Free Quantitative Reasoning MCQs with Answers

141. An empty 1,200 gallon tank is filled with water at a rate of 6 gallons of water per minute. At the same time, another 1,200 gallon tank full of water is being drained at a rate of 9 gallons per minute. How many minutes will it take for the amount of water in both tanks to become the same?

• A. 60
• B. 80
• C. 100
• D. 120

Explanation: To solve this problem, we need to equate the amount of water in both tanks after a certain time m minutes.Tank 1 starts empty and fills at 6 gallons per minute, so the amount of water in Tank 1 after m minutes is 6m.Tank 2 starts full at 1200 gallons and drains at 9 gallons per minute, so the amount of water in Tank 2 after m minutes is 1200 - 9m.Setting these equal gives: 6m = 1200 - 9mSolving for m gives:6m + 9m = 120015m = 1200m = 80Thus, after 80 minutes, both tanks will contain 480 gallons of water each. The other options do not satisfy this condition as calculated above.

142. At a bagel shop the first 6 bagels purchased cost 55 cents apiece, and additional bagels cost c cents apiece. If a customer paid $5.70 for 12 bagels, what is the value of c?

• A. 25
• B. 30
• C. 35
• D. 40

Explanation: The correct answer is Option D. The value of c is 40 cents. By calculating the total cost of the first 6 bagels and subtracting it from the total amount paid, we find that the remaining amount is 240 cents for the last 6 bagels, resulting in c = 40 cents. Options A, B, and C do not match the remaining amount and are therefore incorrect.

143. David used 1/10 of his monthly salary for groceries and 3/18 of his remaining money for his car payment. He also paid twice as much money for rent as for his car payment. If David has $1,620 left after paying for groceries, car payment, and rent, how much is his monthly salary?

• A. $3,240
• B. $3,320
• C. $3,480
• D. $3,600

Explanation: Let's denote David's monthly salary as x. He spends 1/10 of his salary on groceries, so the amount spent on groceries is x * 1/10 = x/10. After groceries, he has 9/10 of his salary left.From this remaining amount, he spends 3/18 on his car payment. The car payment is calculated as (9/10)x * 3/18 = x/20.Rent is twice the car payment, so rent is 2 * (x/20) = x/10.After all these expenses, David has $1,620 left. Therefore, the equation becomes:x/10 (groceries) + x/20 (car) + x/10 (rent) + $1,620 = x.Combining terms gives x/10 + x/20 + x/10 = x - $1,620.Finding a common denominator for the fractions, we have (2x + x + 2x)/20 = x - $1,620.This simplifies to 5x/20 = x - $1,620, or x/4 = x - $1,620.So, x - x/4 = $1,620, which simplifies to 3x/4 = $1,620. Solving for x gives x = $3,600.Thus, David's monthly salary is $3,600. The other options miscalculate the expenses or the remaining balance.

144. Adam and Betty purchased a printer together for $258. If Adam paid $18 less than twice of what Betty paid, how much money did Adam pay for the printer?

• A. 172
• B. 166
• C. 158
• D. 146

Explanation: To solve this problem, set up two equations based on the given information: Adam's payment as x and Betty's payment as y. The equations are x + y = 258 and x = 2y - 18. By solving these equations simultaneously, it is found that Adam pays $166 for the printer. The incorrect options resulted from miscalculations or misinterpretation of the equations.

145. There are 28 tables for customers at Mesa Grill Restaurant. The tables are either two-seat tables or four-seat tables. When all the tables are full, there will be 90 customers in the restaurant. How many two-seat tables are at the restaurant?

• A. 11
• B. 13
• C. 15
• D. 17

Explanation: To solve this problem, set up two equations based on the information given:Let x be the number of two-seat tables and y be the number of four-seat tables. Then, x + y = 28, because there are 28 tables in total.The total number of seats is given as 90, so you have another equation: 2x + 4y = 90.Solving these equations simultaneously, substitute y = 28 - x into the second equation:2x + 4(28 - x) = 902x + 112 - 4x = 90-2x + 112 = 90-2x = 90 - 112-2x = -22x = 11So, there are 11 two-seat tables. The other options provide incorrect results because they do not satisfy both conditions of the problem.

