Nov 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.

Here are 7 word problems.

Click GoogleForm to submit answers by Sat, Nov 18.

Week of Nov 12 – Nov 18.

Nov 12: Jack answered all 25 questions on a test. He got 5 points for each correct answer and LOST 3 points for each wrong answer. (With 1 correct and 1 wrong answer, he would get 5-3 = 2 points.) If Jack’s score was 85, how many wrong answers did he get?

Answer: 5 wrong, 20 correct

Nov 13: On a spelling test, John received 4 points for every word spelled correctly and lost 6 points for every word spelled incorrectly. After 20 words, John’s score was zero. How many words did John spell correctly?

Answer: 12 correct, 8 wrong

Nov 14: The distance from city A to city B is 100 miles, and the distance from city B to city C is 120 miles. The distance between A and C could be anywhere from ___ miles to ___ miles.

Answer: 20 to 220

Nov 15: A palindrome is a number that reads the same forward and backward. For example, 191 and 2442 are palindromes. The year 2002 is a palindrome. What is the difference between the year that is the closest palindrome before 2002 and the closest palindrome after 2002?

Answer: 2112 – 1991 = 121

Nov 16: In a parking lot, there are trailers with 18 wheels and trailers with 14 wheels. If there are a total of 152 wheels, and there are more 14-wheel trailers than 18-wheel ones, what is the largest possible number of 14-wheel trailers?

Answer: 7 14-wheel, 3 18-wheel

Nov 17: Emma counts all the ears, eyes, paws and tails on all tigers in the zoo. The total she got is the same as the number of all the lions’ paws in the zoo. The total number of tigers and lions  in the zoo is between 20 and 30. How many tigers are there in the zoo?

Answer: 8 tigers

Nov 18: On a farm there are chickens and horses. There are 10 more chickens than horses. The total number of legs is 152.  How many horses are there?

Answers: 22 horses, 32 chickens

Here are 7 more problems on number properties.

Click GoogleForm to submit answers by Sat, Nov 11.

Week of Nov 5 – Nov 11.

Nov 5: How many multiples of 7 are there between 54 and 184?

Answer: 19.  From 56 to 182, every 7.  

Nov 6: What is the smallest 5-digit number that is divisible by 2, 3, 4, 5, 6 and 7?

Answer: 10080

Nov 7: There are ___ 2-digit numbers such that the number is decreased by 27 when the 2 digits are swapped.

Answer: 6.  96-69, 85-58, 74-47, 63-36, 52-25, 41-14.

Nov 8: What is the remainder when 231^{172} divided by 10?  (What is the unit digit of 231^{172}?)

Answer: 1

Nov 9: Find the sum of the two prime numbers less than 100 that are both one more than a multiple of 5 and two less than a multiple of 3.

Answer: 92 = 61+31.

Nov 10: The 125 lockers at school are number consecutively from 1 to 125. The digit 5 is used ___ times.

Answer: 23. Digit 5 is used 10 times in the tens digit (50-59) and 13 times in the units digit (5, 15, … 125) 

Nov 11: The staircase at school has fewer than 35 steps. If you go up 2 steps at a time, 1 step is left at the end. If you got up 3 steps at a time, 2 steps are left. If you go up 5 steps at a time, 4 steps are left.  How many steps are on the staircase?

Answer: 29.  This number plus 1 is a multiple of 2, 3 and 5.