Free Quantitative Reasoning MCQs with Answers

41. Which point in the standard (x,y) coordinate plane below has the coordinates (2, -5)?

• A. A
• B. B
• C. C
• D. D

Explanation: The correct answer is Option C because the coordinates (2, -5) indicate a point 2 units to the right of the origin on the x-axis and 5 units down on the y-axis. Points A, B, and D are all positioned incorrectly based on the given coordinates, making them incorrect choices.

42. Which of the following equations represents the parabola shown in the xy-plane above?

• A. y = (x-3)2-8
• B. y = (x+3)2+8
• C. y=2(x-3)2-8
• D. y = 2(x+3)2 - 8

Explanation: Given the focus (h,k) and the directrix y=mx+b, the equation for a parabola is (y - mx - b)2 / (m2 +1) = (x - h)2 + (y - k)2.Using the vertex form of a parabola f(x) = a(x - h)2 + k where (h,k) is the vertex of the parabola.The axis of symmetry is x = 0 so h also equals 0.a = 1.Substituting the a value into the first equation of the linear systemIn mathematics, a parabola can be given in standard form, y = ax2 + bx + c, vertex form, y = a(x - h)2 + k where (h,k) is the vertex of the parabola, or intercept form, y = a(x - p)(x - q) where the x-intercepts of the parabola are at x = p and x = q.

43. Which of the following is a simplified form of4x-4y+ 3x?

• A. x(7-4y)
• B. x - y + 3x
• C. -8xy + 3x
• D. 7x-4y
• E. -4y-x

Explanation: To simplify the expression 4x - 4y + 3x, first combine the like terms, which are the terms involving 'x'. Add 4x and 3x to get 7x. Thus, the simplified expression becomes 7x - 4y, which is Option D. The other options do not correctly simplify the expression:Option A incorrectly factors the expression.Option B does not combine the like terms correctly.Option C introduces incorrect terms.Option E rearranges terms without proper combination.

44. Which value of c makes x2-7x+c a perfect square?

• A. 7/2
• B. 49/4
• C. 7
• D. 49

Explanation: Only this value gives the correct solution as mentioned in the question, this is correct.

45. On the first 7 statistics tests of the semester, Jamal scored 61, 76, 79, 80, 80, 84, and 91. The mean, median, and mode of his scores were 79, 80, and 80, respectively. On the 8th statistics test, Jamal scored 90. How do the mean, median, and mode of all 8 of his scores compare to the mean, median, and mode of his first 7 scores?

• A. A
• B. B
• C. C
• D. D
• E. E

Explanation: The total 8 test scores arranged in ascending order are:61, 76, 79,80, 80, 84, 90, 91The mode of these is 80 the number that appears the most, same as the mode for the previous 7 scores. Hence mode is equalMedian can term is calculated using the formula (n + 1)/2 where n is the number of terms 8(8+1) / 2 = 4.5th term is the medianTo find the 4.5th term we will find the mean of the 4th and 5th term. So, they are 80 and 80 and their mean will also be 80.Hence, the median is 80 and is equal.For mean, we will divide the sum of the terms by the number of the terms.So, the sum will be 61+76+79+80+80+84+90+91 = 641mean = 641/8 = 80.125 which is greater than the previous mean 79. So, the mean is greater.Hence,Mean = GreaterMedian= EqualMode = Equal

46. Four identical glasses are shown below. One glass is empty, and the other 3 glasses are ¼ full,1/2 full, and ⅘ full of water, respectively. If the water were redistributed equally among the 4 glasses, what fractional part of each glass would be filled?

• A. 2/11
• B. 8/11
• C. 3/22
• D. 31/60
• E. 31/80

Explanation: To solve the problem, first calculate the total amount of water in the three filled glasses: ¼, ½, and ⅘. Convert these fractions to a common denominator (20) to make calculation easier: ¼ = 5/20, ½ = 10/20, ⅘ = 16/20. Adding these gives you a total of 5/20 + 10/20 + 16/20 = 31/20. Since there are 4 glasses, divide the total water, 31/20, by 4 to find the amount of water per glass: (31/20) ÷ 4 = 31/80. Therefore, each glass would be filled to 31/80 of its capacity when the water is redistributed equally. Options A, B, C, and D do not match this calculation and are therefore incorrect.

