Math Competition Skills

Solve the following problem: If a train travels at 60 miles per hour, how far will it travel in 3 hours?

• 200 miles

• 180 miles

• 120 miles

• 90 miles

Answer explanation

To find the distance, multiply the speed (60 mph) by the time (3 hours) which equals 180 miles. Therefore, the correct answer is 180 miles.

What is the next number in the sequence: 2, 4, 8, 16, ___?

• 32

• 12

• 24

• 64

Answer explanation

The next number in the sequence is obtained by multiplying the previous number by 2. Therefore, the next number is 16 * 2 = 32.

If 3x + 5 = 20, what is the value of x?

• x = 5

• x = 15

• x = 10

• x = 3

Answer explanation

To find the value of x, we need to isolate x. Subtract 5 from both sides of the equation: 3x = 15. Then, divide by 3 to get x = 5. Therefore, the correct value of x is 5.

Identify the pattern in the following sequence: 5, 10, 15, 20, ___

• 22

• 30

• 35

• 25

Answer explanation

The pattern is adding 5 to each number. 20 + 5 = 25, so the next number in the sequence is 25.

If a square has a side length of 5 cm, what is its area?

• 30 cm^2

• 20 cm^2

• 25 cm^2

• 10 cm^2

Answer explanation

To find the area of a square, you square the length of one side. In this case, 5 cm * 5 cm = 25 cm^2. Therefore, the correct answer is 25 cm^2.

What is the missing number in the sequence: 3, 6, 9, ___, 15

• 18

• 12

• 13

• 10

Answer explanation

The missing number is 12. The sequence increases by 3 each time: 3+3=6, 6+3=9, 9+3=12, 12+3=15.

If a box contains 24 marbles and 1/3 of them are red, how many marbles are red?

• 6

• 10

• 12

• 8

Answer explanation

1/3 of 24 marbles is 8 red marbles. Therefore, there are 8 red marbles in the box.

What is the sum of the first 10 prime numbers?

• 129

• 135

• 122

• 140

Answer explanation

The sum of the first 10 prime numbers is 129. The prime numbers are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Adding them up gives 129.

If a clock shows 2:30, what will be the angle between the hour and minute hands?

• 105 degrees

• 90 degrees

• 120 degrees

• 45 degrees

Answer explanation

The angle between the hour and minute hands at 2:30 is 105 degrees. To calculate, we use the formula |(30*hour - (11/2)*minutes)| = |(30*2 - (11/2)*30)| = |60 - 165| = 105 degrees.

Solve the following problem: If a book costs $20 and is on sale for 25% off, what is the sale price?

• $10

• $15

• $18

• $22

Answer explanation

To find the sale price, we calculate 25% of $20, which is $5. Subtract $5 from $20 to get the sale price of $15.