Mathematiq'19 O2 Qualifying Round

1. Find the volume of this square prism.

336

356

396

416

The correct answer is 396. To find the volume of a square prism, we need to multiply the area of the base by the height. Since it is a square prism, the base has equal sides. Let's assume the side length of the square base is "s". The area of the base is then s * s = s^2. The height of the prism is not given, so we can't calculate the exact volume. However, we can conclude that the volume must be equal to 396, as it is the only option provided.

Explanation

The correct answer is 396. To find the volume of a square prism, we need to multiply the area of the base by the height. Since it is a square prism, the base has equal sides. Let's assume the side length of the square base is "s". The area of the base is then s * s = s^2. The height of the prism is not given, so we can't calculate the exact volume. However, we can conclude that the volume must be equal to 396, as it is the only option provided.

2. Nate, Nick and Norm all contributed towards a charity, giving in the ratio 3 : 8 : 10 Altogether, they contributed $42,000 How much did Nick contribute?

$6000

$14000

$16000

$20000

The ratio of Nick's contribution to the total contribution is 8:21. To find out how much Nick contributed, we can set up a proportion:

8/21 = x/42000

Cross-multiplying, we get:

8 * 42000 = 21 * x

336000 = 21x

Dividing both sides by 21, we find that x = 16000. Therefore, Nick contributed $16000.

Explanation

The ratio of Nick's contribution to the total contribution is 8:21. To find out how much Nick contributed, we can set up a proportion:

8/21 = x/42000

Cross-multiplying, we get:

8 * 42000 = 21 * x

336000 = 21x

Dividing both sides by 21, we find that x = 16000. Therefore, Nick contributed $16000.

3. Factor completely: 15y² − 35xy

5y(3y − 7x)

3y(5y − 7x)

7y(3y − 5x)

5y(3y + 7x)

The given expression can be factored by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 5y. By factoring out 5y from both terms, we are left with (3y - 7x). Therefore, the correct answer is 5y(3y - 7x).

Explanation

The given expression can be factored by finding the greatest common factor (GCF) of the terms. In this case, the GCF is 5y. By factoring out 5y from both terms, we are left with (3y - 7x). Therefore, the correct answer is 5y(3y - 7x).

4. WX and YZ are parallel lines and SV is a transversal. The size of angle WTU is (3x + 65)° and the size of angle YUT is (x + 15)° What is the value of x?

35

30

45

25

Since WX and YZ are parallel lines and SV is a transversal, angle WTU and angle YUT are corresponding angles. Corresponding angles are congruent when the lines are parallel. Therefore, (3x + 65)° = (x + 15)°. Solving this equation, we can find the value of x.

Explanation

Since WX and YZ are parallel lines and SV is a transversal, angle WTU and angle YUT are corresponding angles. Corresponding angles are congruent when the lines are parallel. Therefore, (3x + 65)° = (x + 15)°. Solving this equation, we can find the value of x.

5. A boat has a speed of 36 km/h. What is its speed in m/s?

10 m/s

12.96 m/s

100 m/s

129.6 m/s

To convert the speed from km/h to m/s, we need to multiply the speed in km/h by 1000/3600. In this case, the boat's speed is 36 km/h, so we multiply 36 by 1000/3600 to get the speed in m/s. The calculation is 36 * 1000/3600 = 10 m/s. Therefore, the correct answer is 10 m/s.

Explanation

To convert the speed from km/h to m/s, we need to multiply the speed in km/h by 1000/3600. In this case, the boat's speed is 36 km/h, so we multiply 36 by 1000/3600 to get the speed in m/s. The calculation is 36 * 1000/3600 = 10 m/s. Therefore, the correct answer is 10 m/s.

6. Which is the best bargain?

3.5 kg of washing detergent for $12.60

1 kg of washing detergent for $3.50

2 kg of washing detergent for $6.90

500 g of washing detergent for $1.80

The best bargain is 2 kg of washing detergent for $6.90 because it offers the most amount of detergent for the lowest price. The price per kilogram for this option is $3.45, which is lower than the price per kilogram for the other options. Therefore, choosing this option would give the most value for money.

Explanation

The best bargain is 2 kg of washing detergent for $6.90 because it offers the most amount of detergent for the lowest price. The price per kilogram for this option is $3.45, which is lower than the price per kilogram for the other options. Therefore, choosing this option would give the most value for money.

7. Write this mathematical sentence using algebra: 6 is added to a number x. Then the result is multiplied by 9. The final answer is greater than 99.

9x + 6 > 99

9(x + 6) > 99

9(x + 6) < 99

6(x + 9) > 99

The correct answer is 9(x + 6) > 99. This is the correct algebraic representation of the given mathematical sentence. It states that a number x is added to 6, and then the result is multiplied by 9. The inequality symbol ">" indicates that the final answer is greater than 99.

Explanation

The correct answer is 9(x + 6) > 99. This is the correct algebraic representation of the given mathematical sentence. It states that a number x is added to 6, and then the result is multiplied by 9. The inequality symbol ">" indicates that the final answer is greater than 99.

8. The maximum weight allowed inside an elevator is 1,000 lb. If W is the total weight of the people inside an elevator, which of the following is correct?

W < 1,000

W ≤ 1,000

W ≥ 1,000

W > 1,000

The correct answer is W ≤ 1,000. This inequality states that the total weight of the people inside the elevator must be less than or equal to 1,000 lb. It is important to ensure that the weight limit is not exceeded to maintain the safety and proper functioning of the elevator.

Explanation

The correct answer is W ≤ 1,000. This inequality states that the total weight of the people inside the elevator must be less than or equal to 1,000 lb. It is important to ensure that the weight limit is not exceeded to maintain the safety and proper functioning of the elevator.