47. The price for hiring a car is determined by the number of days for which it is to be hired and the number of people who will be using it. The table below shows the prices for groups of up to 5 people hiring cars for up to 7 days.Patrick is part of a group of 5 people on a holiday for 5 days. They will be going on outings each day, and had planned to hire one car for all of them for all 5 days. However, two of the group will only be there for the first 3 days, so an alternative is to hire one car for this period and another for the final two days. What will be the difference if they choose this alternative?

• A. It will be $5 cheaper
• B. It will be $2 cheaper
• C. It will be $2 more expensive
• D. It will be $5 more expensive

Explanation: Cost of car for 5 people for 5 days=$14 Cost of car for 5 people for 3 days=$10 Cost of car for 3 people for 2 days=$6 Alternative Cost= Cost of car for 5 people for 3 days + Cost of car for 3 people for 2 days = $10 + $6 = $16 Alternative Cost - Actual Cost = $16 - $14 = $2 If they choose the alternative, it will be $2 more expensive. Hence, the answer is option C.

48. In a restaurant recently, I received the following bill:Starter $7.00Main Course $20.75Dessert $9.75Drink $4.50Service Charge $5.25TOTAL $47.25What percentage of the cost of the food and drink had been added to the bill as service charge?

• A. 11.1%
• B. 12.5%
• C. 14.0%
• D. 15.0%

Explanation: To find the percentage of the cost of food and drink that was added as a service charge, we need to first calculate the total cost of food and drink.Total cost of food and drink = $7.00 + $20.75 + $9.75 + $4.50 = $42.00Now, we can calculate the percentage of the cost of food and drink that was added as a service charge:Service charge percentage = (Service charge / Total cost of food and drink) x 100%Plugging in the values, we get:Service charge percentage = ($5.25 / $42.00) x 100% = 12.5%Therefore, the answer is B) 12.5%.

49. William buys a bus ticket every day, Monday to Friday, for $2.50. The bus company has just introduced a card which can be bought to get a discount on all bus fares. Each card is valid for 1 week. William has worked out that he will pay exactly the same amount if he gets the card as he will if he continues to buy tickets at the normal price. Which of the following could be the price and discount for the card?

• A. $5 for the card and a discount of 10% on ticket prices
• B. $5 for the card and a discount of 50% on ticket prices
• C. $10 for the card and a discount of 50% on ticket prices
• D. $10 for the card and a discount of 80% on ticket prices

Explanation: William buys a bus ticket every day from Monday to Friday, so he buys 5 tickets per week. If he continues to buy tickets at the normal price, he will spend:5 tickets/week × $2.50/ticket = $12.50/weekSince William has worked out that he will pay exactly the same amount if he gets the card, we can set up an equation to solve for the cost of the card and the discount on ticket prices:(cost of card) + [(discounted ticket price) × (cost of 5 tickets per week)]Let's try each option:Option A: $5 for the card and a discount of 10% on ticket prices:The cost of the card is $5. The discount on ticket prices is 10%, which reduces the price to $2.25 per ticket.= $5 + ($2.25 x 5) = $16.25/weekOption B: $5 for the card and a discount of 50% on ticket prices:The cost of the card is $5. The discount on ticket prices is 50%, which reduces the price to $1.25 per ticket.= $5 + ($1.25 x 5) = $11.25/weekOption C: $10 for the card and a discount of 50% on ticket prices:The cost of the card is $10. The discount on ticket prices is 50%, which reduces the price to $1.25 per ticket.= $10 + ($1.25 × 5) = $16.25/weekOption D: $10 for the card and a discount of 80% on ticket prices:The cost of the card is $10. The discount on ticket prices is 80%, which reduces the price to $0.50.= $10 + ($0.50 x 5) = $12.50/weekThis is the same as the cost of buying tickets at the normal price, so option D could be correct

50. Gemma is on a coach trip. After a short sleep she has woken up just in time to see this sign on the side of the motorway.The last thing she remembers seeing before she fell asleep is this sign:How far has the coach travelled while Gemma has been asleep?

• A. 4km
• B. 17km
• C. 39km
• D. 56km

Explanation: We can judge how far the coach travelled by picking up a data point common in both signs. In the first sign, Targen is at a distance of 7km from the coach, whereas in the second sign, Targen is at a distance of 46km from the coach.How far Gemma has travelled = 46km - 7km = 39kmTherefore, Option C is the answer.