Problem Solving Flashcards

A box contains 7 black pencils and 28 blue ones. What is the ratio between the black and blue pens?

Answer: 1:4

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.

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?

Answer: 1334 meters

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.

If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes?

Answer: 5/p

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 sale price of the car is $12,590, which is 20% off the original price. What is the original price?

Answer: $15,737.50

Explanation: Original price = x, 80/100 = 12590/X, 80X = 1259000, X = 15,737.50

Richard gives ‘s’ amount of salary to each of his ‘n’ employees weekly. If he has ‘x’ amount of money, how many days he can employ these ‘n’ employees.

Answer: 7x/ns

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’?

Answer: $20.00

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.

After taking several practice tests, Brian improved the results of his GRE test by 30%. Given that the first time he took the test Brian had answered 150 questions correctly, how many correct answers did he answer in the second test?

Answer: 195

Explanation: The first time, Brian answered 150 questions correctly and the second time he answered 30% more correctly, so, 150 + (30/100 * 150) ; 30% of 150 = 45, or (30 * 150)/100 so 150 + 45 = 195

My father’s age divided by 5 is equal to my brother’s age divided by 3. My brother is 3 years older than me. My father’s age is 3 less than 2 times my age. How old is my father?

Answer: 45

Explanation: My age: x My brother is 3 years older than me: x + 3 My father is 3 less than 2 times my age: 2x – 3 My father’s age divided by 5 is equal to my brother’s age divided by 3: (2x – 3) / 5 = (x + 3) / 3 By cross multiplication: 5(x + 3) = 3(2x – 3) 5x + 15 = 6x – 9 x = 24 My father’s age: 2.24 – 3= 48 – 3 = 45

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?

Answer: 2 hours and 24 minutes

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, and 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

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?

Answer: $306.00

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

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?

Answer: $3500

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