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Free Quantitative Reasoning MCQs with Answers

625 Quantitative Reasoning MCQs from Analytical and Logical Reasoning, each with the correct answer and a written explanation of why it is correct. Free and unlimited, with no account needed.

Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.

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625 questions · page 3 of 32

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…

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Correct answer: C

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…

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Correct answer: y=2(x-3)2-8

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.

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Correct answer: 7x-4y

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.

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Correct answer: 49/4

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…

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Correct answer: E

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.

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Correct answer: 31/80

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=…

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Correct answer: It will be $2 more expensive

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…

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Correct answer: 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.

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Correct answer: $10 for the card and a discount of 80% on ticket prices

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.

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Correct answer: 39km

51. Monthly sales of new cars in Illyria are always highest in March and September. At the end of each month, the sales figures from the 1st January up to the end of the month are recorded. These figures are then presented on a chart. Which of the four charts below could represent the car sales in lllyria?

  • A. A
  • B. B
  • C. C
  • D. D

Explanation: The correct answer is Option C, as it accurately reflects the largest increases in car sales occurring in March and September, which…

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Correct answer: C

52. What is the mode of this data set?

  • A. 15
  • B. 11
  • C. 16
  • D. 17

Explanation: The mode is the value that appears most often in a set of data values.1950s →20 hurricanes1960s →15 hurricanes1970s →12 hurricanes1980s…

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Correct answer: 15

53. What number is covered by the flower?

  • A. 1
  • B. 2
  • C. 3
  • D. 4

Explanation: To solve this problem, assign variables to each symbol: let circles = a, triangles = b, and squares = c.First, solve the equation with…

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Correct answer: 4

54. Study the following graph and answer the question. For which of the following pairs of years the total exports from the three Companies together are equal?

  • A. 1995 and 1998
  • B. 1996 and 1998
  • C. 1997 and 1998
  • D. 1995 and 1996

Explanation: In 1995, the total exports were 220 and similarly, in 1996, the total exports were 220 as well.

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Correct answer: 1995 and 1996

55. P (t) = 1,800 (1.02)t The function P gives the estimated number of marine mammals in a certain area, where t is the number of years since a study began. What is the best interpretation of P(0) = 1,800 in this context?

  • A. The estimated number of marine mammals in the area was 102 when the study began.
  • B. The estimated number of marine mammals in the area was 1,800 when the study began.
  • C. The estimated number of marine mammals in the area increased by 102 each year during the study.
  • D. The estimated number of marine mammals in the area increased by 1,800 each year during the study.

Explanation: Choice B is correct. The function P gives the estimated number of marine mammals in a certain area, where t is the number of years since a…

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Correct answer: The estimated number of marine mammals in the area was 1,800 when the study began.

56. A manager is responsible for ordering supplies for a shaved ice shop. The shop's inventory starts with 4,500 paper cups, and the manager estimates that 70 of these paper cups are used each day. Based on this estimate, in how many days will the supply of paper cups reach 1,700?

  • A. 20
  • B. 40
  • C. 60
  • D. 80

Explanation: Choice B is correct. It's given that the shop's inventory starts with 4,500 paper cups and that the manager estimates that 70 of these…

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Correct answer: 40

57. In 2008, Zinah earned 14% more than in 2007, and in 2009 Zinah earned 4% more than in 2008. If Zinah earned y times as much in 2009 as in 2007, what is the value of y?

  • A. 0.5600
  • B. 1.0056
  • C. 1.1800
  • D. 1.1856

Explanation: Choice D is correct. It's given that in 2008 Zinah earned 14% more than in 2007.

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Correct answer: 1.1856

58. On a street with 7 houses, 2 houses are blue. If a house from this street is selected at random, what is the probability of selecting a house that is blue?

  • A. 1/7
  • B. 2/7
  • C. 5/7
  • D. 7/7

Explanation: Choice B is correct. If a house from the street is selected at random, the probability of selecting a house that is blue is equal to the…

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Correct answer: 2/7

59. The amount of Hanna's bill for a food order was $50. Hanna gave a tip of 20% of the amount of the bill. What is the amount, in dollars, of the tip Hanna gave?

  • A. 10
  • B. 12
  • C. 15
  • D. 20

Explanation: The correct answer is 10. It's given that the amount of Hanna's food order was $50 and that Hanna gave a tip of 20% of the amount of the…

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Correct answer: 10

60. Brian saves 2/5 of the $215 he earns each week from his job. If Brian continues to save at this rate, how much money, in dollars, will Brian save in 9 weeks?

  • A. 760
  • B. 774
  • C. 770
  • D. 780

Explanation: The correct answer is 774. It's given that Brian saves 2/5 of the $215 he earns each week from his job.

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Correct answer: 774
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