Brainteasers

Question 1

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?

Answer 1

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.

Question 2

What is the angle formed by the hands of the clock when it is 1:45?

Answer 2

360/12 = 30 degrees - so there is 120 degrees btwn 9 and 12 (4 numbers apart)

• -but the hour hand is not at 12..it always moves as time goes on - at 45 degrees it has been 3/4 of the hour…so hour hand will have moved 3/4 of 30 degrees so 22.5 degrees
• -angle is actually 120 + 22.5 degrees

Question 3

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?

Answer 3

start with quarters

• -4 quarters is $1.00 so can’t do that… so use 3 = $.75
• -dimes - if use 5 dimes with 2 quartes it would add to $1000 so use 4 bc can’t possibly add to $1.00 with that
• -nickels - can’t have any bc a single nickel $.05 would add up to $1.00 when added to 3 quarters and 2 times
• -4 is max for pennies bc it can easily be added to 1
• -so have 3 quarters + 4 dimes + 4 pennies = $1.19

Question 4

you have a 3 liter bucket and 5 liter bucket. how do you get exactly 4 liters of water?

Answer 4

fill 3 liter bucket and pour it into 5 liter (3 in there) then re-fill 3 liter bucket and pour into 5 liter bucket - that leaves 1 liter in liter bucket and 5 in 5 liter.
dump out the 5 and pour the 1 liter in the 3 back in the 5. then fill up the 3 and add it back to the 5 which makes 4 liters in there