Math Olympiad Section B

A tournament had six players. Each player played every other player only once, with no ties. If Theresa won 4 games, Sherita won 3 games, Angela won 2 games, Sondra won 2 games and Lavonda won 2 games, how many games did Monica win?

• 0

• 1

• 2

• 3

• 4

Answer explanation

In total, there are 15 games played (6 players, each playing 5 games). The wins add up to 4 + 3 + 2 + 2 + 2 = 13. Therefore, Monica must have won 2 games to make the total wins equal to 15.

Tags

CCSS.3.MD.B.3

How many numbers are there in the sequence 10, 13, 16, 19, ..., 70, 73?

• A. 20

• B. 21

• C. 22

• D. 60

• E. 61

Answer explanation

The sequence starts at 10 and increases by 3 each time. To find the number of terms, use the formula for the nth term: 10 + (n-1) * 3 = 73. Solving gives n = 22. Thus, there are 22 numbers in the sequence, making C the correct answer.

Tags

CCSS.HSF.BF.A.2

There are two plants in Mrs. Williams' garden. One is 44 cm tall, and it grows 3 cm every 2 years. The other is 80 cm tall, and it grows 5 cm every 6 years. In how many years will the two plants have the same height?

• 36 years

• 40 years

• 48 years

• 52 years

• 54 years

Answer explanation

Let the height of the first plant after x years be 44 + (3/2)x and the second plant be 80 + (5/6)x. Setting them equal gives 44 + (3/2)x = 80 + (5/6)x. Solving this leads to x = 54 years, making it the correct answer.

Tags

CCSS.8.EE.C.7B

A "leap year" is a year with 366 days, including February 29 as an additional day. Any year divisible by 4 is a leap year, but a year divisible by 100 is a leap year ONLY if it is divisible by 400.

How many leap years are there from 2000 to 2025?

• 4

• 5

• 6

• 7

• 8

Answer explanation

From 2000 to 2025, the leap years are 2000, 2004, 2008, 2012, 2016, 2020, and 2024. This totals 7 leap years, making the correct answer 7.

A snail fell into a hole that is 10 meters deep. Every day it would climb 3 meters up, but then it would fall 2 meters down while sleeping during the night. After how many days would the snail climb out of the hole?

• 8 days

• 7 days

• 10 days

• 5 days

• 9 days

Answer explanation

Each day, the snail effectively climbs 1 meter (3 up - 2 down). After 7 days, it reaches 7 meters. On the 8th day, it climbs 3 meters to 10 meters and escapes, so it takes 8 days to climb out of the hole.

Tags

CCSS.HSF.BF.A.2

The distance from Amit’s house to the school is 4 times the distance from the post office to the school. The distance from the school to his house is 2 km. What is the distance from his house to the post office?

• 1.75 km

• 1.5 km

• 2.2 km

• 2.5 km

• 8 km

Answer explanation

The distance from Amit's house to the school is 2 km. Since this distance is 4 times the distance from the post office to the school, the distance from the post office to the school is 0.5 km. Therefore, the distance from his house to the post office is 1.5 km.

Tags

CCSS.4.MD.A.2

A cheetah was running at 5 km per hour for 10 seconds until it spotted an impala it wanted to catch.

The cheetah then ran faster and averaged 60 km per hour for the next 40 seconds.

The impala went away and the cheetah slowed down to an average of 5 km per hour for ten seconds.

Rounded to the nearest km per hour, what was the cheetah’s average speed for the entire minute?

• 54 km/h

• 50 km/h

• 46 km/h

• 42 km/h

• 35 km/h

Answer explanation

The cheetah ran 5 km/h for 10s (1.39m), 60 km/h for 40s (666.67m), and 5 km/h for 10s (1.39m). Total distance = 669.45m in 60s. Average speed = 669.45m/60s = 42 km/h, rounded to the nearest km/h.

Tags

CCSS.6.RP.A.3D

I added the first ten whole numbers greater than 0. I forgot to include one whole number and I got 50 as the sum. Which one of these ten whole numbers I did not add?

• 1

• 3

• 5

• 7

• 6

Answer explanation

The sum of the first ten whole numbers (1 to 10) is 55. If the sum is 50, then 55 - 50 = 5 is the number that was not added. Therefore, the missing number is 5.

Tags

CCSS.2.MD.B.6

Five fishermen, Bash, Aiden, Teddy, Christian, and Hunter, all wanted to go out fishing. However, they only had three fishing poles, so only three of them could go out each day. How many different groups of 3 fishermen can be formed?

• 25

• 20

• 15

• 12

• 10

Answer explanation

To find the number of different groups of 3 fishermen from 5, use the combination formula C(n, r) = n! / (r!(n-r)!). Here, n=5 and r=3. Thus, C(5, 3) = 5! / (3!2!) = 10. Therefore, the correct answer is 10.

To go from Town A to Town B, a car can take different paths

(one way) as illustrated to the left.

How many different paths can the car take from Town A to Town B?

• A. 8

• B. 12

• C. 6

• D. 14

• E. 7

Answer explanation

To find the number of paths from Town A to Town B, we can count the combinations of routes available. The total number of unique paths is 12, making option B the correct answer.

Tags

CCSS.7.SP.C.8B