

x + (x/5) (4y-1)
5x/5 + (4xy – x)/5
(4x+4xy)/5

Correct option: B

Approach Solution (2):

Let y be 1 mile
x = 20 cents
As per given info
In 1 mile we have 4 quarter mile
So for the first mile x = 20 cents and x/5 cents = 20/5 = 4 cents for every additional quarter mile
So total = 20 + 4 + 4 + 4 = 32 cents charge for complete ride

Correct option: B

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