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

Suggested GMAT Problem Solving Samples

• The Interior Angles of a Polygon are in Arithmetic Progression GMAT Problem Solving
• For Any Four Digit Number, abcd, *abcd*= (3^a)(5^b)(7^c)(11^d) GMAT Problem Solving
• GMAT Problem Solving- Find the greatest number that will divide 43, 91 and 183
• If \(2^{98}=256L+N\) , Where L and N are Integers and \(0 \leq N \leq 4\) , What is the Value of N? GMAT Problem Solving
• What is the Value of x? 1) x^2 + x + 10 = 16 2) x = 4y^4+2y^2+2 GMAT Problem Solving
• For How Many Values of k is 12^12 the Least Common Multiple GMAT Problem Solving
• Is Square Root = Always Positive? GMAT Problem Solving
• \(\frac{15^{11}-15^{10}}{14}=?\) GMAT Problem Solving
• The symbol ∆ Denotes One of The Four Arithmetic Operations: Addition, Subtraction, Multiplication, or Division GMAT Problem Solving 
• A Contractor Estimated that his 10-Man Crew Could Complete the Construction in 110 Days if There Was no Rain. GMAT Problem Solving
• If n = \(3^8\)– \(2^8\), Which of the Following is Not a Factor of n? GMAT Problem Solving
• Two Consultants, Mary and Jim, Can Type up a Report in 12.5 Hours and Edit it in 7.5 Hours. GMAT Problem Solving
• GMAT Problem Solving - The Price of Raw Materials Has Gone up by 15%
• Greg Assembles Units of a Certain Product at a Factory. GMAT Problem Solving
• After 6 Games, Team B Had an Average of 61.5 Points Per Game. GMAT Problem Solving
• If 10, 12 and ‘x’ are Sides of an Acute Angled Triangle, How Many Integer Values of ‘x’ are Possible? GMAT Problem Solving
• Six Bells Commence Tolling Together and Toll at Intervals of 2, 4, 6, 8 10 and 12 seconds Respectively GMAT Problem Solving 
• Excluding Stoppages, The Speed of a Bus is 54km/hr and Including Stoppage, It is 45km/hr GMAT Problem Solving 
• GMAT Problem Solving - Iqbal Dealt Some Cards to Mushtaq and himself from a Full Pack of Playing Cards
• A Rectangular Box has Dimensions 12*10*8 Inches GMAT Problem Solving