FREE CAAT Problem-Solving Questions and Answers
How much pay does Mr. Johnson receive if he gives half of his pay to his family, $250 to his land¬lord, and has exactly 3/7 of his pay left over?
Explanation:
We check the fractions taking place in the question. We see that there is a “half” (that is 1/2) and 3/7. So, we multiply the denominators of these fractions to decide how to name the total money. We say that Mr. Johnson has 14x at the beginning; he gives half of this, meaning 7x, to his family. $250 to his landlord. He has 3/7 of his money left. 3/7 of 14x is equal to:
14x * (3/7) = 6x
So,
Spent money is: 7x + 250
Unspent money is: 6×51
Total money is: 14x
Write an equation: total money = spent money + unspent money
14x = 7x + 250 + 6x
14x – 7x – 6x = 250
x = 250
We are asked to find the total money that is 14x:
14x = 14 * 250 = $3500
If Sally can paint a house in 4 hours, and John can paint the same house in 6 hours, how long will it take for both to paint a house?
Explanation:
This is an inverse ratio problem.
1/x = 1/a + 1/b where a is the time Sally can paint a house, b is the time John can paint a house, x is the time Sally and John can together paint a house.
So,
1/x = 1/4 + 1/6 … We use the least common multiple in the denominator that is 24:
1/x = 6/24 + 4/24
1/x = 10/24
x = 24/10
x = 2.4 hours.
In other words; 2 hours + 0.4 hours = 2 hours + 0.4•60 minutes = 2 hours 24 minutes.
Richard gives ‘s’ amount of salary to each of his ‘n’ employees weekly. If he has ‘x’ amount of money, how many days can he employ these ‘n’ employees?
Explanation:
We are given that each of the n employees earns s amount of salary weekly. This means that one employee earns s salary weekly. So; Richard has ‘ns’ amount of money to employ n employees for a week.
We are asked to find the number of days n employees can be employed with x amount of money. We can do simple direct proportion:
If Richard can employ n employees for 7 days with ‘ns’ amount of money,
Richard can employ n employees for y days with x amount of money … y is the number of days we need to find.
We can do cross multiplication:
y = (x * 7)/(ns)
y = 7x/ns
The cost of waterproofing canvas is .50 a square yard. What’s the total cost for waterproofing a canvas truck cover that is 15’ x 24’?
Explanation:
First calculate total square feet, which is 15 * 24 = 360 ft2. Next, convert this value to square yards, (1 yards2 = 9 ft2) which is 360/9 = 40 yards2. At $0.50 per square yard, the total cost is 40 * 0.50 = $20.
In a local election at polling station A, 945 voters cast their vote out of 1270 registered voters. At poll¬ing station B, 860 cast their vote out of 1050 registered voters, and at station C, 1210 cast their vote out of 1440 registered voters. What is the total turnout from all three polling stations?
Explanation:
The total turnout is calculated by dividing the total number of votes cast by the total number of registered voters and then multiplying by 100 to get the percentage. The turnout percentage is approximately 80%.
A box contains 7 black pencils and 28 blue ones. What is the ratio between the black and blue pens?
Explanation:
The ratio between black and blue pens is 7 to 28 or 7:28. Bring to the lowest terms by dividing both sides by 7 gives 1:4.
If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes?
Explanation:
This is a simple direct proportion problem:
If Lynn can type 1 page in p minutes, then she can type x pages in 5 minutes.
We do cross multiplication: x * p = 5 * 1
Then, x = 5/p
The manager of a weaving factory estimates that if 10 machines run at 100% efficiency for 8 hours, they will produce 1450 meters of cloth. Due to some technical problems, 4 machines run at 95% efficiency and the remaining 6 at 90% efficiency. How many meters of cloth can these machines produce in 8 hours?
Explanation:
At 100% efficiency, 1 machine produces 1450/10 = 145 m of cloth.
At 95% efficiency, 4 machines produce 4 * 145 * 95/100 = 551 m of cloth.
At 90% efficiency, 6 machines produce 6 * 145 * 90/100 = 783 m of cloth.
Total cloth produced by all 10 machines = 551 + 783 = 1334 m
Since the information provided and the question are based on 8 hours, we did not need to use time to reach the answer.
Employees of a discount appliance store receive an additional 20% off the lowest price on any item. If an employee purchases a dishwasher during a 15% off sale, how much will he pay if the dishwasher originally cost $450?
Explanation:
The original price of the dishwasher is $450. During a 15% off sale, the price of the dishwasher will be reduced by:
15% of $450 = 0.15 x $450 = $67.50
So the sale price of the dishwasher will be:
$450 – $67.50 = $382.50
As an employee, the person receives an additional 20% off the lowest price, which is $382.50. We can calculate the additional discount as:
20% of $382.50 = 0.20 x $382.50 = $76.50
So the final price that the employee will pay for the dishwasher is:
$382.50 – $76.50 = $306.00
The sale price of the car is $12,590, which is 20% off the original price. What is the original price?
Explanation:
Original price = x,
80/100 = 12590/X,
80X = 1259000,
X = 15,737.50.
A distributor purchased 550 kilograms of potatoes for $165. He distributed these at a rate of $6.4 per 20 kilograms to 15 shops, $3.4 per 10 kilograms to 12 shops, and the remainder at $1.8 per 5 kilo¬grams. If his total distribution cost is $10, what will his profit be?
Explanation:
The distribution is done at three different rates and in three different amounts:
$6.4 per 20 kilograms to 15 shops … 20•15 = 300 kilograms distributed
$3.4 per 10 kilograms to 12 shops … 10•12 = 120 kilograms distributed
550 – (300 + 120) = 550 – 420 = 130 kilograms left. This 50 amount is distributed in 5-kilogram portions. So, this means that there are 130/5 = 26 shops. $1.8 per 130 kilograms.
We need to find the amount he earned overall these distributions.
$6.4 per 20 kilograms : 6.4•15 = $96 for 300 kilograms
$3.4 per 10 kilograms : 3.4 *12 = $40.8 for 120 kilograms
$1.8 per 5 kilograms : 1.8 * 26 = $46.8 for 130 kilograms
So, he earned 96 + 40.8 + 46.8 = $ 183.6
The total distribution cost is given as $10
The profit is found by: Money earned – money spent … It is important to remember that he bought 550 kilograms of potatoes for $165 at the beginning:
Profit = 183.6 – 10 – 165 = $8.6