# Dec 2018 (CML)

I will post seven new problems every weekend, one for each day of the week. The idea is that you work on your own during the week and I will post answers the following Saturday. For those of you who practiced with me last year, the process is similar.

For instructions on submitting weekly answers, click on the “Logistics” tab.
For previously posted problems, click on the “Archive” tab.
For previous prizes, click on the “News” tab.

We are taking a break. Happy Holidays to all! I’ll be back Jan 2019.

Week of Dec 16 – Dec 22

Dec 16: If a # b = a + 2b, for integers a and b, what is the value of 3 # 4?

Dec 17: Carver jogs 4 times a week. Last week, his distances were 4, 3.5, 6.2, and 5, all measured in miles. What was Carver’s average distance for the 4 days?

Dec 18: Hamburgers are priced \$3 each and 3 for \$7. What is the maximum number of hamburgers that can be purchased for \$20?

Answer: 6 hamburgers for \$14 and 2 more for \$6. So a total of 8 hamburgers.

Dec 19: By the time Shana had completed 1/4 of her first lap in a race, she had also completed 1/32 of the entire race. How many laps were there in the race?

Dec 20: If one-half of a number is 8 less than the number, what is the number?

Dec 21: A shirt company charges a one-time setup fee plus a certain price per shirt. An order of 10 shirts costs \$84. An order of 20 shirts costs \$48 more. How much does an order of 30 shirts cost?

Dec 22: After a 25% reduction, the price of a computer was \$600. What was the price of the computer before the reduction?

Week of Dec 9 – Dec 15

Dec 9: Ethan can run 4 miles in 40 minutes. How long will take him to run 5 miles at that speed?

Dec 10: There are a total of 22 cars and motorcycles crossing a bridge. David counts a total of 74 wheels. How many cars are there?

Answer: 15 cars and 7 motorcycles.

Dec 11: Mr. H has 6 cases of oil with 16 cans in each case. If each can holds a quart of oil, how many gallons of oil does Mr. H have? (4 quarts = 1 gallon)

Dec 12: Seven apples cost the same as 5 mangos. If a mango is 42 cents, then how much are 4 apples?

Dec 13: On Friday morning, 2 clocks are correctly set to 6am. One clock gains 1 minute every 2 hours. The other clock loses 1 minute every hour. When the real time is 6am the following morning, how many minutes is the fast clock ahead of the slow clock?

Answer: The two clocks are 1.5 minutes further apart every hour. They are 1.5*24=36 minutes apart 24 hours later.

Dec 14: There are 396 people at a conference. If each of 36 people brought 3 guests, each of 20 people brought 2 guests, and each of 33 people brought 1 guest, how many people brought no guests?

Dec 15: Twenty minute ago was halfway between 3:05 and 3:11pm. What is the time an hour from now?

Week of Dec 2 – Dec 8

Dec 2: A barrel full of oranges weighs 33 pounds. The same barrel full of sand weighs 79 pounds. The sand weighs 3 times as much as the oranges. How heavy is the empty barrel?

Dec 3: Dora has quarters and dimes, the same number of each, and no other coins. She has \$1.40. How many coins does she have?

Answer: 4 quarters and 4 dimes.

Dec 4: How many whole numbers between 100 and 200 are divisible by 3, but not divisible by 2?

Answer: 33-17 = 16  (102, 105, .. 198, a total of 33 multiples of 3. 102, 108, … 198, a total of 17 multiples of 6.)

Dec 5: If you start with 4 and count by 3s, you obtain the following sequence 4, 7, 10, 13, … What is the 100th number in this sequence?

Dec 6: If 100 clerks filed 2000 pieces of paper in 10 minutes, what is the average number of pieces of paper filed per minute by the average clerk?

Answer: 2 pieces per minute per clerk.

Dec 7: The average of 9 numbers is 20. When a 10th number is added the average becomes 19. What is the 10th number?

Answer: 190 – 180 = 10

Dec 8: The sum of 5 positive integers is 256. The 4 smaller ones are consecutive integers. The 2 larger ones are consecutive even integers. What is the largest of the 5 numbers?

Answer: The 5 numbers are 49, 50, 51, 52, 54. The largest is 54.