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Questions and Answers
If the heights of 5 students are 160 cm, 165 cm, 170 cm, 175 cm, and 180 cm, what is the median height?
If the heights of 5 students are 160 cm, 165 cm, 170 cm, 175 cm, and 180 cm, what is the median height?
- 175 cm
- 172.5 cm
- 167.5 cm
- 170 cm (correct)
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability of drawing a green marble?
A bag contains 3 red marbles, 5 blue marbles, and 2 green marbles. If a marble is drawn at random, what is the probability of drawing a green marble?
- 2/10 (correct)
- 1/5
- 2/5
- 1/10
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm. What is the volume of the prism in cubic centimeters?
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm. What is the volume of the prism in cubic centimeters?
- 72 cm³
- 48 cm³
- 36 cm³
- 60 cm³ (correct)
In a class of 25 students, the mean score on a test was 80. If the scores of 5 students were not included, the mean score would have been 84. What was the sum of the scores of the 5 students who were not included?
In a class of 25 students, the mean score on a test was 80. If the scores of 5 students were not included, the mean score would have been 84. What was the sum of the scores of the 5 students who were not included?
If the sum of three consecutive odd integers is 45, what is the product of these three integers?
If the sum of three consecutive odd integers is 45, what is the product of these three integers?
If $x \times y = 120$ and $x + y = 20$, what is the value of $x^2 + y^2$?
If $x \times y = 120$ and $x + y = 20$, what is the value of $x^2 + y^2$?
What is the value of the median of the set {334, 419}?
What is the value of the median of the set {334, 419}?
If a fair coin is tossed twice, what is the probability of getting at least one head?
If a fair coin is tossed twice, what is the probability of getting at least one head?
If the base of a triangular prism is a right triangle with legs 3 cm and 4 cm, and the height of the prism is 5 cm, what is the volume of the prism?
If the base of a triangular prism is a right triangle with legs 3 cm and 4 cm, and the height of the prism is 5 cm, what is the volume of the prism?
If the class mean score on a test is 75, and 20 students scored above the mean, what is the total number of students in the class?
If the class mean score on a test is 75, and 20 students scored above the mean, what is the total number of students in the class?
How many odd integers between 100 and 200 have a product of digits equal to 15?
How many odd integers between 100 and 200 have a product of digits equal to 15?
If the product of the digits of a two-digit number is 24, what is the sum of the digits?
If the product of the digits of a two-digit number is 24, what is the sum of the digits?
If the mean of the numbers 1 through 25 is M, what is the value of M?
If the mean of the numbers 1 through 25 is M, what is the value of M?
What is the probability of randomly selecting an odd number from the list 1 through 25?
What is the probability of randomly selecting an odd number from the list 1 through 25?
If a rectangular prism has a base of 5 units by 3 units, and a height of 2 units, what is its volume?
If a rectangular prism has a base of 5 units by 3 units, and a height of 2 units, what is its volume?
If the class mean for a test is 75, and the highest score is 100, what is the lowest possible score?
If the class mean for a test is 75, and the highest score is 100, what is the lowest possible score?
How many odd integers between 1 and 25 are divisible by 3?
How many odd integers between 1 and 25 are divisible by 3?
What is the product of all the prime numbers between 1 and 25?
What is the product of all the prime numbers between 1 and 25?
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Study Notes
Statistics and Probability
- Median height of 5 students is 170 cm, as it is the middle value when arranged in order.
- Probability of drawing a green marble is 2/10 = 1/5, as there are 2 green marbles out of a total of 10.
- Volume of a rectangular prism with length 5 cm, width 3 cm, and height 4 cm is 5 × 3 × 4 = 60 cubic centimeters.
Algebra
- If x × y = 120 and x + y = 20, then x^2 + y^2 = 400.
- If the sum of three consecutive odd integers is 45, their product is 45 × 3 × 5 = 675.
- If the product of the digits of a two-digit number is 24, the sum of the digits is 6 + 4 = 10.
Geometry
- Volume of a triangular prism with base right triangle (legs 3 cm and 4 cm) and height 5 cm is (1/2) × 3 × 4 × 5 = 30 cubic centimeters.
- Volume of a rectangular prism with base 5 units by 3 units and height 2 units is 5 × 3 × 2 = 30 cubic units.
Data Analysis
- If the mean score on a test is 75 and 20 students scored above the mean, the total number of students in the class is more than 20.
- If the class mean score on a test is 75 and the highest score is 100, the lowest possible score is 45.
- Mean of the numbers 1 through 25 is 13.
- Probability of randomly selecting an odd number from the list 1 through 25 is 13/25.
Number Properties
- Number of odd integers between 100 and 200 with a product of digits equal to 15 is 4 (115, 155, 175, and 195).
- Number of odd integers between 1 and 25 divisible by 3 is 4 (3, 9, 15, and 21).
- Product of all prime numbers between 1 and 25 is 2 × 3 × 5 × 7 × 11 × 13 × 17 × 19 × 23 = 3628800.
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