1998 CEMC Gauss (Grade 7) Problems
Contents
Part A: Each correct answer is worth 5 points
- If any diagrams are missing, consult the pdf: https://www.cemc.uwaterloo.ca/contests/past_contests/1998/1998Gauss7Contest.pdf
Problem 1
The value of is
Problem 2
The number is tripled. The ones digit (units digit) in the resulting number is
Problem 3
If , what is ?
Problem 4
Jean writes five tests and achieves the marks shown on the graph. What is her average mark on these five tests?
[insert bar graph with 5 bars: 80, 70, 60, 90, 80]
Problem 5
If a machine produces 150 items in one minute, how many would it produce in 10 seconds?
Problem 6
In the multiplication question, the sum of the digits in the four boxes is:
[Multiply using long multiplication. Find the sum of the four numbers in the thousands place column.]
Problem 7
A rectangular field is 80 m long and 60 m wide. If fence posts are placed at the corners and are 10 m apart along the 4 sides of the field, how many posts are needed to completely fence the field?
Problem 8
Tuesday’s high temperature was 4 C warmer than that of Monday’s. Wednesday’s high temperature was 6 C cooler than that of Monday’s. If Tuesday’s high temperature was 22 C, what was Wednesday’s high temperature?
(all in Celsius)
Problem 9
Two numbers have a sum of 32. If one of the numbers is – 36, what is the other number?
Problem 10
At the waterpark, Bonnie and Wendy decided to race each other down a waterslide. Wendy won by 0.25 seconds. If Bonnie’s time was exactly 7.80 seconds, how long did it take for Wendy to go down the slide?
Part B: Each correct answer is worth 6 points
Problem 11
Kalyn cut rectangle R from a sheet of paper. A smaller rectangle is then cut from the large rectangle R to produce figure S. In comparing R to S,
[R is a rectangle with sides 8 and 6 cm. S is the same as R with a 4x1 rectangle cut from one of its corners.]
Problem 12
Steve plants ten trees every three minutes. If he continues planting at the same rate, how long will it take him to plant 2500 trees?
Problem 13
The pattern of figures (triangle, dark circle, square, dark triangle, circle) is repeated over and over again. The 214th figure in the sequence is
Problem 14
A cube has a volume of What is the area of one face of the cube?
Problem 15
The diagram shows a magic square in which the sums of the numbers in any row, column or diagonal are equal. What is the value of n?
[A 3x3 magic square grid is shown. 8 is in the 1st row 1st column. 9 is in the 2nd row 1st column. 4 is in the 2nd row 3rd column. 4 is in the 3rd row 1st column. is in the 3rd row 2nd column.]
Problem 16
Each of the digits 3, 5, 6, 7, and 8 is placed one to a box in the diagram. If the two digit number is subtracted from the three digit number, what is the smallest difference?
[Align three boxes to the right and two boxes below so it looks like a three digit number subtracting a two digit number.]
Problem 17
Claire takes a square piece of paper and folds it in half four times without unfolding, making an isosceles right triangle each time. After unfolding the paper to form a square again, the creases on the paper would look like:
(see attached pdf for diagrams)
Problem 18
The letters of the word ‘GAUSS’ and the digits in the number ‘1998’ are each cycled separately and then numbered as shown: If the pattern continues in this way, what number will appear in front of GAUSS 1998?
Problem 19
Juan and Mary play a two-person game in which the winner gains 2 points and the loser loses 1 point. If Juan won exactly 3 games and Mary had a final score of 5 points, how many games did they play?
Problem 20
Each of the 12 edges of a cube is coloured either red or green. Every face of the cube has at least one red edge. What is the smallest number of red edges?
Part C: Each correct answer is worth 8 points
Problem 21
Ten points are spaced equally around a circle. How many different chords can be formed by joining any 2 of these points? (A chord is a straight line joining two points on the circumference of a circle.)
Problem 22
Each time a bar of soap is used, its volume decreases by 10%. What is the minimum number of times a new bar would have to be used so that less than one-half its volume remains?
Problem 23
A cube measures 10 by 10 by 10 cm. Three cuts are made parallel to the faces of the cube as shown (in three perpendicular directions) creating eight separate solids which are then separated. What is the increase in the total surface area?
Problem 24
On a large piece of paper, Dana creates a “rectangular spiral” by drawing line segments of lengths, in cm, of 1, 1, 2, 2, 3, 3, 4, 4, ... as shown. Dana’s pen runs out of ink after the total of all the lengths he has drawn is 3000 cm. What is the length of the longest line segment that Dana draws?
Problem 25
Two natural numbers, and do not end in zero. The product of any pair, and is a power of 10 (that is, 10, 100, 1000, 10 000 , ...). If , the last digit of cannot be
See also
1998 CEMC Gauss (Grade 7) (Problems • Answer Key • Resources) | ||
Preceded by First Competition |
Followed by 1999 CEMC Gauss (Grade 7) | |
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CEMC Gauss (Grade 7) |