* 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.

*posted problems, click on the “Archive” tab.*

**For previously****, click on the “News” tab.**

*For previous prizes*

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

Week of Dec 16 – Dec 22

Click GoogleForm to submit answers by Sat, Dec 22.

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

Answer: 3+2×4 = 11

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?

Answer: (4+3.5+6.2+5)/4 = 4.675

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?

Answer: 8 laps.

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

Answer: 16.

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?

Answer: $84+$48+$48 = $180.

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

Answer: $800.

Week of Dec 9 – Dec 15

Click GoogleForm to submit answers by Sat, Dec 15.

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

Answer: 50 minutes

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)

Answer: 6*16/4=24 gallons.

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

Answer: 42*5/7*4=120cents=$1.2

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?

Answer: 396-36*4-20*3-33*2=126

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

Answer: 4:28pm.

Week of Dec 2 – Dec 8

Click GoogleForm to submit answers by Sat, 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?

Answer: 10 pounds.

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?

Answer: 301

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.