Question 1

A cylinder contains some water. A solid cone with the same height

h

and half the radius

r/2

of the cylinder is submerged into the water until it sits on the base. The depth of the water becomes

h/2

. If the cone is removed, the new depth of the water will be what fraction of the height of the cylinder?

Accepted Answer

11/24

Answer

5/12

Answer

3/16

Answer

7/16

Question 2

Two lines with slope 1÷4  and 5÷4 intersect at the point (1&#44;1)What is the area of the triangle formed by these two lines and the vertical line x=5

Accepted Answer

8

Answer

10

Answer

5

Answer

12

Question 3

The line with equation y=2x-6 is reflected in the y-axis What is the x - intercept of the resulting line?

Accepted Answer

-3

Answer

0

Answer

3

Answer

-6

Question 4

A positive number is increased by 60%. By what percentage should the resulting value be decreased to return to its original value?

Accepted Answer

37.5%

Answer

60%

Answer

62.5%

Answer

40%

Question 5

A square has an area of  10. Each of its side lengths is multiplied by the same positive integer K to produce a new square. Which of the following could be the area of the new square?

Accepted Answer

90

Answer

60

Answer

80

Answer

70

Question 6

There are 186 students on a class trip. Each student is placed into exactly one of 50 groups. Each group has exactly 3 students or exactly 4 students. There are

h

groups that have 3 students and

r/2

groups that have 4 students. The value of

h/2

is:

Accepted Answer

−22

Answer

−18

Answer

−10

Answer

−14

Question 7

What is the tens digit of the smallest positive integer that is divisible by each of 20, 16, and 2016?

Accepted Answer

0

Answer

2

Answer

4

Answer

8

Question 8

Two identical smaller cubes are stacked next to a larger cube. Each of the two smaller cubes has a volume of

h

. The combined height of the two smaller cubes equals the height of the larger cube. What is the volume of the larger cube?

Accepted Answer

64

Answer

32

Answer

128

Answer

16

Question 9

The expression

h

is equal to:

Accepted Answer

125

Answer

625

Answer

5

Answer

10000

Question 10

Rachel, Christophe and Alfonzo are paid to organize some books. In total, they are paid $50. Alfonzo is paid $14. Rachel is paid twice what Christophe is paid. How much is Christophe paid?

Accepted Answer

$12

Answer

$10

Answer

$16

Answer

$14

Question 11

The value of 3(5÷ 3 − 1÷ 3 )?
is

Accepted Answer

4

Answer

1

Answer

3

Answer

2

Question 12

Which of the following is equal to 110% of 500?(A) 610(B) 510(C) 650(D) 505(E) 550

Accepted Answer

550

Answer

610

Answer

505

Answer

510

Question 13

Two lines with slopes 1÷4 and 5÷4 intersect at (1, 1). What is the area of the triangle formed by these two lines and the vertical line x = 5?

Accepted Answer

8

Answer

10

Answer

15

Answer

12

Question 14

6 m by 8 m rectangular field has a fence around it. There is a post at each of the four corners of the field. Starting at each corner, there is a post every 2 m along each side of the fence. How many posts are there?

Accepted Answer

14

Answer

20

Answer

12

Answer

16

Question 15

Karim has 23 candies. He eats n candies and divides the remaining candies equally among his three children so that each child gets an integer number of candies. Which of the following is not a possible value of n?

Accepted Answer

9

Answer

5

Answer

11

Answer

2

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