2004 National Competition

Countdown Round

MATHCOUNTS

The time right now is 9 o’clock. On a 12-hour clock, what time will it be 2004 hours from now?

Answer: 9 (o’clock)

The first spinner is divided into 4 equal sections, and the second is divided into 3 equal sections. When these 2 fair spinners are each spun once, what is the probability that the product of the 2 numbers to which the arrows point is odd? Express your answer as a common fraction.

1 6

75

4 8

3

Answer:1

4

How many liters of water must be added to 40 liters of a 40% salt solution in order to produce a 25% salt solution?

Answer: 24 (liters)

Matt has exactly $1.60 in his pocket. He only has nickels and dimes. There are twice as many nickels as dimes. What is the number of coins in Matt’s pocket?

Answer: 24 (coins)

What is the largest prime factor of 999?

Answer: 37

What is the units digit of 32004?

Answer: 1

At the recent cat show, Moon scored 40 points lower than Foof in the judging. Foof’s score was double Kook’s score. How many points did Kook score if Moon’s score was 32 points?

Answer: 36 (points)

When this net is folded to form a cube, which face (A, B, C, D or E) will be opposite the face labeled “S”?

A

B

S

C

DE

Answer: (face) C

If 5x = 100, what is the value of 5x+2?

Answer: 2500

Twenty percent of the 20 boys in Ms. Schmidt’s class live on a farm. Thirty percent of the 30 girls in her class also live on a farm. What percent of the students in the class live on a farm?

Answer: 26 (percent)

If and x < 0, what is the value of x?

4 2 10x

Answer: 3

The height of a right cylinder is 2.5 times its radius. If the surface area of the cylinder is 112 cm2, what is the radius of the cylinder in centimeters?

Answer: 4 (centimeters)

A strip of paper is available for each whole number length from 1 inch to 15 inches. What is the probability that if a strip is randomly selected, it can be used as the third side of a triangle with two sides of 5 inches and 7 inches? Express your answer as a common fraction.

Answer:3

5

Solve for N: 82,400 + 4780 + 500 = 82,300 + 4760 + N.

Answer: 620

A square is divided into five congruent rectangles, as shown. If the perimeter of each of these five rectangles is 36 inches, what is the perimeter of the square, in inches?

Answer: 60 (inches)

The ratio of irises to roses in Nikki’s garden is 2:5. She currently has 25 roses. She is planning to add 20 more roses and enough irises to keep the same ratio. How many irises will she have in total after this addition?

Answer: 18 (irises)

What is the number of square units in the area of trapezoid ABCD with vertices A(0, 0), B(0, 2), C(4, 0) and D(4, 6)?

Answer: 16 (square units)

The four-digit number “25AB” is divisible by nine, with A the tens digit and B the units digit. How many different such four-digit numbers could “25AB” represent?

Answer: 11 (numbers)

At what point does the line 3y 4x = 12 intersect the x-axis? Express your answer as an ordered pair.

Answer: (3, 0)

How many even perfect square factors does 24 · 79 have?

Answer: 10 (factors)

The number of cubic inches in the volume of a 6-inch high cylindrical can equals the number of square inches in the area of the label that covers the lateral surface of the can. In inches, what is the radius of the can?

Answer: 2 (inches)

Evaluate .

Express your answer as a common fraction.

2

7

5

9

5

7

5

9FHGIKJFHGIKJ

Answer:5

9

What is the ratio of the number of 22 squares to the number of 33 squares in the 55 square diagram shown (using only the existing horizontal and vertical segments)? Express your answer as a common fraction.

Answer:16

9

Evaluate x2 x3 if x = 0.5. Express your answer as a common fraction.

Answer:3

8

Angle EAB is a right angle, and BE = 9 units. What is the number of square units in the sum of the areas of the two squares ABCD and AEFG?

A

EG

F

C

BD

9

Answer: 81 (square units)