146. In a game of basketball, a field goal is either 2 or 3 points. In a college basketball tournament, Jim made 73 more 2-point field goals than 3-point field goals. If he scored a total of 216 points in the tournament, how many 3-point field goals did he make?

• A. 12
• B. 14
• C. 16
• D. 18

Explanation: To find the number of 3-point field goals, let the number of 3-point field goals be y. Then, the number of 2-point field goals would be y + 73. The total points scored from 3-point field goals is 3y, and from 2-point field goals is 2(y + 73). Given the total points is 216, we can set up the equation:3y + 2(y + 73) = 216Simplifying, we get:3y + 2y + 146 = 2165y + 146 = 2165y = 70y = 14Thus, Jim made 14 three-point field goals. Checking the totals, 14 three-point goals contribute 42 points, and 87 two-point goals (since 14 + 73 = 87) contribute 174 points, totaling 216 points. Therefore, Option B is correct. Options A, C, and D are incorrect as they do not match the required total of 216 points.

147. Twice the product of m and n decreased by the square of the sum of m and n. Which of the following is an expression for the statement above?

• A. 2mn2 - (m2 + n2)
• B. 2mn - (m+n)2
• C. (m+n)2 - 2mn
• D. (m2 + n2) - 2mn

Explanation: The correct expression is 2mn - (m+n)2. The statement specifies that you should first find the product of m and n, multiply it by two, and then subtract the square of the sum of m and n. Option B accurately reflects this procedure. Option A incorrectly uses the square of each variable separately. Option C reverses the order, and Option D also incorrectly uses individual squares instead of the square of the sum.

148. In a car dealership, all of the vehicles are either a sedan or a SUV. If 36 sedans are sold and 36 SUVs are added, there will be an equal number of sedans and SUVs. If 8 SUVs are sold and 8 sedans are added, there will be twice as many sedans as SUVs. How many sedans were at the dealership before any vehicle was sold?

• A. 132
• B. 144
• C. 156
• D. 168

Explanation: Let number of sedans originally = SLet number of SUVs originally = UIf 36 sedans are sold and 36 SUVs are added, there will be an equal number of sedans and SUVs.S - 36 = U + 36S - U = 72 eq-(1)If 8 SUVs are sold and 8 sedans are added, there will be twice as many sedans as SUVs.S+8=2(U−8)S+8=2U−16S=2U−24 eq-(2)From (1):S=U+72Substitute into (2):U+72=2U−2472+24=2U−UU=96Now substitute back:S=U+72=96+72=168Hence the correct answer is 168. Options A, B, and C are incorrect as they do not align with the calculated original number of sedans.

149. Tom wants to rent a truck for two days and pay no more than $300. How far can he drive the truck if the truck rental costs $49 a day plus $0.40 a mile?

• A. 490
• B. 505
• C. 520
• D. 535

Explanation: Rent for two days = $49 + $49 = $98 Leftover Fuel Expense = $300 - $98 = $202 Number of miles = Leftover Fuel Expense/Expense per mile = 202/0.4 = 505 miles

150. The ratio of 1 ¾ to 2 ½ is equal to the ratio of 14 to what number?

• A. 18
• B. 20
• C. 22
• D. 24

Explanation: To solve the problem, start by converting the mixed numbers to improper fractions. 1 ¾ becomes 7/4, and 2 ½ becomes 5/2. Set up the ratio as 7/4 : 5/2 = 14 : x. Cross-multiply to find x: (7/4)x = (5/2) * 14. Simplify to find x = (5/2) * 14 / (7/4) = (5 * 14) / (2 * 7/4). Simplifying further gives x = 20. Thus, the correct answer is Option B: 20. The other options result from errors in conversion, cross-multiplication, or simplification.