In response to my post, “A Presidential Math Test“, neither Mr. Obama nor Mr. McCain submitted either an answer sheet or an excuse. As promised, here are the answers…
1. What is the difference between the mean and the median of a statistical grouping?
Answer: The mean (arithmetic) of a list of numbers is the sum of all the members of the list divided by the number of items in the list. The median of a list of numbers is that number such that half of the list of numbers have values are greater and half of the list of numbers have values that are less than the value of the median number. If there is an even number of observations, the median is not unique, so one often takes the mean of the two middle values. To make it absurdly simple, the mean is the average, the median is the middle value.
2. Bill wanted to leave the waiter an 18% tip, and her bill was $21.50. How much will the total cost of his dinner and tip be if she rounds the tip itself to the next higher dollar?
3. A square has an area of 49 square centimeters. A circle is inscribed within the square so that the sides of the square are tangent to the circle. What is the area of the inscribed circle? Express your answer as a decimal to the nearest tenth.
Answer: 38.5 square centimeters
4. Joe’s Store guarantees that it will refund what you paid for an item and give you an additional 10% if you find the item for less at a different store. Li paid $137.80 for a DVD player at Joe’s Store. Li then found an ad for the same DVD player at Mike’s Store for less. How much money should Joe’s Store give to Li?
5. What is the value of x such that (x, 0) is a solution of the equation y = 3x – 4? Express your answer as a common fraction.
6. The sum of three numbers is 98. The ratio of the first to the second is 2:3, and the ratio of the second to the third is 5:8. What is the value of the second number?
7. What is the greatest possible value of a in the system of equations 5a + 2b = 0 and ab = -10?
8. Office Surplus promises delivery of orders within three working hours of receipt of any order. Working hours are 8 a.m. to 5 p.m., Monday through Friday. Clyde’s order is received at 3 p.m. on a Friday and takes the maximum promised number of working hours to be delivered. How many actual hours elapse from the time the order is placed until it is delivered?
Answer: 66 hours
9. On a certain day, 10 U.S. dollars were worth 7.60 euros, and 1 euro was worth 155 Japanese yen. How many yen were the 10 U.S. dollars worth?
Answer: 1,178 yen
10. In forming his budget for this year, Jamal decided to use his average cost for utilities last year to project his expenses for the future. Last year he spent an average of $216 per month on utilities, but he anticipates a 5% increase in the annual cost of utilities. Based on this information, how much should he expect to pay for utilities each month this year?
Bonus Question for Extra Credit: The sum of four consecutive integers is 2. What is the smallest of the four integers?