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A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are

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A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are

by Gmat_mission » Sun May 03, 2020 1:14 pm

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A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are used only by government vehicles while the letters D through Z are used by non-government vehicles. Kerrania's intelligence agency has recently captured a message from the country Gonzalia indicating that an electronic transmitter has been installed in a Kerrania government vehicle with a license plate starting with 79. If it takes the police 10 minutes to inspect each vehicle, what is the probability that the police will find the transmitter within three hours?

(A) 18/79
(B) 1/6
(C) 1/25
(D) 1/50
(E) 1/900

[spoiler]OA=D[/spoiler]

Source: Manhattan GMAT
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Re: A license plate in the country Kerrania consists of four digits followed by two letters. The letters A, B, and C are

by deloitte247 » Fri May 08, 2020 11:05 am
A license plate consists of 4 digits + 2 letters
The police can search 1 car in 10 minutes
They will search x cars in 60/10 * 3 hours = 18 cars in 3 hours
The police are looking for an electronic transmitter in a government vehicle
Government vehicles' license plate only consist of letters A, B, and C, and the first 2 digit is 79

$$Government\ license\ plates\ =>\ 7\ 9\ x_{1\ \ }x_{2\ }\ y_{1\ }\ y_2$$
The possible digits that can be in position x1 is any number between 0 and 9. So, there are 10 different option for x1 the same goes for x2

The possible letters that can be in position y1 is either A, B, or C. There are 3 different option for y1 same goes for y2

The total number of possible plates/vehicles for police to search = 10 * 10 * 3 * 3 = 900
If 1 vehicle was inspected in 10 minutes
900 vehicle will be inspected in 900 * 10/1 = 9000 minutes
$$\Pr obability\ of\ finding\ the\ transmitter=\frac{no\ of\ favourable\ event}{sample\ space}$$
Where favourable event = number of vehicles that can be inspected in 3 hours
Sample space = total vehicles/plates matching the requirements
$$\Pr obability\ of\ finding\ transmitter=\frac{18}{900}=\frac{1}{50}$$

Answer = D
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