Jan 2019 (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.


Happy New Year!

Week of Jan 13 – Jan 19.

Click GoogleForm to submit answers by Sat, Jan 19.

Jan 13: In Mr. D’s class, 1/5 of the students failed the math test. Of the remaining students, 1/4 scored an A. What fraction of the students passed the test, but did not score an A?

Jan 14: John is 14 and his mom is 41. Their ages have the same 2 digits. The next time that their ages have the same 2 digits, how old is John?

Jan 15: If 8 less than k is 6 more than m, how much bigger is k than m?

Jan 16: Six people can be seated comfortably in a room 6′ by 8′. How many people can be seated comfortably in a room 12′ by 16′?

Jan 17: If 1/4 is greater than m/16 where m is an integer, what is the biggest possible value of m?

Jan 18: Two numbers are in the ratio of 4:5. If the smaller of the two numbers is 16, what is the bigger number?

Jan 19: A local pizza shop has 10 different choices of toppings. What is the number of combinations for 2 toppings?


Week of Jan 6 – Jan 12.

Click GoogleForm to submit answers by Sat, Jan 12.

Jan 6: Two sides of a triangle have lengths 7” and 15”. If the third side also has an integral length, what is the longest possible length of the third side?

Answer: 21”

Jan 7: If 3/4 of a job can be done in 15 days, how many days does it take to finish the whole job?

Answer: 20 days

Jan 8: There are 3 contestants in a hot dog eating contest. By the time Al finishes one hot dog, Ben finishes 3 and Carl finishes 2. The contest is over when Ben finishes his 27th hot dog. How many hot dogs do the three people eat altogether?

Answer: Al: 9, Ben: 27, C: 18. So the total is 54.

Jan 9: If 3 people can make 3 widgets in 3 hours, then how many widgets can 25 people make in 3 hours?

Answer: 25 widgets.

Jan 10: John gives 1/2 of his marbles to Marty, 1/4 of his collection to Norm, 1/6 to Otto and the remaining 30 marbles to Pete. How many marbles does Marty receive?

Answer: Pete gets 1/12 of the marbles, or equivalently 30 marbles. So Marty gets 90 marbles. 

Jan 11: A rectangular kitchen floor is 11 ft by 15 ft. Each square tile has perimeter 24 inches. How many tiles are needed to cover the kitchen floor?

Answer: The square tile is 1/2 ft by 1/2 ft. So the kitchen floor needs 4*11*15 = 660 square tiles.

Jan 12:  During a track practice, A runs 3/5 of a mile, B runs 4/7 of a mile, C runs 1/2 a mile and D runs 2/3 of a mile. Who runs the farthest?

Answer: D.