# OAT Quantitative Reasoning Practice Test 2024 Untimed [Explanation]

OAT Quantitative Reasoning Practice Test 2024 Untimed [Explanation] 40 Questions Answers. Try our free Optometry Admission Test (OAT) Quantitative Reasoning online quiz for better OAT test prep. The Quantitative Reasoning section of the OAT requires considerable outside knowledge, proficient test-taking skills, and strategic use of the calculator.

The Quantitative Reasoning section is the only section of the OAT that allows using a calculator. However, the calculator tends to be pretty time-consuming. As such, its value tends to be overestimated.

The Quantitative Reasoning section of the OAT is designed to test the math skills required in Optometry school. The area contains 40 multiple-choice questions; you will have 45 minutes to complete them. A basic on-screen calculator like the one below will be available only in this section. It can be opened by clicking the “Calculator” button at the bottom of the screen. The calculator can add, subtract, multiply, divide, and take square roots, percentages, and reciprocals.

## OAT Quantitative Reasoning Practice Test 2024 Untimed

What is the value of \frac{3}{4} + \frac{2}{5}?

• (A) \frac{7}{9}
• (B) \frac{11}{20}
• (C) \frac{23}{20}
• (D) \frac{17}{20}
• (E) \frac{19}{20}
Answer: (D) \frac{17}{20} Explanation: Convert \frac{3}{4} and \frac{2}{5} to a common denominator, which is 20. \frac{3}{4} becomes \frac{15}{20} and \frac{2}{5} becomes \frac{8}{20}. Adding these gives \frac{23}{20}, which simplifies to \frac{17}{20}.

What is the solution to the equation 2x - 5 = 15?

• (A) 5
• (B) 10
• (C) 7.5
• (D) 20
• (E) 8
Answer: (A) 10 Explanation: Add 5 to both sides of the equation to get 2x = 20. Divide both sides by 2 to find x = 10.

If x + y = 10 and x - y = 4, what is the value of x?

• (A) 3
• (B) 5
• (C) 7
• (D) 9
• (E) 11
Answer: (C) 7 Explanation: Solve the system of equations by adding them together. You get 2x = 14, so x = 7.

Data Analysis, Interpretation, and Sufficiency

A data set has a mean of 20 and a standard deviation of 5. What percentage of the data lies between 15 and 25?

• (A) 68%
• (B) 95%
• (C) 99.7%
• (D) 85%
• (E) 75%
Answer: (A) 68% Explanation: According to the empirical rule, approximately 68% of data in a normal distribution lies within one standard deviation of the mean (15 to 25).

What is the median of the following numbers: 3, 7, 9, 15 and 21?

• (A) 7
• (B) 9
• (C) 12
• (D) 15
• (E) 21
Answer: (B) 9 Explanation: The median is the middle value when the data are arranged in order. Here, it is 9.

Quantitative Comparison

Which is greater, 2^3 or 3^2?

• (A) 2^3
• (B) 3^2
• (C) They are equal
• (D) The relationship cannot be determined
• (E) None of the above
Answer: (C) They are equal Explanation: 2^3 = 8 and 3^2 = 9, but 2^3 = 8 and 3^2 = 9.

Probability and Statistics

A single six-sided die is rolled. What is the probability of rolling a number greater than 4?

(A) \frac{1}{6}

(B) \frac{1}{3}

(C) \frac{1}{2}

(D) \frac{2}{3}

(E) \frac{1}{4}

Answer: (B) \frac{1}{3} Explanation: Numbers greater than 4 are 5 and 6. Thus, the probability is \frac{2}{6} = \frac{1}{3}.

Applied Mathematics (Word) Problems

What is its average speed if a car travels 360 kilometers in 4 hours?

• (A) 90 \text{ km/h}
• (B) 80 \text{ km/h}
• (C) 70 \text{ km/h}
• (D) 60 \text{ km/h}
• (E) 50 \text{ km/h}
Answer: (A) 90 \text{ km/h} Explanation: Average speed is total distance divided by total time. Thus, \frac{360 \text{ km}}{4 \text{ h}} = 90 \text{ km/h}.

Algebra

What is the solution to the inequality 5x - 3 > 12?

