2013 Grade Four Spirit of Math Contest Solutions

2013 Grade Four Spirit of Math Contest Solutions

2013 Grade Four Spirit of Math Contest Solutions

  1. C
/ Relocate the terms for ease of calculation:
  1. C
/ Since the year 2007 is not a leap year, it has 365 days. If George read one book every day, then he read 365 books.
  1. D
/ A dozen dozen is 12 groups of 12.
  1. B
/ If she ate the one that is not the orange, she ate the apple. So she had the orange left over.
  1. D
/ A pentagon has 5 sides and a triangle has 3 sides.
  1. B
/ Sophie needed six pieces in total. Five cuts would make six pieces (# of cuts = # of pieces – 1)
  1. C
/ Erin used up all her pencils, except 5. Thus, she used pencils by June.
  1. C
/ In Roman numerals, 4 is IV and 12 is XII.
  1. B
/ A chicken has two legs, and three times two is six. A polygon with six sides is a hexagon.
  1. C
/ If Jasmine started on the top of page 9, she did not read 8 pages. If you add to that the number of pages she did read (31), then you will find the last page she read, which was page 39.
  1. D
/ Each year, the number of pieces of coal that Colin collects is the sum of the pieces he collected in the two previous years (i.e. the Fibonacci sequence). Following this pattern, Colin collects 13 pieces in 2006.
  1. B
/ If each person hugged 8 other people, there would be hugs. But since each person is only hugged once, divide by 2 to get 36 hugs in total.
  1. D
/ Using an equation, start with July 13 and work backwards: .
Ryan’s gameis on July 16.
  1. B
/ All the palindromes between 400 and 500 must start and end with a 4, so 404 is the smallest palindrome. The ‘0’ can be replaced with each of the digits from 1 – 9 to get 10 palindromes in total: 404, 414, 424, 434, 444, 454, 464, 474, 484, and 494.
  1. D
/ Since a tetrahedral die has 4 sides, the probability of rolling a ‘1’ is . The die is being rolled twice, so the probability of rolling a ‘1’ twice in a row is or .
  1. B
/ The answer is the sum of all the numbers given minus 6 who liked both because they have been counted twice. 12 + 18 – 6 + 5 = 29.So there are 29 students in Ms. Kwan’s class.
  1. C
/ 15 quarters: ; 25 nickels: ; The total is:
  1. C
/
  1. A
/ Seher only likes prime numbers, so she will not like 21.
  1. C
/ Assume at first there are only ants, so give each head 6 legs: legs used.This leaves
legs left over, or pairs of legs left over.The remaining pairs of legs go to the spiders. Therefore there are 8 spiders
  1. C
/ If she wants to get an average of 8/10 on all four quizzes, she needs to have a total of 8x4=32 marks. Currently, she has marks, so she needs more marks. Therefore, she will need to get 10/10 on her next quiz.
  1. A
/ is not greater than, but is equivalent to since
  1. B
/ There are 3 lollipops and 16 of everything else, so it is possible that he could pull out 16 items and not one of them would be a lollipop. Pulling out 17 items guarantees that at least one lollipop will be pulled out.
  1. D
/
  1. B
/ Hypatia makes 6 tangram pieces in 90 minutes. Euler makes 4 tangram pieces in 90 minutes. Together they make 10 tangram pieces in 90 minutes, or 5 tangram pieces in 45 minutes.
  1. A
/ If she is biking, it will take her 10 minutes to get halfway there. If she walks the rest of the way, that would be another 15 minutes. She therefore took 25 minutes to get to work. 25 minutes after 8:35 am is 9:00 am, so she made it on time.
  1. B
/ The only 3 consecutive numbers that have a product of 120 are 4, 5, and 6 (4 x 5 x 6 = 120) Their sum is
  1. A
/ Working backwards, one third of 600 is . Half of 200 is . One fourth of 100 is
  1. C
/ The nameJOHNNY has 6 letters, including 2 Ns:

  1. C
/ Label each region and make a chart:
Number of Letters / “Name” of Triangle / Number of Triangles
1 / B, D, E, G, H, I, J, K / 8
2 / AB, BH, CD, EF, EJ, GH, JK / 7
3 / BHI, CEJ, EIJ / 3
TOTAL: / 18

*there are no triangles with 4, 5, 6, 7, 8, 9, 10, or 11 letters

© 2013Spirit of Math® Schools Inc Page 1 of 2

Top View