Explanation:
The series is decreasing by a certain number each time. The difference between the first two numbers is 17, the difference between the second and third numbers is 21, and so on. Therefore, the difference between the fourth and fifth numbers should be 25. Subtracting 25 from 599 gives us the missing number, which is 574.
Explanation:
The probability of selecting a car at random that is either red or has a radio can be calculated by adding the probability of selecting a red car with the probability of selecting a car with a radio and then subtracting the probability of selecting a red car with no radio. The probability of selecting a red car is 40% and the probability of selecting a car with a radio is 70% of the 40% of red cars, which gives us 28%. The probability of selecting a red car with no radio is 30% of the 40% of red cars, which gives us 12%. Adding 28% and 12% gives us 40%, which is the probability of selecting a car that is either red or has a radio. Therefore, the correct answer is 22/25.
Explanation:
The pattern in the series is that each number is obtained by adding consecutive odd numbers starting from 1. The first number is 3, obtained by adding 1 to 2. The second number is 6, obtained by adding 1 to 5. The third number is 11, obtained by adding 1 to 10. The fourth number is 18, obtained by adding 1 to 17. Therefore, the missing number at the end of the series would be obtained by adding 1 to 18, resulting in 19. However, this number is not given as an option. The closest option is 27, which is obtained by adding 1 to 26.
Explanation:
When miles per gallon go up by 50%, it means that the vehicle is able to travel a greater distance with the same amount of fuel. This implies that the number of gallons required to travel a mile decreases. Since the answer option "Goes down by a third" indicates a decrease of one-third, it aligns with the concept that the gallons per mile would decrease when miles per gallon go up by 50%.
Explanation:
The ladder needs to reach the window, which is 40 feet above the ground. The distance from the foot of the ladder to the wall is given as 9 feet. To find the length of the ladder, we can use the Pythagorean theorem, which states that the square of the hypotenuse (ladder) is equal to the sum of the squares of the other two sides (vertical distance and horizontal distance). In this case, the vertical distance is 40 feet and the horizontal distance is 9 feet. Using the Pythagorean theorem, we can calculate that the ladder should be 41 feet long.
Explanation:
The series is increasing by 8 each time. Starting from 3, adding 8 gives 11, then adding 8 again gives 19, and so on. Therefore, the missing number at the end of the series should be 27 + 8 = 35.
Explanation:
If 10 cats can catch 10 rats in 10 seconds, it means that each cat catches one rat in 10 seconds. Therefore, if we want to catch 100 rats in 100 seconds, we still only need 10 cats because each cat can catch one rat in 10 seconds.
Explanation:
The given series is decreasing by 19 in each step. Therefore, to find the missing number at the end of the series, we subtract 19 from the previous number. 459 - 19 = 440.
Explanation:
If 30% of a number is 12.6, we can set up the equation 0.3x = 12.6, where x represents the number we are trying to find. To solve for x, we divide both sides of the equation by 0.3. This gives us x = 12.6 / 0.3, which simplifies to x = 42. Therefore, the number is 42.
Explanation:
To find the number that must be added to 6, 16, and 8 to get an average of 13, we can use the formula for the average: sum of numbers divided by the count of numbers. The sum of 6, 16, and 8 is 30. We want the average to be 13, so we need to divide 30 by 3 (the count of numbers) to get the current average. This gives us 10. To increase the average to 13, we need to add a number that will increase the sum to 39. Therefore, the number that must be added is 22.
Explanation:
Each agent earns three times as much as an employee in the headquarters. Since the company needs 30 employees in the headquarters and 90 agents, the total number of employees is 30 + 90 = 120. Let's assume the salary of an employee in the headquarters is x. Therefore, the salary of an agent is 3x. The total payroll paid out is 30*x + 90*3x = 30x + 270x = 300x. The share of the salary of one agent on the total payroll paid out is (3x/300x) * 100 = 1%.
