A Password to a Certain Database Consists of Digits that Can GMAT Problem Solving

Question: A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of atleast 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?

1. \(\frac{8!}{5}\)
2. \(\frac{8!}{2}\)
3. 8!
4. \(\frac{10!}{2}\)
5. \(\frac{5}{2}*10!\)

“A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of atleast 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?”- 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):

Total # of passwords possible for 8 digits is =\(P^8_{10} \)=\(\frac{10!}{2}\)

Total # of passwords possible for 9 digits is =\(P^9_{10} \)=10!

Total # of passwords possible for 10 digits is =\(P^{10}_{10} \)=10!

Time needed to guarantee access to database is \((\frac{10!}{2}+10!+10!)*\frac{1}{5}=\frac{10!}{2}minutes\) 

Correct option: D

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