1.
There is a parking lot with 100 red and blue cars on it. 40% of the cars are red, and 70% of the red cars have radios, whereas 20% of blue cars do not have radios. What is the probability that the car is red given that you already know that it has a radio?
Correct Answer
D. 37/100
Explanation
The probability that the car is red given that it has a radio can be calculated using conditional probability. We know that 40% of the cars are red and 70% of the red cars have radios. Therefore, the probability of a car being red and having a radio is 0.4 * 0.7 = 0.28. We also know that 20% of blue cars do not have radios, so the probability of a car being blue and not having a radio is 0.6 * 0.2 = 0.12. The total probability of a car having a radio is the sum of these two probabilities, which is 0.28 + 0.12 = 0.4. Finally, the probability that the car is red given that it has a radio is the probability of a car being red and having a radio divided by the probability of a car having a radio, which is 0.28 / 0.4 = 7/10 = 0.37 = 37/100.
2.
There is a parking lot with 100 red and blue cars on it. 40% of the cars are red, and 70% of the red cars have radios, whereas 20% of blue cars do not have radios. What is the probability of selecting a car at random that is either red or has a radio?
Correct Answer
B. 22/25
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.
3.
If miles per gallon goes up by 50%, what happens to gallons per mile?
Correct Answer
D. Goes down by a third
Explanation
When miles per gallon goes 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 goes up by 50%. Thus, the answer is "Goes down by a third".
4.
Companies A, B, and C all invested in buying a new building. There were no other investors. Company A paid £10m more than 1/4 of the cost of the building while Company B paid £5m less than 1/3 of the cost. Company C contributed £15m. How much did the building cost?
Correct Answer
C. £48m
Explanation
The building cost £48m. Company A paid £10m more than 1/4 of the cost, which means they paid 1/4 + £10m. Company B paid £5m less than 1/3 of the cost, which means they paid 1/3 - £5m. Company C contributed £15m. To find the total cost, we can add the amounts paid by each company: 1/4 + £10m + 1/3 - £5m + £15m = £48m.
5.
At the start of the year, half of the money in a fund was invested in stocks earning 10% a year, 25% invested in bonds earning 8% a year, 1/5 invested in a mutual fund losing 5% a year and the remaining £10,000 was in a non-interest-bearing account. At the end of the year, by what proportion has the fund increased?
Correct Answer
B. 6.0%
Explanation
The fund is divided into four investments: stocks, bonds, mutual funds, and a non-interest-bearing account. The stocks earn 10% a year, the bonds earn 8% a year, and the mutual fund loses 5% a year. Since the proportion of money invested in each category is not given, we cannot calculate the exact increase in the fund. Therefore, the answer "Cannot say from the data given" is the correct choice.
6.
Last year, sales of children’s bicycles accounted for one-third of total bicycle sales in the U.K. This year, the total market grew by 20% and sales of children’s bicycles are 90% of what they were last year. By how much did the sales of other bicycles grow relative to their sales last year?
Correct Answer
D. 35%
Explanation
The sales of children's bicycles are given to be 90% of what they were last year. Since the total market grew by 20%, it means that the sales of other bicycles must have grown by the remaining 10% (100% - 90%). Therefore, the sales of other bicycles grew by 10% relative to their sales last year. To find the growth percentage relative to last year's sales, we can divide this 10% growth by the sales of other bicycles last year (which is not given in the data). Hence, we cannot determine the exact growth percentage and the answer is "Cannot say from the data given."
7.
Carco is a company that sells only 2 models of cars: A and BCarco sold each Model B for £10,000 in 1991. What was the approximate value of the total Model B sales income in 1995?
Correct Answer
D. £437m
8.
Carco is a company that sells only 2 models of cars: A and BCarco’s total sales income for Model B in 1993 equaled half the sales income of Model A in the same year. Given that Carco sold each Model B for £10,000 in 1991, what was the selling price of each Model A in 1993?
Correct Answer
A. £4,400
Explanation
Carco's total sales income for Model B in 1993 was half the sales income of Model A in the same year. Since the selling price of Model B in 1991 was given as £10,000, it can be inferred that the total sales income for Model B in 1993 was £10,000. Therefore, the total sales income for Model A in 1993 must be £20,000. Since the question asks for the selling price of each Model A in 1993, we divide the total sales income (£20,000) by the number of Model A cars sold to find that each Model A was sold for £4,400.
9.
The table below shows the average spend per shopper in each of my three stores. My store in Nottingham only has three quarters as many shoppers as my Manchester store. However, my Liverpool store has twice as many shoppers as the Manchester store. What is the average spend per shopper over all the shoppers in all my three stores?
Store
Average spend per shopper
Nottingham
£20
Manchester
£25
Liverpool
£10
Correct Answer
C. £16
Explanation
The average spend per shopper over all the shoppers in all three stores can be calculated by taking the total spend in all three stores and dividing it by the total number of shoppers. Since the number of shoppers in Nottingham is three quarters of the number of shoppers in Manchester, and the number of shoppers in Liverpool is twice the number of shoppers in Manchester, we can calculate the total number of shoppers as follows: Manchester shoppers + Nottingham shoppers + Liverpool shoppers = Manchester shoppers + (3/4)Manchester shoppers + 2Manchester shoppers = 4Manchester shoppers. Therefore, the average spend per shopper over all three stores is the total spend in all three stores divided by 4Manchester shoppers.
10.
A life insurance company is looking for external employees (agents) and for employees in the headquarters. An agent earns three times as much as an employee in the headquarters. The company needs 30 employees in the headquarters and 90 agents. How large is the share of the salary of one agent on the total payroll paid out?
Correct Answer
D. 1.00%
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%.