Countdown Round 1 (Mostly Chapter)

How many even positive integers are factors of 354?

4

How many positive integers n < 10,000 have an odd number of positive factors and also have exactly two odd positive factors?

0

How many minutes does it take Danica to drive 10 miles at 150 mi/h?

4

Oliver has twelve pets, which are all cats or dogs. If the ratio of cats to dogs is

1:2, how many of his pets are dogs?

8

The number 102,100 ends with 2 zeros. How many zeros are at the end of 100!?

24

What is the greatest three-digit number whose digits have a product of 24?

831

Raj made $200 doing odd jobs last month. He spent 49% of the money on video

game accessories. How many dollars did Raj spend?

98

What percentage of positive integers less than or equal to a hundred are greater

than or equal to 50?

51%

9/16

Tucker owns a tuk-tuk, a motorized three-wheeled vehicle, which he uses to run a taxi tour. He charges $5 for every mile traveled on a tour, and the tuk-tuk can travel a maximum of 16 miles per hour. What is the minimum number of minutes that it would take Tucker’s tuk-tuk taxi tour to tally $200 in total earnings?

150

The total amount Raven paid for a book was $9.45, which included a 5% sales

tax. What was the pre-tax price of the book, in dollars?

9

What percentage of positive integer divisors of 120 are even?

75%

Two integers have a sum of 100 and a product of 2400. What is their absolute

difference?

20

7

Consider the set of all positive integers less than 50 that are divisible by 3. What is the mean of the set? Express your answer as a decimal to the nearest tenth.

25.5

A recipe for applesauce calls for 6 apples to make 8 servings. How many whole

servings can be made if one uses 10 apples?

13

What is the degree measure of the acute angle between the hour and the minute

hands of a standard 12-hour clock showing the time 3:30?

240

Consider the sequence 1, 11, 111, 1111, ..., where the nth term is the n-digit number whose digits are all 1s. What is the arithmetic mean of the first ten entries in this sequence?

123,456,790

5

What is the sum of all positive integer factors of 150?

372

How many even positive integers are factors of 354?

4

Fifteen years from now, George will be three times as old as he was 5 years ago.

How old is George now?

15

Flowers can be purchased in bundles of either 6 or 13. What is the greatest

number of flowers that cannot be purchased?

59

Gretchen has 10 indistinguishable rocks to be grouped into three different piles. All of the piles must have at least one rock, and the order of the piles does not matter. In how many different ways can Gretchen group her rocks?

8

Julia lists all the possible four-digit numbers that use only the digits 2, 3, 5 and 7, where each digit is used exactly once. She chooses one of the numbers at

random. What is the probability that the number Julia chooses is even? Express

your answer to the nearest percent.

25%

At a farmer’s market, Henry pays $2 for 8 apples and $3 for 5 pears. How many dollars in total will she expect to pay for 12 apples and 10 pears?

$9

At Del’s Deli, three sandwiches and two drinks cost $18, while four sandwiches and one drink cost $23. What is the absolute difference in dollars, between the price of one sandwich and the price of one drink at Del’s Deli?

5

8/3

A circle has 9 points evenly spaced around the circumference. How many

different segments can be formed by joining a pair of these points?

36

13

0

In the right triangle shown, the ratio of AB to BC is the same as

the ratio of AB to AC. What is the degree measure of angle B?

45

What is the circumference of a circle whose area is 225π in^2 ? Express your answer in terms of π.

30π

The figure shows the graph of the line x = ay + b. What is the value of a + b? Express your answer as a common fraction.

9/2

8

The stem-and-leaf plot shown compares the number of miles driven last week for service calls for Company A and Company B. What was the median number of miles driven among all of

the service calls?

26

A cylinder has radius 2 cm and height 5 cm. If the radius and height are each

increased by 1 cm, by what percent is the cylinder’s volume increased? Express

your answer to the nearest whole percent.

170%

What is the absolute difference between 75% of 900 and 900% of 75?

0

19

4/3

1

Suppose that m + n = 20 and m − 3n = 23. What is the value of m − n? Express

your answer as a common fraction.

43/2

What is the remainder when 123,000,000,000,321 is divided by 300?

21

The sum of three distinct primes is 14. What is the product of these primes?

70

Manny is thinking of a number. If Manny’s number is divided by 13, then

multiplied by 11, then decreased by 12, and then added to 73, the result is 94.

What is Manny’s original number?

39

You have 6 blue shirts, 5 red shirts, 2 white shirts, 9 black shirts, 12 green shirts

and 4 yellow shirts. If you randomly select one shirt, what is the probability you select a blue, black, or white shirt? Express your answer as a common fraction.

17/38

Jeremy has been wearing a hat for n years. If he wears it for six more years, he

will have worn the hat for n^2 years. How many years has Jeremy been wearing

his hat?

3

The quantity 60 is 320% of what number? Express your answer as a decimal to the nearest hundredth.

18.75

What is the absolute difference of the sum of the first 2023 even positive

integers and the first 2023 odd positive integers?

2023

The ratio of Aaron’s monthly wage to Jacy’s monthly wage is 5 to 3. If Aaron’s

monthly wage is $3500, what is Jacy’s monthly wage, in dollars?

2100

Chris is painting a wall at a constant rate. At 2:00 p.m., he has painted 3/4 of the wall. Thirty minutes later, he has painted 4/5 of the wall. How many more minutes will it take Chris to finish painting the wall?

120

How much less is 1/4 of 2/3 than 3/4 of 1/3? Express your answer as a common

fraction.

1/12

Kathy is given 30 doses of medicine and is told to take a single dose on days

1 through 14. Beginning on day 15, Kathy is told to take twice the daily dose

each day until she has taken all the medicine. On what day will Kathy take her last dose?

22