• (A) x > 3
• (B) x > 1.5
• (C) x > 3
• (D) x > 3.5
• (E) x > 2
Answer: (A) x > 3 Explanation: Solve the inequality by adding 3 to both sides to get 5x > 15, then divide by 5 to find x > 3.

If x^2 = 49, what are the possible values of x?

• (A) x = 7
• (B) x = -7
• (C) x = \pm7
• (D) x = 0
• (E) x = 14
Answer: (C) x = \pm7 Explanation: The equation x^2 = 49 has two solutions, x = 7 and x = -7.

Data Analysis, Interpretation, and Sufficiency

Given a set of numbers 2, 3, 6, 6, 7, 10, 12, what is the mode?

• (A) 2
• (B) 6
• (C) 7
• (D) 10
• (E) 12
Answer: (B) 6 Explanation: The mode is the number that appears most frequently in a set. Here, 6 appears twice.

A graph shows a linear relationship between time spent studying and exam scores. What can be inferred about the slope of the line?

• (A) It is positive.
• (B) It is negative.
• (C) It is zero.
• (D) It is undefined.
• (E) It varies.
Answer: (A) It is positive. Explanation: A positive slope indicates that as the time spent studying increases, exam scores also increase.

Quantitative Comparison

Compare \frac{2}{3} and 0.66.

• (A) \frac{2}{3} is greater.
• (B) 0.66 is greater.
• (C) They are equal.
• (D) The relationship cannot be determined.
• (E) None of the above.
Answer: (A) \frac{2}{3} is greater. Explanation: \frac{2}{3} is approximately 0.6667, which is slightly greater than 0.66.

Probability and Statistics

What is the probability of drawing a blue marble if a jar contains 3 red, 4 blue, and 5 green marbles?

• (A) \frac{3}{12}
• (B) \frac{4}{12}
• (C) \frac{5}{12}
• (D) \frac{1}{3}
• (E) \frac{1}{4}
Answer: (D) \frac{1}{3} Explanation: There are 12 marbles in total, and 4 are blue. The probability is \frac{4}{12} = \frac{1}{3}.

Applied Mathematics (Word) Problems

John buys an item for $120 and sells it at a 25% profit. How much does he sell it for? • (A)$135
• (B) $140 • (C)$150
• (D) $160 • (E)$165
Answer: (C) $150 Explanation: A 25% profit on$120 is $30 (25% of 120), so he sells it for$120 + $30 =$150.

A rectangle has a length of 8 \text{ cm} and a width of 3 \text{ cm}. What is its area?

• (A) 11 \text{ cm}^2
• (B) 24 \text{ cm}^2
• (C) 25 \text{ cm}^2
• (D) 34 \text{ cm}^2
• (E) 48 \text{ cm}^2
Answer: (B) 24 \text{ cm}^2 Explanation: Area of a rectangle is given by length multiplied by width. Thus, 8 \text{ cm} \times 3 \text{ cm} = 24 \text{ cm}^2.

Algebra

Simplify 3(2x - 4) + 5x.

• (A) 11x - 12
• (B) 11x + 12
• (C) 6x - 7
• (D) 6x + 8
• (E) 10x - 12
Answer: (A) 11x - 12 Explanation: Distribute and combine like terms: 6x - 12 + 5x = 11x - 12.

What is the vertex form of the quadratic equation y = x^2 - 4x + 7?

• (A) y = (x - 2)^2 + 3
• (B) y = (x + 2)^2 + 3
• (C) y = (x - 2)^2 - 3
• (D) y = (x + 2)^2 - 3
• (E) y = (x - 4)^2 + 7
Answer: (A) y = (x - 2)^2 + 3 Explanation: Complete the square to rewrite in vertex form. y = (x - 2)^2 - 4 + 7 = (x - 2)^2 + 3.

Data Analysis, Interpretation, and Sufficiency

Which of the following measures of central tendency is affected most by outliers?

• (A) Mean
• (B) Median
• (C) Mode
• (D) Range
• (E) Standard deviation
Answer: (A) Mean Explanation: The mean is the average of all data points and is significantly affected by outliers, unlike the median or mode.

A survey reports that 15 out of 20 students prefer online classes. What percentage is this?

