Dec 2017 (CML)

I will post seven new problems every weekend.  If you like you can try to finish the first 6 problems in 30 minutes, just like in a typical CML test.  The 7th problem is a bonus. 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.

I hope you are having fun during your week off from school.  Happy holidays to all!

Click GoogleForm to submit answers by Sat, Dec 30. (I’m posting answers on Jan 7.)

Week of Dec 24 – Jan 30

Dec 24: Willy can ride his bike 5 miles in 20 minutes.  His is traveling at ___ m.p.h.

Answer: 5*3=15 mph

Dec 25: One whole Christmas candle can be made from 5 candle stubs (the part left after a candle burns down). Mr. Santa had 25 candles and each candle burns down to a stub in one night. From those 25 candles he can burn one candle a night for ___ nights.  (Remember he can make a new candle from 5 stubs.)

Answer: 25+5+1 = 31

Dec 26: Joe left his house in the morning with some money. He spent one half of his money on lunch, one third on a snack and one tenth on a magazine. When he got home he had 60 cents left. How much money did Joe spend on lunch?

Answer: $4.50 (1/2 + 1/3 + 1/10 = 28/30; 60 cents correspond to 2/30; total amount = $9)

Dec 27: Andy took a full bag of sand and poured 2/3 of it into the sand box. Bob poured 1/2 of what was left between the brick and patio. Charles took the remaining 1 pound for his fish tank. Originally, the bag of sand weighed ___ pounds?

Answer: 6 pounds 

Dec 28: A, B, C and D are distinct integers from 1, 2, 3, and 4. What is the difference between largest possible product of AB x CD and least possible product?  (If A=1, B=2, C=3, D=4, ABxCD means 12×34.)

Answer:   41*32 – 13*24 = 1000

Dec 29: A number was added to 23. The same number was added to 47. The sum of these two new numbers is 109. What number was added to 23?

Answer: (109-23-47)/2 = 19.5

Dec 30: There are 8 people in a ping-pong tournament. Each person must play every other person exactly 2 times. How many games will there be in the tournament?

Answer: 8*7*2 / 2 = 56

Click GoogleForm to submit answers by Sat, Dec 23.

Dec 17:  If Marlon the mailman had sunny weather on exactly 21 of the 30 days last month, on what percent of days was the weather not sunny?

Answer: 30%

Dec 18: Last month I spent $24 on magnets that cost 60¢ each, and this month I spent $24 on magnets that cost $1.20 each. The average cost per magnet was ___.

Answer: $0.8 = 48/(24/0.6 + 24/1.2)

Dec 19: On a number line, __ is the same distance from 2.25 as it is from 7.75.

Answer: 5

Dec 20: In a garage, the ratio of red cars to black cars is 7:5, and the ratio of black cars to white cars is 3:2. The minimum number of cars in the garage is ___.

Answer: 46 (21:15:10) 

Dec 21:  The sum of 6 consecutive integers, the largest of which is 30, is equal to the sum of 10 consecutive integers, the largest of which is ___.

Answer: 21 (6 consecutive integers: 25-30, sum=165; 10 consecutive integers: 12-21)

Dec 22: I wrote a list of consecutive positive integers beginning with 1. I then removed all multiples of 4, and I had 2345 integers left. What was the largest integer on my list after the numbers were removed?

Answer: 3126  (x-floor(x/4)=2345; x=3126)

Dec 23:   If a radius of a circle whose area is 36π equals the width of a rectangle, and the diameter of the circle is half the length of the rectangle, then the perimeter of the rectangle is ___.

Answer: 60 (r=6; w=6; l=24)

Click GoogleForm to submit answers by Sat, Dec 16.

Dec 10: How much larger is 1/3 of 27 than 1/6 of 12?

Answer: 7

Dec 11: If 1/4 is greater than m/16 where m is a whole number, what is the largest possible value of m?

Answer: 3

Dec 12: If 4\times A>20 and 5 \times A<35, then A represents what number?

Answer: 6

Dec 13: The car that Mrs. A drives gets 36 miles to a gallon of gas. The tank hold 16 gallons. If the tank is 1/4 full, how many miles can she drive?

Answer: 144

Dec 14: The tank of a tractor holds 45 gallons of gas. The tractor requires 6 gallons of gas to plow 5 acres.  How many acres can the tractor plow with a full tank?

Answer: 37.5

Dec 15: When Rachel writes a composition she always writes 8 words in a line. The 1300th word in the composition will be the __th word in the __th line.

Answer: 4th word 163rd line  

Dec 16: The special at the bagel shop is “buy 1 dozen and get 3 bagels for free”. Bagels cost $4.50 per dozen.  How much does a customer pay to get 45 bagels?

Answer: $13.5

Click GoogleForm to submit answers by Sat, Dec 9.

Week of Dec 3 – Dec 9.

Dec 3: Jack divides a number by 10 and has a remainder of 3.  If Jack first multiplies the number by 3 and then divides by 10, what is the remainder now?

Answer: 9

Dec 4: The scale of a map shows that 1.5 inches = 30 miles. A park on the map is shown by a rectangle of  3in x 6in. The park has an actual area of __ square miles.

Answer: 7200

Dec 5: The scale on a map reads 1 inch = 40 miles. Two cities 300 miles apart are ___ inches apart on the map.

Answer: 7.5

Dec 6: A house plan uses the scale 1/8 in = 1 foot. In the plan, the living room is 2 inches long. If the scale is changed to 1/2 in = 1 foot, what would be the length of the living room in the new house plan?

Answer: 8

Dec 7: If 3/4 of a job can be done in 24 days, then working at the same rate, how many days does it take to finish the entire job?

Answer: 32

Dec 8: A Fibonacci sequence looks like 1, 1, 2, 3, 5, 8, 13, 21, 34, …. It continues indefinitely. The 1st number is 1 and the 2nd number is 1. From the 3rd number and on, it is the sum of the previous two numbers. Note that the 3rd number is even, the 4th number is odd.  Of the 50th, 51st and 52nd numbers, which one is even?

Answer: 51

Dec 9: The original price of a coat is $500.  Store A first reduced the price by 25% and then another 25% off the reduced price. Store B took off 50% off the original price of the coat. Mrs. X bought the coat from shop A; Mrs. Y bought it from shop B.  Who paid more and by how much?

Answer: Mrs. X by $31.25