Reasoning and answer: Derek doubles his allowance savings each month, so in May, Derek has $16 * 2 = $32. In June, Derek has $32 * 2 = $64. In July, Derek has $64 * 2 = $128. In August, Derek has $128 * 2 = $256. In September, Derek has $256 * 2 = $512. In October, Derek has $512 * 2 = $1024. In November, Derek has $1024 * 2 = $2048. By December, Derek has $2048 * 2 = $4096 to save.
The answer: 4096
What was the question?
Question: Derek finally gets his own allowance. He puts $2 away in January, $4 away in February, $8 away in March, $16 away in April and follows this savings pattern through to December. How much money does he have to spare and save by December?


Each boat will require 3 feet across to fit itself and 2 feet space on one side for a total of 2 + 3 = 5 feet per boat. The last boat will need an additional 2 feet space on its other side, so this 2 feet should be subtracted first from the 42 feet which leaves 42 - 2 = 40 feet. 5 feet per boat on the remaining 40 feet for a total of 40 / 5 = 8 boats.
The answer: 8
Reverse engineering the question: A river is to be used for a boat race. If each boat is 3 feet across and they must have at least 2 feet between them or the riverbank, how many boats can race in a river that is 42 feet across?


Reasoning and answer: First find how fast each runs. Apple = 24 miles / 3 miles per hour = 8 hours. Mac = 24 miles / 4 miles per hour = 6 hours. Mac runs 8 hours - 6 hours = 2 hours faster. 1 hour = 60 minutes, so, Mac runs faster by 2 hours * 60 minutes = 120 minutes.
The answer: 120
What was the question?
Question: Apple can run at a rate of 3 miles per hour. Mac can run at a rate of 4 miles per hour. In minutes, how much faster will Mac run a 24 mile race?


5 students scored a combined total of 92 * 5 = 460. 4 additional students scored a combined total of 80 * 4 = 320. 9 students therefore scored a combined total of 460 + 320 = 780. We know the total combined score for 10 students must be at least 85 average * 10 students = 850. Therefore, the last student must score at least an 850 - 780 = 70.
The answer: 70
Reverse engineering the question: The math teacher would be happy if the class average test score was at least 85. There are 10 students in the class, 5 of which scored a 92 on the test and 4 of which scored an 80. What would the last student have to score to at least make the teacher happy?


Reasoning and answer: Her card has a $150.00 balance and she makes a $50.00 payment so the new balance is 150 - 50 = $100.00. She didn't pay it off so she is charged 20% interest on her $100.00 balance so the interest is .20 * 100 = $20.00. Her balance was $100.00 and she was charged $20.00 in interest so her new balance is 100 + 20 = $120.00.
The answer: 120
What was the question?
Question: Tonya has $150.00 on her credit card. If she leaves any balance on her card at the end of the month, she is charged 20% interest. If she makes a $50.00 payment on her card, what will be the new balance?


Reasoning and answer: 3 weeks translate to 3 * 7 days = 21 days. To meet Dr. Juan’s recommendation would mean drinking 105 / 21 = 5 gallons daily. This means that Flora must drink 5 - 3 = 2 more gallons daily.
The answer: 2
What was the question?
Question:
Flora has been experiencing frequent fractures. Dr. Juan has asked her to strengthen her bones by drinking 105 gallons of milk within 3 weeks. Flora thinks that drinking 3 gallons of milk daily will be enough, but her brother says she'll still need to drink more. To fulfill Dr. Juan’s requirement, how many more gallons must Flora drink daily?