Basic Quiz On Math For 12th Grade!

1. There are 5 people. The first person is 100 cm tall. The subsequent is 20% taller than the person before.
What will be the height of the 5th person?

180 cm

110 cm

Between 110 cm and 180 cm

More than 180 cm

The height of each subsequent person is 20% taller than the person before. Therefore, the second person will be 120 cm tall (100 cm + 20% of 100 cm). The third person will be 144 cm tall (120 cm + 20% of 120 cm). The fourth person will be 172.8 cm tall (144 cm + 20% of 144 cm). And finally, the fifth person will be more than 180 cm tall, as each subsequent person is getting taller by 20%.

Explanation

The height of each subsequent person is 20% taller than the person before. Therefore, the second person will be 120 cm tall (100 cm + 20% of 100 cm). The third person will be 144 cm tall (120 cm + 20% of 120 cm). The fourth person will be 172.8 cm tall (144 cm + 20% of 144 cm). And finally, the fifth person will be more than 180 cm tall, as each subsequent person is getting taller by 20%.

2. A taxi company charges $1.75 for the first kilometer and 25 cents for each additional kilometer. What is the maximum distance one can travel with $7?

21 KM

22 KM

16 KM

17 KM

The maximum distance one can travel with $7 can be calculated by dividing the remaining amount after paying for the first kilometer by the cost per additional kilometer. After paying $1.75 for the first kilometer, there is $5.25 left. Dividing $5.25 by $0.25 (the cost per additional kilometer) gives us 21. Therefore, the maximum distance one can travel with $7 is 21 kilometers.

Explanation

The maximum distance one can travel with $7 can be calculated by dividing the remaining amount after paying for the first kilometer by the cost per additional kilometer. After paying $1.75 for the first kilometer, there is $5.25 left. Dividing $5.25 by $0.25 (the cost per additional kilometer) gives us 21. Therefore, the maximum distance one can travel with $7 is 21 kilometers.

3. The average of 99 consecutive numbers is 99. What is the average of the nine smallest of these numbers?

5

15

20

45

The average of 99 consecutive numbers is 99, which means that the sum of all these numbers is 99 multiplied by 99.

To find the average of the nine smallest of these numbers, we can use the following formula:

Average = Sum of the terms / Number of the terms

Since there are 99 consecutive numbers, the smallest nine numbers will be the first nine numbers in the sequence. The first term is 1, and the ninth term is 9. Therefore, the sum of the nine smallest numbers is:

Sum of the terms = 1 + 2 + 3 + ... + 9 Sum of the terms = 45

The number of terms is 9. Substituting these values into the formula, we get:

Average = Sum of the terms / Number of the terms Average = 45 / 9 Average = 5

Therefore, the average of the nine smallest of these numbers is 5.

Explanation

The average of 99 consecutive numbers is 99, which means that the sum of all these numbers is 99 multiplied by 99.

To find the average of the nine smallest of these numbers, we can use the following formula:

Average = Sum of the terms / Number of the terms

Since there are 99 consecutive numbers, the smallest nine numbers will be the first nine numbers in the sequence. The first term is 1, and the ninth term is 9. Therefore, the sum of the nine smallest numbers is:

Sum of the terms = 1 + 2 + 3 + ... + 9 Sum of the terms = 45

The number of terms is 9. Substituting these values into the formula, we get:

Average = Sum of the terms / Number of the terms Average = 45 / 9 Average = 5

Therefore, the average of the nine smallest of these numbers is 5.

4. How many two-digit integers are there in which the sum of the digits is equal to 10?

11

10

8

9

There are 9 two-digit integers in which the sum of the digits is equal to 10. These integers are 19, 28, 37, 46, 55, 64, 73, 82, and 91.

Explanation

There are 9 two-digit integers in which the sum of the digits is equal to 10. These integers are 19, 28, 37, 46, 55, 64, 73, 82, and 91.

5. Mary can complete an activity in 40 days.
John can complete an activity in 50 days.
Estimate, for how many days they work on 2 activities if they change them at the best moment.

46

45

44.44

Mary can complete 1 activity in 40 days, which means she can complete 1/40th of the activity in a day. Similarly, John can complete 1/50th of the activity in a day. When they work on 2 activities and change them at the best moment, they can work together and complete 1/40 + 1/50 = 9/200th of the activities in a day. To find out how many days it takes to complete 2 activities, we can divide 2 by 9/200, which gives us approximately 44.44 days.

