McKinsey / Accenture / More than 300 real MBB cases / Collected all Big 3 offers / Harvard Business School
Book a coaching

Brain teaser "clock observation"

Anonymous A

Hey everyone,

would anyone be able to elaborate on the clock observation brainteaser? As in, how do you arrive at this particular solution.

Best

K

  • Upvotes
  • Date ascending
  • Date descending
Vlad replied on 10/25/2017
McKinsey / Accenture / More than 300 real MBB cases / Collected all Big 3 offers / Harvard Business School

Hi,

It would be helpful if you provide more details.

If that is the case:

"The hour hand is exactly at a minute mark, and the minute hand is six minutes ahead of it in the first glance. When the clock is looked at again, the hour hand is exactly on a different minute mark, and the minute hand is seven minutes ahead of it this time."

Then the solution is:

In the first observation, the time was 1:12. In the second observation, the time was 3:24.
Therefore, 2 hours and 12 minutes have elapsed.

Best

Anonymous A replied on 10/27/2017

Hey everyone, here is a longer solution that the preblounge team sent me. Maybe it helps you too.

The hour hand of a clock is exactly on the minute mark five times each hour i.e. on the hour, twelve minutes past the hour, twenty four minutes past the hour, thirty six minutes past the hour and forty eight minutes past the hour. Now we will use an equation with two unknowns to solve the problem. Let us suppose that X are the number of hours and Y are the number of minutes past the hour. When the hour hand is on the minute mark, the position of the hour hand is: 5X + Y/12 The position of the minute hand is: Y Thus, when the first observation is made the corresponding equation is: Y = 5X + Y/12 + 6 This is also equivalent to 60X = 11Y - 72. But from what we know, Y can only be equal to 0, 12, 24, 36 or 48. Thus, the only value possible for X and Y are 1 and 12 respectively. This means that the time is 1:12 when the second observation is made. When the second observation is made the corresponding equation is: Y = 5X + Y/12 + 7 This is also equivalent to 60X = 11Y - 84. The possible values for X and Y here are 3 and 24 respectively. This means that the time is 3:24 when the second observation is made. Now we know the time of the first oberservation and of the second observation and can easily calculate the time that has elapsed between the two of them: From 1:12 till 3:24 it is 2 hours and 12 minutes.

Related BootCamp article(s)

Brain Teasers

Learn how to tackle brain teasers and what purpose they serve in consulting case interviews

2 Comment(s)

Typical Question Types in Written Tests

Questions among all tests can be categorized in math, GMAT-style, chart reading and brain teaser questions. Each type needs to be approached differently.

4 Comment(s)

Related case(s)

Brain Teasers - U2 Concert

Solved 4.5k times
4.3 5 150
| Rating: (4.3 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Number sequence Situation: “You and I will take turns saying numbers. The first person will say a number between 1 and 10. Then, the other person will say a number that is greater than the first number. The difference between both numbers must be between 1 and 10. We will keep going back and f ... Open whole case

Brain Teasers - Firefighter

Solved 3.7k times
4.4 5 46
| Rating: (4.4 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Firefighter Situation: A firefighter stood on the middle rung of a ladder, spraying water on a burning house. He then climbed up 6 rungs before the heat of the flames caused him to come down 10 rungs. After some minutes he was able to climb 18 rungs to the very top of the ladder. Question: ... Open whole case

Brain Teasers - Barbershop

Solved 3.6k times
4.1 5 25
| Rating: (4.1 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Barbershop Statement: A business man is in a village for a meeting. He has time to spare before the meeting, so he decides to get a haircut. He looks at a street map and was surprised to find that there are only two barbers in town, right across the road from each other. He went into the f ... Open whole case

Brain Teasers - Lethal Duel

Solved 3.1k times
4.5 5 30
| Rating: (4.5 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Duel Situation: Three men, Adam, Bertie and Charlie, agree to take part in a lethal three-way duel. They each have a pistol and several rounds of ammo, and they draw lots to see who will shoot first and who second. Then they stand an equal distance apart, and they take turns to fire. When it i ... Open whole case

Brain Teasers - Motel

Solved 2.0k times
4.7 5 280
| Rating: (4.7 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Motel Situation: Three friends check into a motel for the night. The clerk tells them the bill is $30, payable in advance. They each pay the clerk $10 and go to their room. A few minutes later, the clerk realizes he has made an error and overcharged the trio by $5. He asks the bellhop to return ... Open whole case