Free GATB Problem Solving Questions and Answers — Questions and Answers
Question 1: A box contains 7 black pencils and 28 blue ones. What is the ratio between the black and blue pens?
- 1:4 (Correct answer)
- 2:7
- 1:8
- 1:9
Correct answer: 1:4
Explanation: <br> 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.
Question 2: 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?
- 1334 meters (Correct answer)
- 1310 meters
- 1300 meters
- 1285 meters
Correct answer: 1334 meters
Explanation: <br> At 100% efficiency, 1 machine produces 1450/10 = 145 m of cloth. <br> At 95% efficiency, 4 machines produce 4 * 145 * 95/100 = 551 m of cloth. <br> At 90% efficiency, 6 machines produce 6 * 145 * 90/100 = 783 m of cloth. <br> Total cloth produced by all 10 machines = 551 + 783 = 1334 m <br> Since the information provided and the question are based on 8 hours, we did not need to use time to reach the answer.
Question 3: If Lynn can type a page in p minutes, what portion of the page can she do in 5 minutes?
- p/5
- p – 5
- p + 5
- 5/p (Correct answer)
Correct answer: 5/p
Explanation: <br> This is a simple direct proportion problem: <br> If Lynn can type 1 page in p minutes, then she can type x pages in 5 minutes <br> We do cross multiplication: x * p = 5 * 1 <br> Then, x = 5/p
Question 4: The sale price of the car is $12,590, which is 20% off the original price. What is the original price?
- $14,310.40
- $14,990.90
- $15,108.00
- $15,737.50 (Correct answer)
Correct answer: $15,737.50
Explanation: <br> Original price = x, <br> 80/100 = 12590/X, <br> 80X = 1259000, <br> X = 15,737.50
Question 5: 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.
- sx/7n
- 7x/nx
- nx/7s
- 7x/ns (Correct answer)
Correct answer: 7x/ns
Explanation: <br> 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. <br> 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: <br> 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. <br> We can do cross multiplication: <br> y = (x * 7)/(ns) <br> y = 7x/ns
Question 6: 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’?
- $18.00
- $20.00 (Correct answer)
- $6.67
- $180.00
Correct answer: $20.00
Explanation: <br> 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.
Question 7: 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?
- 105
- 120
- 180
- 195 (Correct answer)
Correct answer: 195
Explanation: <br> The first time, Brian answered 150 questions correctly and the second time he answered 30% more correctly, so, <br> 150 + (30/100 * 150) ; 30% of 150 = 45, or (30 * 150)/100 <br> so 150 + 45 = 195
Question 8: 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?
- 34
- 45 (Correct answer)
- 56
- 61
Correct answer: 45
Explanation: <br> My age: x <br> My brother is 3 years older than me: x + 3 <br> My father is 3 less than 2 times my age: 2x – 3 <br> My father’s age divided by 5 is equal to my brother’s age divided by 3: (2x – 3) / 5 = (x + 3) / 3 <br><br> By cross multiplication: <br> 5(x + 3) = 3(2x – 3) <br> 5x + 15 = 6x – 9 <br> x = 24 <br><br> My father’s age: 2.24 – 3= 48 – 3 = 45
Question 9: 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?
- 2 hours and 24 minutes (Correct answer)
- 3 hours and 12 minutes
- 3 hours and 44 minutes
- 4 hours and 10 minutes
Correct answer: 2 hours and 24 minutes
Explanation: <br> This is an inverse ratio problem. <br> 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. <br> So, <br> 1/x = 1/4 + 1/6 … We use the least common multiple in the denominator that is 24: <br> 1/x = 6/24 + 4/24 <br> 1/x = 10/24 <br> x = 24/10 <br> x = 2.4 hours. <br><br> In other words; 2 hours + 0.4 hours = 2 hours + 0.4•60 minutes <br> = 2 hours 24 minutes
Question 10: 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?
- $280.90
- $287.00
- $292.50
- $306.00 (Correct answer)
Correct answer: $306.00
Explanation: <br> The original price of the dishwasher is $450. During a 15% off sale, the price of the dishwasher will be reduced by: <br> 15% of $450 = 0.15 x $450 = $67.50 <br><br> So the sale price of the dishwasher will be: <br> $450 – $67.50 = $382.50 <br><br> As an employee, the person receives an additional 20% off the lowest price, which is $382.50. We can calculate the additional discount as: <br> 20% of $382.50 = 0.20 x $382.50 = $76.50 <br><br> So the final price that the employee will pay for the dishwasher is: <br> $382.50 – $76.50 = $306.00
Question 11: 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?
- $3600
- $3500 (Correct answer)
- $2800
- $175042
Correct answer: $3500
Explanation: <br> 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: <br> 14x * (3/7) = 6x <br><br> So, <br> Spent money is: 7x + 250 <br> Unspent money is: 6×51 <br> Total money is: 14x <br> Write an equation: total money = spent money + unspent money <br> 14x = 7x + 250 + 6x <br> 14x – 7x – 6x = 250 x = 250 <br> We are asked to find the total money that is 14x: <br> 14x = 14 * 250 = $3500
Free GATB Problem Solving Questions and Answers
A box contains 7 black pencils and 28 blue ones.
What is the ratio between the black and blue pens?