• (A) 65%
• (B) 70%
• (C) 75%
• (D) 80%
• (E) 85%
Answer: (C) 75% Explanation: Calculate the percentage: \frac{15}{20} \times 100% = 75%.

Quantitative Comparison

Is \frac{2}{3} closer to 1 than 0.75?

• (A) Yes
• (B) No
• (C) They are the same distance
• (D) The information is insufficient
• (E) None of the above
Answer: (B) No Explanation: \frac{2}{3} \approx 0.666, which is further from 1 than 0.75.

Probability and Statistics

A fair coin is flipped three times. What is the probability of getting exactly two heads?

• (A) \frac{1}{8}
• (B) \frac{1}{4}
• (C) \frac{3}{8}
• (D) \frac{1}{2}
• (E) \frac{3}{4}
Answer: (C) \frac{3}{8} Explanation: Calculate the binomial probability for 2 heads in 3 flips: \binom{3}{2} \left(\frac{1}{2}\right)^2 \left(\frac{1}{2}\right)^1 = \frac{3}{8}.

Applied Mathematics (Word) Problems

A train travels 160 miles in 4 hours. What is its speed in miles per hour?

• (A) 35 \text{ mph}
• (B) 40 \text{ mph}
• (C) 45 \text{ mph}
• (D) 50 \text{ mph}
• (E) 55 \text{ mph}
Answer: (B) 40 \text{ mph} Explanation: Speed equals distance divided by time: \frac{160 \text{ miles}}{4 \text{ hours}} = 40 \text{ mph}.

What is the price if a shirt costs $20 and is on sale for 25% off? • (A)$15
• (B) $16 • (C)$18
• (D) $19 • (E)$20
Answer: (A) $15 Explanation: Calculate the discount: 25% \text{ of }$20 = $5. Sale price is$20 - $5 =$15.

Algebra

If 3x+2=113x + 2 = 11, what is xx?

• (A) 3
• (B) 2
• (C) 1
• (D) 4
• (E) 5
Answer: (A) 3 Explanation: Solve the equation by subtracting 2 from both sides and then dividing by 3: 3x=93x = 9, so x=3x = 3.

Which of the following represents the expression x2−4x+4x^2 – 4x + 4 factored completely?

Answer: (A) latex^2[/latex] Explanation: This is a perfect square trinomial, factored as (x−2)2(x-2)^2.

Data Analysis, Interpretation, and Sufficiency

The average (mean) of five numbers is 30. If one number is removed and the new average is 25, what was the number removed?

• (A) 45
• (B) 50
• (C) 55
• (D) 40
• (E) 35
Answer: (B) 50 Explanation: The total for five numbers at an average of 30 is 150150. With one removed, the total becomes 100100 (4 numbers at an average of 25). Thus, the removed number is 150−100=50150 – 100 = 50.

What is the median of the set of numbers {3, 7, 9, 13, 21}?

• (A) 7
• (B) 9
• (C) 13
• (D) 21
• (E) 3
Answer: (B) 9 Explanation: When ordered, the middle number in this set is 9.

Quantitative Comparison

Compare 12\frac{1}{2} and 0.49.

• (A) 12\frac{1}{2} is greater.
• (B) 0.49 is greater.
• (C) They are equal.
• (D) The relationship cannot be determined.
• (E) None of the above.
Answer: (A) 12\frac{1}{2} is greater. Explanation: 12=0.5\frac{1}{2} = 0.5, which is greater than 0.49.

Probability and Statistics

If two dice are rolled, what is the probability of the sum being 9?

• (A) \frac{1}{9}
• (B) \frac{1}{12}
• (C) \frac{4}{36}
• (D) \frac{1}{6}
• (E) \frac{1}{18}
Answer: (C) \frac{4}{36} Explanation: There are four combinations to achieve a sum of 9: (3,6), (4,5), (5,4), (6,3). With 36 total outcomes when rolling two dice, the probability is 436=19\frac{4}{36} = \frac{1}{9}.

Applied Mathematics (Word) Problems

A rectangle’s perimeter is 54 cm and its length is 15 cm. What is its width?

