# Feb 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.

Week of Feb 10 – Feb 16.

Feb 10: The digits 1357913579… are written on a screen. if 96 digits can be written on one line, then the first digit on the 5th line is ___.

Feb 11: The first 4 odd numbers are 1, 3, 5, and 7. What is the 100th odd number?

Feb 12: 116 is divided into 8 parts proportional to 1, 1/4 and 1/3. The smallest of the three numbers is ___.

Feb 13: What is the smallest integer $a$ so that $180a$ is a square number?

Feb 14: How many diagonals does a regular octagon have?

Feb 15: For what original price is 20% off the same as \$30 off?

Feb 16: Find the measure of the acute angle formed by the hour hand and minute hand on a clock at 12:15pm?

Week of Feb 3 – Feb 9. Happy Lunar New Year!

Feb 3: An office building has 300 offices. Each office has a window or an AC unit or both. If 225 offices have a window and 200 offices have an AC unit, how many offices have both?

Feb 4: Mary spent \$3 for plums, some at 30 cents a dozen and some at 40 cents a dozen. She sold all the plums at 3 cents each and made a profit of 24 cents. How many dozen plums did she buy at 40 cents a dozen?

Answer: Suppose Mary bought x dozen at 30 cents a dozen and y dozen at 40 cents a dozen. 30x+40y = 300, 6x-4y=24. Therefore x=6, y=3. Mary bought 3 dozen at 40 cents a dozen.

Feb 5: Mike counted all the ears, eyes, paws and tails on all the tigers in the zoo. The total he got is the same as the number of all the lions’ paws in the zoo. The total number of lions in the zoo must be a multiple of what integer?

Answer: 9T = 4L. The number of lions is a multiple of 9.

Feb 6: Mrs. E was born in 1974. When her daughter Linda was born, Mrs. E was 28 years old. In what year will Linda be 15 years old?

Feb 7: Harry can mow a lawn in 24 minutes. Jack can mow the same lawn in 16 minutes. If they mow together for 8 minutes, what fraction of the lawn is mowed?

Answer: 8/24 + 6/24 = 1/3 + 1/4 = 7/12.

Feb 8: Al can lift 250 lbs weight, Bob can lift 80% of what Al can lift. Charlie can lift 80% of what Bob can lift. How many lbs can Charlie lift?

Answer: 250 * 80% * 80% = 160.

Feb 9: How many numbers between 1 and 50 are divisible by either 3 or 4 but not both?

Answer: 16 + 12 – 4 – 4 = 20