Nov 2018 (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 Nov 25 – Dec 1

Click GoogleForm to submit answers by Sat, Dec 1.

Nov 25: How many distinct positive factors does 2018 have?

Answer: 2 primes. 2018 = 2*1009. 

Nov 26: What is the first year after 2019 that is a palindrome?

Answer: 2112

Nov 27: Kim is knitting a baby blanket that requires 750 meters of yarn. There are 180 meters of yarn in each ball. How many balls of yarn must Kim buy to ensure she has enough yarn to complete her blanket?

Answer: 5 balls.  Round up 750/180. 

Nov 28: Gerald Scheetz is building a log cabin. If each log is 9 inches in diameter, how many logs must be stacked on top of one another to create a wall that has a height of 12 feet?

Answer: 12*12/9 = 36

Nov 29: A square with area 8 units is inscribed in a circle. What is the area of the circle? Express your answer in terms of π.

Answer: Area of the square is 2r*r=8. Area of the circle is r*rπ = 4π.

Nov 30: Maura is 5 years younger than her sister Cara. Seven years ago, Maura was half as old as her sister. How old is Maura now?

Answer: 12 

Dec 1: How many 4-inch square tiles are needed to cover a wall that measures 6 feet by 8 feet?

Answer: 6*12*8*12/(4*4) = 432

Week of Nov 18 – Nov 24: Can you do these seven problems in your head in seven minutes?

Click GoogleForm to submit answers by Sat, Nov 24.

Nov 18: What is the average of the prime numbers between 20 and 30?

Answer: (23+29)/2 = 26

Nov 19: How many lines of symmetry does an isosceles right triangle have?

Answer: 1

Nov 20: What is the volume of a rectangular prism of height 5 cm, width 7 cm and depth 3 cm?

Answer: 105

Nov 21: If the value of x is 10, what is the value of 3x + 4x + 5x?

Answer: 120

Nov 22: Given that 75% of a certain number is 88, what is 3/8 of the number?

Answer: 44

Nov 23: If ab = 2c, bd = c, b ≠ 0 and d = 16, what is the value of a?

Answer: 32

Nov 24: Yixin thinks of a positive number that is a perfect cube, and Aly thinks of number that is a perfect square. If the sum of their numbers is 31, what is the product of their numbers?

Answer: 6


Week of Nov 11 – Nov 17: More on perimeter, area, and volume.

Click GoogleForm to submit answers by Sat, Nov 10.

Nov 11: The floor of a bridge is to be 4′ wide and 252′ long. How many 2′ by 4′ boards are needed to build the floor of the bridge?

Answer: 126

Nov 12: A farmer decides to keep his chicken in an area shaped like a regular pentagon (a pentagon of equal sizes and equal angles). One side of the pentagon is to be built along the road and so the fencing is more expensive. The total cost of the fencing is $1200. Each side costs the same except that the side along the road is twice as expensive. The cost of the fence along the road is ________?

Answer: $400

Nov 13: Maranda’s garden is in the shape of a square and has an area of 100 square feet. Brett’s garden is rectangular. Its length is 3 times as long as Maranda’s garden but only half as wide. The perimeter of Brett’s garden is _______ more feet than Maranda’s garden.

Answer: M’s garden is 10′ by 10′. Brett’s garden is 30′ by 5′. The difference in the perimeter is 70-40=30′.

Nov 14: Joe is painting his room of 12′ by 15′. He is painting his ceiling as well as the 4 walls. He has 3 windows of 1.5′ by 3.5′ and 2 doors of 2.5′ by 6.5′. What information are you missing in computing the area that Joe needs to paint?

Answer: The height of the room.

Nov 15: A small cup and a large cup are proportional in radius and height. The large cup is twice as tall and twice as big in radius. If the small cup can hold 10 ounces of water, how many ounces can the large cup hold?

Answer: 8 times.

Nov 16: The circumference of a circle is 10 inches more than its radius. What is its radius?

Answer: 2pi r = 10+r. Therefore, r=10/(2pi – 1) = 1.89 inches.

Nov 17: What is the height of a triangle if its base is 20 and its area is 100?

Answer: 10


Week of Nov 4 – Nov 10: Perimeter, area, and volume. 

Click GoogleForm to submit answers by Sat, Nov 10.

Nov 4: A piece of wire is in the shape of a rectangle 10 ft by 14 ft. The wire is then shaped into a square. What is the area of the square in square feet?

Answer: 144 square feet

Nov 5 A piece of wire is bent to form a square. Each side of the square is 15”. If the same wire is bent to form an equilateral triangle, how long is each side of the triangle?

Answer: 20”

Nov 6: A rectangular frame for a 5” by 7” photo has 1/2” border on 4 sides (surrounding the photo). What is the area of the border?

Answer: 2*7*(1/2) + 2*5*(1/2) + 4*(1/2)*(1/2) = 13 square inches

Nov 7: Adam made a square from a wire of 13 inches long. Charlie made a square from a wire twice as long. What is the ratio of the area of Charlie’s square to Adam’s square?

Answer: 4

Nov 8: A side of a square is 9”. A rectangle whose length is twice as long as its width has the same perimeter as the square. How much bigger is the area of the square than the area of the rectangle?

Answer: Rectangle dimension 12′ by 6′. 81-72 = 9 square inches.

Nov 9: A tank is 3/4 full of water. When 15 gallons are run off, the tank is 1/3 full. How many gallons of water does the tank hold when full?

Answer: 15 gallons is 3/4-1/3 = 5/12 of the full tank. So the full tank is 15*(12/5) = 36 gallons.

Nov 10: From the 2-inch mark on a ruler to the 3-inch mark there are marks for 1/8 inch intervals as well as 1/6 inch intervals. Not including the 2-inch and 3-inch marks, how many marks are between the 2-inch and 3-inch marks on the ruler?

Answer: 8+6-1=13