Question 1

What is the value of 8 − 7 + 6 − 5 + 4 − 3 + 2 − 1?

Accepted Answer

4

Answer

8

Answer

5

Answer

6

Question 2

What is the closest integer value of √37?

Accepted Answer

6

Answer

7

Answer

18

Answer

5

Question 3

In the equation 2 + 2 + 2 + 2 = 2^x, what is the value of x?

Accepted Answer

3

Answer

5

Answer

4

Answer

6

Question 4

If the numbers 2 3/4, 2.3, 2 1/4, 2.45, and 2 9/10 are arranged from least to greatest, what is the middle number?

Accepted Answer

2.45

Answer

2.3

Answer

2 3/4

Answer

2 1/4

Question 5

In the cube diagram where 9 edges are visible&#44; how many edges are not visible?

Accepted Answer

3

Answer

0

Answer

2

Answer

1

Question 6

For a train consisting of one engine and n freight cars with a total length of 140 m, what is the value of n if the engine is 20 m and each freight car is 15 m long?

Accepted Answer

8

Answer

6

Answer

5

Answer

7

Question 7

Which integer has the same remainder when divided by 3 as when divided by 4?

Accepted Answer

11

Answer

13

Answer

10

Answer

9

Question 8

In the equilateral triangle diagram, if ∠STP = 120◦, what is the measure of ∠PQR?

Accepted Answer

105◦

Answer

90◦

Answer

145◦

Answer

120◦

Question 9

How many 4 × 4 squares have exactly 25% of their area shaded?

Accepted Answer

4

Answer

2

Answer

5

Answer

3

Question 10

In the diagram, the number placed in each rectangle must equal the sum of the numbers in the two rectangles directly below it. For example, the rectangles containing 1 and 3 are directly below the rectangle containing x, and so x = 1 + 3 = 4. What is the value of y?

Accepted Answer

7

Answer

8

Answer

9

Answer

10

Answer

11

Question 11

A lock requires a three-digit combination with the following characteristics: each digit is between

1

and

9

inclusive, all three digits are distinct, the digits are in increasing order, and the third digit is the sum of the first two digits. How many possible lock combinations satisfy these characteristics?

Accepted Answer

12

Answer

8

Answer

10

Answer

16

Question 12

Consider five distinct integers:

1

and

9

. If the mean (average) of these five integers is equal to their median, what is the sum of all possible values of

x

?

Accepted Answer

63

Answer

70

Answer

51

Answer

42

Question 13

A square has a side length of

1

. Four semi-circles are drawn inside the square, such that each side of the square is the diameter of one semi-circle. These semi-circles overlap to form a shaded four-petal flower in the center. If

9

is the closest integer to the area of this shaded flower, what is the value of

x

?

Accepted Answer

57

Answer

43

Answer

50

Answer

64

Question 14

The string of digits

1

is formed by alternately writing the digits

9

, in that order, and then writing some number of consecutive

x

. Specifically, there are exactly

k

consecutive

5s

immediately following the

k

-th occurrence of

1234

. If

S

is the sum of the first

2026

digits of the string, what is the sum of the digits of

S

?

Accepted Answer

16

Answer

14

Answer

15

Answer

13

Question 15

Triangle

1

is equilateral with side length

9

. Three smaller equilateral triangles with positive integer side lengths

x

are removed from the corners of

k

. If the conditions

5s

and

k

are met, the resulting shape is a hexagon

1234

that can be divided into exactly

S

identical equilateral triangles with side length

2026

. If

S

is the sum of all possible values of

n

, what are the rightmost two digits of

M

?

Accepted Answer

83

Answer

61

Answer

92

Answer

75

Question 16

Max was given

1

books. In March, he read one third of these books. In April, he read 5 more of the books. Max then had 7 books left to read. If Max never read the same book more than once, what is the value of

9

?

Accepted Answer

18

Answer

24

Answer

21

Answer

15

Question 17

The point

1

is reflected in the x-axis and then moved 3 units left. What are the coordinates of the resulting point?

Accepted Answer

(-1, -3)

Answer

(-5, 3)

Answer

(1, 3)

Answer

(5, -3)

Question 18

Peter’s car uses

1

L of fuel per

9

km, while Mike’s hybrid car uses

x

L of fuel per

k

km. Fuel costs

5s

per litre. If both Peter and Mike drive

k

km, how much less does Mike spend on fuel?

Accepted Answer

$10.08

Answer

$8.63

Answer

$7.36

Answer

$5.32

Question 19

The sum of the integers from 17 to 352 is

1

. The sum of the integers from 20 to 355 is

9

. What is the value of

x

?

Accepted Answer

63,003

Answer

62,997

Answer

62,040

Answer

63,000

Question 20

In a bag, there are two quarters (worth

1

each), two dimes (worth

9

each), and two nickels (worth

x

each). Two coins are randomly chosen from the bag. The probability that the combined value of the two coins is

k

or more is:

Accepted Answer

8/15

Answer

3/5

Answer

1/3

Answer

4/5

Question 21

In square

1

with side length 15, point

9

is on

x

such that the distance

k

. What is the area of trapezoid

5s

?

Accepted Answer

165

Answer

157

Answer

97.5

Answer

161.5

Question 22

In a number pyramid, the number in each rectangle is the sum of the numbers in the two rectangles directly below it. If the bottom row contains the numbers

1

,

9

, and

x

(from left to right), and the row above it consists of

k

and

5s

, with a top rectangle containing

k

, what is the value of

1234

if

S

is the sum of the numbers in the first and second rectangles of the bottom row?

Accepted Answer

3

Answer

11

Answer

7

Answer

9

Question 23

P, Q, R, and S are four distinct points on a line segment in the order shown. If

1

and

9

, what is the smallest possible integer length of

x

?

Accepted Answer

16

Answer

14

Answer

23

Answer

18

Question 24

The diagram consists of thirty-four

1

squares arranged in a specific grid. Using only the grid lines to form squares, how many squares of all sizes are in the diagram if the shape is a

9

rectangle with two additional

x

squares attached?

Accepted Answer

70

Answer

72

Answer

71

Answer

69

Question 25

Max was given

1

books. In March, he read one third of these books. In April, he read 5 more of the books. Max then had 7 books left to read. If Max never read the same book more than once, what is the value of

9

?

Accepted Answer

18

Answer

27

Answer

21

Answer

15

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