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}

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

- (A) 5
- (B) 10
- (C) 7.5
- (D) 20
- (E) 8

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

- (A) 3
- (B) 5
- (C) 7
- (D) 9
- (E) 11

**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%

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

- (A) 7
- (B) 9
- (C) 12
- (D) 15
- (E) 21

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

**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}

**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}

**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

**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

**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

**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.

**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.

**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}

**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

**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

Algebra

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

- (A) 11x - 12
- (B) 11x + 12
- (C) 6x - 7
- (D) 6x + 8
- (E) 10x - 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

**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

**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%

**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

**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}

**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}

**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

**Algebra**

**If $3x+2=11$, what is $x$?**

- (A) 3
- (B) 2
- (C) 1
- (D) 4
- (E) 5

**Which of the following represents the expression $x_{2}−4x+4$ factored completely?**

- (A) latex^2[/latex]
- (B) latex(x-2)[/latex]
- (C) latex(x+1)[/latex]
- (D) latex(x+2)[/latex]
- (E) latex^2[/latex]

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

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

- (A) 7
- (B) 9
- (C) 13
- (D) 21
- (E) 3

**Quantitative Comparison**

**Compare $21 $ and 0.49.**

- (A) $21 $ is greater.
- (B) 0.49 is greater.
- (C) They are equal.
- (D) The relationship cannot be determined.
- (E) None of the above.

**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}

**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}

**Algebra**

**Solve for $y$ in the equation $4y+3=19$.**

- (A) 4
- (B) 3
- (C) 5
- (D) 6
- (E) 7

**If $2x_{2}−5x+3=0$, which of the following is a solution for $x$?**

- (A) 1
- (B) 2
- (C) 3
- (D) \frac{3}{2}
- (E) \frac{1}{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.

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

- (A) 6
- (B) 8
- (C) 10
- (D) 12
- (E) 14

**Quantitative Comparison**

**Which is greater: the product of $3$ and $4$, or the square of $5$?**

- (A) Product of $3$ and $4$
- (B) Square of $5$
- (C) They are equal
- (D) The relationship cannot be determined
- (E) None of the above

**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}

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}

**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}

**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

**See also:**

- Biology Practice Test
- General Chemistry Practice Test
- Organic Chemistry Practice Test
- Physics Practice Test
- Quantitative Reasoning Practice Test