3

Brain teaser "clock observation"

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

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

3 answers

  • Upvotes
  • Date ascending
  • Date descending
Best Answer

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.

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.

Book a coaching with Vlad

97% Recommendation Rate

388 Meetings

7,448 Q&A Upvotes

USD 239 / Coaching

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

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

Hey Vlad, thanks a lot for the quick reply. Yes, that's the correct exercise. I saw the solution but was unable to understand how you arrive at it. Would you kindly explain how you got there? Thanks a lot! — Anonymous on Oct 26, 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. — Anonymous on Oct 27, 2017 (edited)

Hello but for me, it is 1 hour and 6 minutes, you can test with any hour, imagine it is around 2 p.m the first observation 2:16 and the second is 3:22 ------? the difference is 1:06

imagine the observation is at 8 p.m ---? 1st observation is 8:46 and 2nd observation 9: 52 ---> the difference is 1 hour and 6 second...... as you can see at all these times, the distance between minute and hour hand are valid...

any elaboration?

Hello but for me, it is 1 hour and 6 minutes, you can test with any hour, imagine it is around 2 p.m the first observation 2:16 and the second is 3:22 ------? the difference is 1:06

imagine the observation is at 8 p.m ---? 1st observation is 8:46 and 2nd observation 9: 52 ---> the difference is 1 hour and 6 second...... as you can see at all these times, the distance between minute and hour hand are valid...

any elaboration?

Related BootCamp article(s)

Brain Teasers

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

1 Q&A

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.

Related case(s)

MBMC Case: Exploring future Business Models on Four Wheels

Solved 200+ times
MBMC Case: Exploring future Business Models on Four Wheels As a consultant at Mercedes-Benz Management Consulting, you are actively shaping the future of mobility. While you are contributing to decisive projects that design the future of the world’s No.1 premium carmaker, you also develop your own career path and you have the unique possibility to build your personal brand and cultivate relationships with the top management. Your client on your current project, the C-Class model series responsible, asks you to explore new profit pools and business opportunities regarding optional equipment. Initially, you shall structure and explore potential business models, and discuss necessary conditions and implications of these business models. In a next step, you shall identify possible options and prepare them for decision. And of course, the client is interested in your recommendation.
3.0 5 2
| Rating: (3.0 / 5.0)

As a consultant at Mercedes-Benz Management Consulting, you are actively shaping the future of mobility. While you are contributing to decisive projects that design the future of the world’s No.1 premium carmaker, you also develop your own career path and you have the unique possibility to build you ... Open whole case

Brain Teasers - U2 Concert

Solved 9.6k times
Brain Teasers - U2 Concert 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 forth in this way until one of us says the number 50. That person wins. You will start.”   Question: What number should you start with? U2 Concert Situation:  U2 has a concert that starts in just 17 minutes. To get there, all the band members must cross a bridge. Since the bridge is old, a maximum of two people can cross the bridge at any one time. To make matters worse, it is dark and there is only one torch. Anyone crossing the bridge must carry a torch. The torch cannot be thrown across the bridge. Instead, someone must walk it back to the other side. Each band member walks at a different speed. If two members cross at the same time, both must walk at the speed of the slower band member. Bono takes 1 minute to cross. Edge takes 2 minutes to cross. Adam takes 5 minutes to cross. Larry takes 10 minutes to cross. Question: Can the band make it to the concert in time? How will they manage this? Buckets Situation: You have a 5-gallon bucket and a 3-gallon bucket. (Assume that you have an unlimited supply of water and that the buckets do not have any markings for measurement. Question: How can you get 4 gallons of water into the 5-gallon bucket? Cigars Situation: A homeless man collects cigar butts. He uses 5 cigar butts to make a new cigar. Today, he has collected 25 cigar butts. Question: How many cigars can he smoke?
4.3 5 402
| 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 forth ... Open whole case

