An Electronic Clock Shows Time in Hours and Minutes GMAT Problem Solving

Question: An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at sometime between 6:00 and 9:00, what is the probability that he will see the digit 8?

1.  \(\frac{1}{5}\)
2. \(\frac{1}{3}\)
3. \(\frac{2}{5}\)
4. \(\frac{4}{9}\)
5. \(\frac{1}{2}\)

Correct option: C

Solution and Explanation:
Approach Solution 1:
The period between 6:00 and 9:00 consists of 180 minutes. During 72 minutes of these 180 the clock will display the digit 8: during 60 minutes of the 8:00 – 9:00 hour and during 6 minutes of each of the hours 6:00 – 7:00 and 7:00 – 8:00. The required probability = \(\frac{72}{180}=\frac{2}{5}\)

Approach Solution 2:

6 to 7 : 6:08; 6:18; 6:28.. 6:58; 6 times also similarly 7-8; 6 times

6-8: 12 times

8-9: 60 times

Total: 72 minutes when 8 would come on display

Total minutes: (9 – 6) hours * 60 = 180 minutes

\(\frac{72}{180}=\frac{2}{5}\)

Approach Solution 3:
first time it shows is 6:08
then 6:18,6:28...38,48,58
6 cases out of 60 between 6 and 7
6 cases out of 60 between 7 and 8
now between 8:00 and 9:00 he will see all the time. All the 60 cases.

So 72 cases out of 180 cases

=72/180 = 2/5

“An electronic clock shows time in hours and minutes. For example, 08:15 means that it is now a quarter past eight. If one looks at the clock at sometime between 6:00 and 9:00, what is the probability that he will see the digit 8?”- 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.

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