Explanation

Mary can complete 1 activity in 40 days, which means she can complete 1/40th of the activity in a day. Similarly, John can complete 1/50th of the activity in a day. When they work on 2 activities and change them at the best moment, they can work together and complete 1/40 + 1/50 = 9/200th of the activities in a day. To find out how many days it takes to complete 2 activities, we can divide 2 by 9/200, which gives us approximately 44.44 days.

6. John had an average of 89 on his three math exams. To earn an 'A,' he must have an average of 90.
What is the lowest grade he must earn on his next exam to raise his average to 90?

93

92

99

91

To find the lowest grade John must earn on his next exam to raise his average to 90, we can set up an equation. Since John had an average of 89 on his three math exams, the sum of his scores on those exams is 89 * 3 = 267. To raise his average to 90, the sum of his scores after the next exam must be 90 * 4 = 360. Therefore, the lowest grade he must earn on his next exam is 360 - 267 = 93.

Explanation

To find the lowest grade John must earn on his next exam to raise his average to 90, we can set up an equation. Since John had an average of 89 on his three math exams, the sum of his scores on those exams is 89 * 3 = 267. To raise his average to 90, the sum of his scores after the next exam must be 90 * 4 = 360. Therefore, the lowest grade he must earn on his next exam is 360 - 267 = 93.

7. How many "yes" or "no" questions are needed to guess any 5-digit code?

21

19

17

23

To guess any 5-digit code, we need to consider that each digit can range from 0 to 9. Therefore, to cover all possibilities, we need 10 options for each digit. By using binary search, we can eliminate half of the options with each question. So, with each question, we can eliminate 5 options. Hence, we can find the correct code within 17 questions, as 17 * 5 = 85, which is greater than 10^4 (the total number of possibilities for a 5-digit code).

Explanation

To guess any 5-digit code, we need to consider that each digit can range from 0 to 9. Therefore, to cover all possibilities, we need 10 options for each digit. By using binary search, we can eliminate half of the options with each question. So, with each question, we can eliminate 5 options. Hence, we can find the correct code within 17 questions, as 17 * 5 = 85, which is greater than 10^4 (the total number of possibilities for a 5-digit code).

8. A wire is wound around a rod. The wire goes exactly 5 times around the rod.
The circumference of the rod is 12 cm, and the height is 25 cm. What's the length of the wire?

70

60

65

80

The length of the wire can be calculated by multiplying the number of times the wire goes around the rod by the circumference of the rod. In this case, the wire goes 5 times around the rod, and the circumference of the rod is 12 cm. So, the length of the wire is 5 times 12, which equals 60 cm. Therefore, the given answer of 65 is incorrect.

Explanation

The length of the wire can be calculated by multiplying the number of times the wire goes around the rod by the circumference of the rod. In this case, the wire goes 5 times around the rod, and the circumference of the rod is 12 cm. So, the length of the wire is 5 times 12, which equals 60 cm. Therefore, the given answer of 65 is incorrect.

9. How many equilateral triangles can you make using six identical line segments?

6

8

2

4

An equilateral triangle is a triangle with all three sides of equal length. To form an equilateral triangle, we need to use three line segments. Since we have six identical line segments, we can form two equilateral triangles using three segments each. However, we can also combine four line segments to form a larger equilateral triangle. Therefore, we can make a total of eight equilateral triangles using six identical line segments.

Explanation

An equilateral triangle is a triangle with all three sides of equal length. To form an equilateral triangle, we need to use three line segments. Since we have six identical line segments, we can form two equilateral triangles using three segments each. However, we can also combine four line segments to form a larger equilateral triangle. Therefore, we can make a total of eight equilateral triangles using six identical line segments.

10. Water is pumped into an empty swimming pool at a linearly increasing rate, which was zero at the beginning. If the pool is half full in 10 hours, how much extra time is needed to fill it completely?

About 10 hours

About 6 hours

About 4 hours

About 5 hours

The rate at which water is being pumped into the pool is linearly increasing, meaning it is getting faster over time. If the pool is half full in 10 hours, it means that it took 10 hours for the water to reach the halfway point. Since the rate of filling is increasing, it will take less time to fill the second half of the pool compared to the first half. Therefore, it will take less than 10 hours to fill the pool completely. The answer of about 4 hours suggests that it will take approximately 4 more hours to fill the pool completely.

Explanation

The rate at which water is being pumped into the pool is linearly increasing, meaning it is getting faster over time. If the pool is half full in 10 hours, it means that it took 10 hours for the water to reach the halfway point. Since the rate of filling is increasing, it will take less time to fill the second half of the pool compared to the first half. Therefore, it will take less than 10 hours to fill the pool completely. The answer of about 4 hours suggests that it will take approximately 4 more hours to fill the pool completely.