Brain Teasers - Motel

Solved 8.6k times
Brain Teasers - Motel 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 $5 to the 3 friends who had just checked in. The bellhop sees this as an opportunity to make $2 as he reasons that the three friends would have a tough time dividing $5 evenly among them; so he decides to tell them that the clerk made a mistake of only $3, giving a dollar back to each of the friends. He pockets the leftover $2 and goes home for the day! Question:  Now, each of the three friends gets a dollar back, thus they each paid $9 for the room which is a total of $27 for the night. We know the bellhop pocketed $2 and adding that to the $27, you get $29, not $30 that was originally spent. Where did the other dollar go? Murder Situation: The midnight train is coming down the mountains. Art Farnanski seems to be sleeping in his seat. At the station, all the passengers get off the train except one. The conductor comes and taps him on the shoulder to let him know they have arrived. Art Farnanski does not answer. He is dead. Hours later the four people that had shared the train compartment with the dead man are at the police station. The man in the dark suit: "I'm innocent. The blonde woman was talking to Farnanski." The blonde woman: "I'm innocent. I did not speak to Farnanski." The man in the light suit: "I'm innocent. The brunette woman killed him." The brunette woman: "I'm innocent. One of the men killed him." Question: The police detective comes up to you and says: “I know that four statements are wrong and four are true. Who killed Farnanski? (Only one person is guilty).” Trees Statement: You have 10 trees and you have to plant them in five rows, but each row must contain 4 trees. Question: How is this possible?
4.6 5 451
| Rating: (4.6 / 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 $5 ... Open whole case

Brain Teasers - Pirates

Solved 7.2k times
Brain Teasers - Pirates Pirates Situation: Five pirates are trying to split up 1000 gold pieces. The rules are as follows: Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose a solution to the remaining 3 pirates, and the same rules will follow. This continues until someone comes up with a plan that earns a majority vote. The pirates are infinitely greedy, infinitely ruthless (the more dead pirates the better), and infinitely intelligent.                        Question: What is the highest amount of gold pieces that pirate #1 can keep and what would his proposal be?             Chicken Situation: A man is traveling with a fox and two chickens, if he leaves the fox alone with the chickens the fox will eat the chickens. He arrives at a river and needs to cross it. He finds a small boat that can carry only him and one animal.          Question: How does he get himself, the fox and the two chickens across the river safely?
4.5 5 406
| Rating: (4.5 / 5.0)
Difficulty: Intermediate | Style: Brain Teaser | Topics: Brain teaser

Pirates Situation: Five pirates are trying to split up 1000 gold pieces. The rules are as follows: Pirate #1 must divide the gold up in such a way that a majority of the pirates (including himself) agree to. If he does not get a majority vote, he will be killed, and pirate #2 will get to propose ... Open whole case

Brain Teasers - Firefighter

Solved 6.7k times
Brain Teasers - Firefighter 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: How many rungs did the ladder have? Bartender Situation: There are two twin old men that go into the same bar every day. The bartender at the bar hates one of the twins, but there is only one way he could tell the difference between them: The one that he hates drinks very slowly and the one that he likes drinks fast. One day the bartender decides to kill the one that he hates. So when they came in that day he put the same amount of the drink in their cups, the same amount of ice, and the same amount of poison. When they are both done with their drinks the one that the bartender hates dies, but the one he likes lives. Question: How is this? Hats Situation: There are 4 people sitting in a row, trying to win a riddle. The one in front was wearing a red hat. The second from the front was wearing a blue hat. The third from the front was wearing a red hat. The last was wearing a blue hat and is blind-folded. Each of them was informed that they are all wearing a hat, the last person is blind-folded and that there are 2 red and 2 blue hats. They can only see the persons in front of them and are not allowed to turn around and see behind them. Question: The one who guesses the color of his hat wins the prize. Who is it?  
4.5 5 66
| Rating: (4.5 / 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: How m ... Open whole case