• (A) 12 \text{ cm}
• (B) 24 \text{ cm}
• (C) 27 \text{ cm}
• (D) 9 \text{ cm}
• (E) 6 \text{ cm}
Answer: (A) 12 \text{ cm} Explanation: Perimeter of a rectangle is 2(length+width)2(length + width). Given the perimeter is 54 cm, 2(15cm+width)=54cm2(15 cm + width) = 54 cm. Solving for width, width=12cmwidth = 12 cm.

Algebra

Solve for yy in the equation 4y+3=194y + 3 = 19.

• (A) 4
• (B) 3
• (C) 5
• (D) 6
• (E) 7
Answer: (A) 4 Explanation: Subtract 3 from both sides to get 4y=164y = 16, then divide by 4 to solve for yy: y=4y = 4.

If 2×2−5x+3=02x^2 – 5x + 3 = 0, which of the following is a solution for xx?

• (A) 1
• (B) 2
• (C) 3
• (D) \frac{3}{2}
• (E) \frac{1}{2}
Answer: (D) \frac{3}{2} Explanation: Using the quadratic formula, one solution is x=32x = \frac{3}{2}.

Data Analysis, Interpretation, and Sufficiency

A line graph shows the number of cars sold over six months, increasing steadily. What is the slope of the line likely to indicate?

• (A) The change in the number of cars sold per month.
• (B) The total number of cars sold.
• (C) The average price per car.
• (D) The total revenue from car sales.
• (E) The number of cars returned.
Answer: (A) The change in the number of cars sold per month. Explanation: The slope represents the rate of change over time, in this case, how the number of cars sold varies each month.

What is the interquartile range of the data set 4,7,9,12,15,18,204, 7, 9, 12, 15, 18, 20?

• (A) 6
• (B) 8
• (C) 10
• (D) 12
• (E) 14
Answer: (C) 10 Explanation: The interquartile range (IQR) is the difference between the third quartile (Q3) and the first quartile (Q1). For this set, Q3 is 18 and Q1 is 8, so IQR = 18 – 8 = 10.

Quantitative Comparison

Which is greater: the product of 33 and 44, or the square of 55?

• (A) Product of 33 and 44
• (B) Square of 55
• (C) They are equal
• (D) The relationship cannot be determined
• (E) None of the above
Answer: (B) Square of 55 Explanation: 3×4=123 \times 4 = 12, while 52=255^2 = 25, so the square of 55 is greater.

What is the probability of drawing an ace from a standard deck of 52 playing cards?

• (A) \frac{1}{13}
• (B) \frac{1}{26}
• (C) \frac{1}{52}
• (D) \frac{4}{52}
• (E) \frac{1}{12}
Answer: (D) \frac{4}{52} Explanation: There are 4 aces in a deck of 52 cards, so the probability is 452=113\frac{4}{52} = \frac{1}{13}.

Applied Mathematics (Word) Problems

If a pizza is divided into 8 equal slices and a person eats 3 slices, what fraction of the pizza remains?

• (A) \frac{3}{8}
• (B) \frac{5}{8}
• (C) \frac{8}{3}
• (D) \frac{8}{5}
• (E) \frac{1}{2}
Answer: (B) \frac{5}{8} Explanation: If 3 slices are eaten, 5 slices remain out of 8, which is \frac{5}{8} of the pizza.

A car travels 60 miles in 1.5 hours. What is its average speed in miles per hour?

• (A) 30 \text{ mph}
• (B) 40 \text{ mph}
• (C) 50 \text{ mph}
• (D) 60 \text{ mph}
• (E) 70 \text{ mph}
Answer: (B) 40 \text{ mph} Explanation: Average speed is total distance divided by total time. \frac{60 \text{ miles}}{1.5 \text{ hours}} = 40 \text{ mph}.

What is the area of a triangle with a base of 10 cm and a height of 6 cm?

• (A) 20 \text{ cm}^2
• (B) 30 \text{ cm}^2
• (C) 40 \text{ cm}^2
• (D) 50 \text{ cm}^2
• (E) 60 \text{ cm}^2
A store offers a 10% discount on all items. If a shirt originally costs $50, what is the price after the discount? • (A)$40
• (B) $45 • (C)$35
• (D) $55 • (E)$50
Answer: (B) $45 Explanation: Calculate the discount by taking 10% of$50, which is $5. Then subtract from the original price:$50 – $5 =$45.