GRADE 8 GAUSS CONTEST - PREPARATION
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Muhammad Yusuf
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Part
A: Each correct answer is
worth 5.
1. The value of 1:000 + 0:101 + 0:011 + 0:001 is
(A) 1.112 (B) 1.113 (C) 1.111 (D) 1.1111 (E) 1.101
2. The value of 1/2 + 3/4 –
5/8 is
(A) 9/14 (B) 0 (C) 5/8 (D) 1/4 (E) 7/8
3. If 800670 = 8 x 10x + 6 x 10y + 7 x 10z,
where x; y and z are whole numbers, then x +
y + z equals
(A) 11 (B) 8
(C) 6 (D) 3
(E) 5
4. When a number is divided by 7,
the quotient is 12 and the remainder is 5. The number is
(A) 47 (B) 79
(C) 67 (D) 119
(E) 89
5. In the diagram, the value of x is
(A) 30 (B) 75
(C) 100
(D) 105 (E) 150
6. What number, when doubled and
then increased by 13, equals 89?
(A) 38 (B) 79
(C) 67 (D) 119
(E) 89
7. If x = -4 and y = 4, which of the following expressions gives the
largest answer?
(A) x/y (B) y –
1 (C) x –
1 (D) -xy
(E) x + y
8. In a jar, the ratio of the
number of oatmeal cookies to the number of chocolate chip cookies is 5:2. If there
are 20 oatmeal cookies, the number of chocolate chip cookies in the jar is
(A) 28 (B) 50
(C) 8 (D) 12
(E) 18
9. There are 30 students in Mr.
McRoberts' Grade 8 class. One-third of the students are girls. Three-quarters
of the boys play basketball. The number of boys in the class who play
basketball is
(A) 3 (B) 22
(C) 10 (D) 20
(E) 15
10. Two positive integers have a
sum of 11. The greatest possible product of these two positive integers is
(A) 11 (B) 18
(C) 28 (D) 35
(E) 30
Part
B: Each correct answer is
worth 6.
11. A palindrome is a positive
integer whose digits are the same when read forwards or backwards. For example,
2002 is a palindrome. What is the smallest number which can be added to 2002 to
produce a larger palindrome?
(A) 11 (B) 110
(C) 108 (D) 18 (E) 1001
12. When the numbers √36 ; 35,2 ; 35,19, and 52 are arranged from smallest to
largest, the correct ordering is
(A) 52 ; 35,19 ;
35,2; √36
(B) 35,19
; 35,2
; 52 ; √36
(C) 52 ; √36 ; 35,19 ; 35,2
(D) √36 ; 52 ;
35,19 ;
35,2
(E) √36 ; 52 ; 35,2 ; 35,19
13. If a + b
= 12; b + c =
16, and c = 7, what is the value of a?
(A) 1 (B) 5
(C) 9 (D) 7
(E) 3
14. A rectangular sign that has
dimensions 9 m by 16 m has a square advertisement painted on it. The border
around the square is required to be at least 1.5 m wide. The area of the
largest square advertisement that can be painted on the sign is
(A) 78 m2 (B) 144 m2 (C) 36 m2 (D) 9 m2 (E) 56.25 m2
15. A perfect number is an
integer that is equal to the sum of all of its positive divisors, except
itself. For example, 28 is a perfect number because 28 = 1+2+4+7+14. Which of
the following is a perfect number?
(A) 10 (B) 13
(C) 6 (D) 8
(E) 9
16. The value of
Is...
(A) 3/5 (B) 5/3 (C) 1/3 (D) 3 (E) 3/2
17. Triangle ABC has vertices at A(2;
0);B(0;
7) and C(8;
8). The area of the
triangle is
(A) 56 (B) 29
(C) 24 (D) 11
(E) 32
18. The scores of eight students
on a quiz are 6, 7, 7, 8, 8, 8, 9, and 10. Which score should be removed to leave
seven scores with the same mode and range as the original eight scores, but
with a higher average (mean)?
(A) 6 (B) 7
(C) 8 (D) 9
(E) 10
19. Chloe has made a code out of
the alphabet by assigning a numerical value to each letter. She then assigns a
numerical value to a word by adding up the numerical values of the letters in
the word. Using her code, the numerical value of BAT is 6. Also, her code gives
numerical values of 8 to CAT and 12 to CAR. Using her code, what is the
numerical value of BAR?
(A) 10 (B) 14
(C) 18 (D) 12
(E) 20
20. The letters G, A, U, S, S are
written on five tiles, one letter per tile. If Amy selects two tiles at random,
what is the probability she gets two S's?
(A) 3/5 (B) 2/5 (C) 1/8 (D) 1/10 (E) 1/20
Part
C: Each correct answer is
worth 8.
21. On Tony's map, the distance
from Saint John, NB to St. John's, NL is 21 cm. The actual distance between
these two cities is 1050 km. What is the scale of Tony's map?
(A) 1:50 000 (B) 1:200 000 (C) 1:500 000 (D) 1:2 000 000 (E) 1:5 000 000
22. Carnina has a total of $3.60
in nickles and dimes. If her dimes were nickels and her nickels were dimes, then
she would have $5.40. How many nickels and dimes does Carnina have?
(A) 56 (B) 57
(C) 58 (D) 60
(E) 61
23. In her backyard garden,
Gabriella has 12 tomato plants in a row. As she walks along the row, she
notices that each plant in the row has one more tomato than the plant before.
If she counts 186 tomatoes in total, how many tomatoes are there on the last
plant in the row?
(A) 15 (B) 16
(C) 20 (D) 21
(E) 22
24. A triangle can be formed
having side lengths 4, 5 and 8. It is impossible, however, to construct a triangle
with side lengths 4, 5 and 9. Ron has eight sticks, each having an integer
length. He observes that he cannot form a triangle using any three of these
sitcks as side lengths. The shortest possible length of the longest of the
eight sticks is
(A) 20 (B) 21
(C) 22 (D) 23
(E) 24
25. A large block, which has
dimensions n by 11 by 10, is made up of a
number of unit cubes and one 2 by 1 by 1 block. There are exactly 2362
positions in which the 2 by 1 by 1 block can be placed. What is the value of n? (A)
7 (B) 8 (C) 9
(D) 10
(E) 11
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