2006 Grade Four Competition Full Solutions

2013 Grade Three Spirit of Math Contest Solutions

/ Any number, or product, when multiplied by zero equals zero.

/ (5 x 1¢) + (3 x 10¢) + (8 x 25¢) = 235 cents, or $2.35.

/ The last two months of the year are November, which has 30 days, and December, which has 31 days. 30 + 31 = 61 days.

/ Comparing the left and right sides of the equation, the number missing from the sum on right side is 16.

/ Since 9 children like cats, but 5 of those children like both cats and dogs, then there are 9 – 5 = 4 children who like only cats.

/ 20 – 3 + 5 = 22, therefore, Emma’s play is on March 22nd.

/ An octagon has 8 sides and . A 5-sided shape is called a pentagon.

/ 6 x 12 = 72. Therefore, you would have 72 beans.

/ 8 + 2 + 5 + 9 = 24.
24 ÷ 4 = 6. The average is 6.

/ 16 + 23 + 19 + 8 = 66 minutes. Since 1 hour is 60 minutes, the boys played for 1 hour and 6 minutes.

/ Since Max is older than Noah and Ethan is older than Max, Ethan must be the oldest.

/ Subtract the pages that you did not read. 28 – 4 pages not read = 24 pages read.

/ Rearrange the sentence and substitute ‘except’ for ‘but’: All tomatoes fell off except 18. This means 18tomatoes did not fall off, so 18 were left on the vine.

/ Dividing 38 students into groups of 7 gives five groups of 7 and one group of 3. So they will need 5 cars with 7 students each and 1 car with 3 students; 6 cars altogether.

/ If all of 12 the students danced with each of the other students once, this would give dances (you can’t dance with yourself). However, using this method, each dance happens twice. So divide by two to get dances. There were 66 dances altogether.

/ The number of pathways that Galois can travel to each intersection is labeled on the diagram below:

Galois can travel 56 different ways.

/ Of the given options, the numbers above that are perfect squares are 81 and 121. The numbers that are palindromes are 99, 121, and 242. The only number that is both a perfect square and a palindrome is 121.

/ Imagine that I have the worst luck possible. I pull out all of the purple socks before pulling out any blue socks. So I pull out all 12 purple socks. Now all that is left in the drawer is blue socks, so pulling out one more sock would give me a blue sock. In total I need to pull out socks.

/ The pattern is increasing consecutive numbers, with ever other number having its digits reversed. So the pattern goes 15, 61 (16 backwards), 17, 81 (81 backwards), and the next number will be 19.

/ There are 6 different arrangements: FUN, FNU, UNF, UFN, NFU, and NUF

/ Of the given options, only 12 and 18 have two digits, and of these two numbers, only 12 is divisible by 2, 3, and 4.

/ Since Maggie had walked half of the way, she walked 1 km before she turned back. Walking back home added another 1 km. Then she walked the whole way from her home to the concert hall which is 2 km. The total distance she travelled is 1 + 1 + 2 = 4 km.

/ A mirror image looks like the object, backwards. The first picture represents a reflection, or mirror image of the object.

/ Altogether the mice ate berries. Altogether the rabbits ate berries. The mice ate more berries.

/ Subtract the coin that Maxine thought was a nickel: ¢. Now you know that Maxine had 48¢ before she made her mistake. The coin that she has left to count is actually a quarter, so add that back in to find out how much she actually has: ¢. Or, since you know that she counted a quarter as being worth 5¢, she actually has 20¢ more than she thought she did and ¢.

/ It is helpful to start by drawing a diagram of the tower when it is one level high. You can see that one level needs blocks. To find the number of blocks Marty will use once the tower is 5 cubes high, multiply . /

/ Since it takes 2 bakers 2 hours to bake 4 cakes, then two baker can bake 2 cakes in 1 hour. So 2 bakers can bake 12 cake in 6 hours.

/ / # of letters / ‘Name’ / # of triangles
1 / A, B, C, D, E, F, G, H, I, J / 10
2 / CD, DE, HI, IJ / 4
3 / CDE, HIJ / 2
Total: / 16