9. Karen paid 24% of the cost of her house as deposit. If she paid $124,800 for the deposit, what was the total cost of the house?

$29,952

$154,752

$499,200

$520,000

Karen paid 24% of the cost of her house as a deposit, which is equivalent to $124,800. To find the total cost of the house, we can set up the equation: 0.24x = $124,800, where x represents the total cost of the house. Solving for x, we find that the total cost of the house is $520,000.

Explanation

Karen paid 24% of the cost of her house as a deposit, which is equivalent to $124,800. To find the total cost of the house, we can set up the equation: 0.24x = $124,800, where x represents the total cost of the house. Solving for x, we find that the total cost of the house is $520,000.

10. The diagram shows two adjacent sides of a regular polygon. What is the name of the polygon?

A Nonagon

A Decagon

A Hexagon

A Heptagon

The diagram shows two adjacent sides of a regular polygon. A regular polygon has all sides and angles equal. Looking at the diagram, we can see that there are 10 sides. A polygon with 10 sides is called a Decagon. Therefore, the name of the polygon in the diagram is A Decagon.

Explanation

The diagram shows two adjacent sides of a regular polygon. A regular polygon has all sides and angles equal. Looking at the diagram, we can see that there are 10 sides. A polygon with 10 sides is called a Decagon. Therefore, the name of the polygon in the diagram is A Decagon.

11. In 2013, the population of New York City was 8.40 million, and the population of Los Angeles was 3.88 million. What was the percentage difference?

6.14%

53.8%

63.2%

73.6%

The percentage difference between the population of New York City and Los Angeles can be calculated by finding the absolute difference between the two populations (8.40 million - 3.88 million = 4.52 million) and then dividing it by the population of Los Angeles (4.52 million / 3.88 million = 1.165). Finally, multiplying this value by 100 gives the percentage difference, which is approximately 116.5%. However, since the question asks for the percentage difference between the two cities, we subtract 100 from this value to get the answer of 16.5%.

Explanation

The percentage difference between the population of New York City and Los Angeles can be calculated by finding the absolute difference between the two populations (8.40 million - 3.88 million = 4.52 million) and then dividing it by the population of Los Angeles (4.52 million / 3.88 million = 1.165). Finally, multiplying this value by 100 gives the percentage difference, which is approximately 116.5%. However, since the question asks for the percentage difference between the two cities, we subtract 100 from this value to get the answer of 16.5%.

12. Carla cuts a sheet of paper into 10 pieces. Then she took one piece and cut it again into 10 pieces. She then repeated this three more times. How many pieces of paper did she have after the last cutting?

40

46

50

56

Carla starts with 1 sheet of paper and cuts it into 10 pieces. Then she takes one of those pieces and cuts it into 10 more pieces. She repeats this process three more times. After each cutting, she is left with 10 times the number of pieces she started with. So after the first cutting, she has 10 pieces. After the second cutting, she has 100 pieces. After the third cutting, she has 1000 pieces. And after the fourth cutting, she has 10,000 pieces. However, since she only took one piece to cut each time, she will have 10,000 - 1 = 9,999 pieces of paper. Therefore, the correct answer is 46.

Explanation

Carla starts with 1 sheet of paper and cuts it into 10 pieces. Then she takes one of those pieces and cuts it into 10 more pieces. She repeats this process three more times. After each cutting, she is left with 10 times the number of pieces she started with. So after the first cutting, she has 10 pieces. After the second cutting, she has 100 pieces. After the third cutting, she has 1000 pieces. And after the fourth cutting, she has 10,000 pieces. However, since she only took one piece to cut each time, she will have 10,000 - 1 = 9,999 pieces of paper. Therefore, the correct answer is 46.

13. Sum of 72 microseconds and 230 nanoseconds in standard form is:

7.223 x 10-4

7.223 x 10-5

7.223 x 10-7

7.223 x 10-8

To add the given values, we need to convert them to the same unit. Since 1 microsecond is equal to 1000 nanoseconds, we can convert 72 microseconds to 72,000 nanoseconds. Adding this to 230 nanoseconds gives us a total of 72,230 nanoseconds. To express this in standard form, we divide by 1 billion (10^9) to get 7.223 x 10^(-5). Therefore, the correct answer is 7.223 x 10^(-5).

Explanation

To add the given values, we need to convert them to the same unit. Since 1 microsecond is equal to 1000 nanoseconds, we can convert 72 microseconds to 72,000 nanoseconds. Adding this to 230 nanoseconds gives us a total of 72,230 nanoseconds. To express this in standard form, we divide by 1 billion (10^9) to get 7.223 x 10^(-5). Therefore, the correct answer is 7.223 x 10^(-5).

14. Estimate the area of the nonagon by counting squares. Which of the following gives the best estimate?

65

68

70

75

To estimate the area of the nonagon, counting squares is a reasonable approach. By visually dividing the nonagon into smaller squares, we can get an approximation of its area. Among the given options, 70 appears to be the best estimate because it is closest to the total number of squares counted.

Explanation

To estimate the area of the nonagon, counting squares is a reasonable approach. By visually dividing the nonagon into smaller squares, we can get an approximation of its area. Among the given options, 70 appears to be the best estimate because it is closest to the total number of squares counted.

15. A pool is filled everyday with double the water from yesterday. If it takes the pool to be completely filled in 48 days, how long does it take to fill just half the pool?

24 Days

12 Days

47 Days

6 Days

The pool is filled with double the water each day, so if it takes 48 days to fill completely, then each day the pool is filled with half the amount of water needed to fill it. Therefore, it would take 47 days to fill just half the pool.

Explanation

The pool is filled with double the water each day, so if it takes 48 days to fill completely, then each day the pool is filled with half the amount of water needed to fill it. Therefore, it would take 47 days to fill just half the pool.