On Certain Road 10% of the Motorists Exceed the Posted Speed Limit GMAT Problem Solving

Question: On certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?

1. 10.5%
2. 12.5%
3. 15%
4. 22%
5. 30%

“On certain road 10% of the motorists exceed the posted speed limit and receive speeding tickets, but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets. What percent of the motorists on the road exceed the posted speed limit?”- 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:

Say there are 100 motorists.
{# of motorists who exceed speed and receive tickets} + {#of motorists who exceed speed and don’t receive tickets} = {Total # of motorists who exceed speed}
Given: {# of motorists who exceed speed} = x
Then 0.2x = {# of motorists who exceed speed and don’t receive tickets}
10 + 0.2x = x
x = 12.5

Correct option: B

Approach Solution 2:

On a certain road, 10% of the motorists exceed the posted speed limit and receive speeding tickets,
10% of the total motorists exceed speed limit and get tickets but 20% of the motorists who exceed the posted speed limit do not receive speeding tickets.
20% who exceed the speed limit do not get tickets. Then 80% who exceed the speed limit must be getting tickets.
What percent of the motorists on the road exceed the posted speed limit?
So 10% of the total motorists = 80% of those who exceed speed limit
So those who exceed speed limits are 1/8 = 12.5% of the motorists

Correct option: B

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