Brain Teasers Flashcards
A car drives 60 miles at an average speed of 30 miles per hour. How fast should the driver drive to travel the same 60 miles in the same time period, but at an average of 60 miles per hour?
This is not possible. To travel 60 miles at an average speed of 30 miles per hour, 2 hours are required; to travel at an average of 60 miles per hour in those same 2 hours, you’d need to go 120 miles rather than 60 miles.
The most common mistake is to respond with 90 miles per hour or 120 miles per hour – if you get a question like this in an interview, be sure to ask clarifying questions that could point you in the right direction.
In this case, for example, we might have reframed the question and asked if it was really, “How do you travel 60 miles in 2 hours at an average speed of 60 miles per hour?” If he said yes, we’d instantly know it was not possible.
What is the angle formed by the hands of the clock when it is 1:45?
142.5 degrees. If we just think of the clock hour hand at 1 and the minute hand at the 45 position (near 9 o’clock), that is 120 degrees since they are 4 “numbers” apart, and each number on the clock represents 30 degrees (360/12).
However, recall that the hour hand has already moved by the time the minute hand has reached the 45 position – it is now closer to 2 o’clock. 45 represent ¾ of an hour, so the hour hand will have moved ¾ of 30 degrees, or 22.5 degrees. If we add them together, we see that 120 + 22.5 = 142.5
The most common mistake is to state the original number we arrived at – 120 degrees – rather than finishing the calculation. Sometimes with this type of question the interviewer will lead you in the right direction if you have a basic idea of how to solve it.
You have stacks of quarters, dimes, nickels and pennies (these represent $0.25, $0.10, $0.05 and $0.01, respectively, in the US monetary system for anyone international). There are an unlimited number of coins in each stack.
You can take coins from a stack in any amount and in any order and place them in your hand. What is the greatest dollar value in coins you can have in your hands without being able to make change for a dollar?
$1.19. There are a few ways to think about this, but the easiest is to start with the largest coin – quarters – first and then work your way down.
4 quarters equals $1.00, so we clearly can’t do that – but 3 quarters are ok because that’s only $0.75.
Next, we have dimes. Recall that we can use any combination of coins to make change for a dollar – if we were to have 5 dimes and put them together with the 2 quarters, that would make $1.00. So we’ll use 4 instead – there’s no combination there that would result in $1.00 when added to the quarters.
Nickels are next. Here, we can’t have any – because even a single nickel, $0.05, would add up to $1.00 when added to the 3 quarters we have ($0.75) and the 2 dimes ($0.20).
Finally, for pennies we know that we can’t have 5 pennies ($0.05) because we could then get to $1.00 using the same logic as we saw for the nickels. So 4 is the maximum here.
With that, we see that 3 Quarters + 4 Dimes + 4 Pennies = $1.19
The most common mistake is not realizing you can use any combination of your existing coins to add up to a dollar – most people understand that you can’t have 4 quarters, but sometimes interviewees forget that 2 quarters + 5 dimes = $1.00 as well.
This is another case where asking clarifying questions – such as whether 2 quarters + 5 dimes would count as $1.00 – really helps.
You have a hose along with a 3 liter bucket and a 5 liter bucket. How do you get exactly 4 liters of water?
First, fill the 3 liter bucket and pour it into the 5 liter one. Then, re-fill the 3 liter bucket and pour it into the 5 liter bucket until it’s full – that leaves 1 liter in the 3 liter bucket and 5 in the 5 liter bucket.
Then, pour out the 5 liter bucket so nothing is left and pour the 1 liter of water from the 3 liter bucket into the 5 liter bucket. Finally, fill the 3 liter bucket completely and pour it into the 5 liter bucket – since it already has 1 liter of water, you’ll get exactly 4 liters.
For this type of question, it’s easiest to use deductive reasoning to get the answer. You know you can’t possibly get 4 liters of water in the 3 liter bucket – it has to be in the 5 liter bucket.
Since you can easily get 3 liters of water, that tells you that the “trick” will involve isolating the remaining 1 liter and getting it into the 5 liter bucket. So then the question comes down to how to get the 1 liter of water in the 3 liter bucket. You know it has to involve pouring water into the 5 liter bucket, and that leads you in the right direction.
