OAT Quantitative Reasoning Practice Test 2023 Questions and Answer: 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 testtaking skills, and strategic use of the calculator.
The Quantitative Reasoning section is the only section of the OAT which allows the use of a calculator. However, the calculator tends to be pretty timeconsuming. 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 multiplechoice questions, and you will have 45 minutes to complete them. A basic onscreen calculator similar to 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
Scored items in the Quantitative Reasoning section directly test your abilities with Fundamentals of Calculation, Conversions, Algebra, Probability, and Statistics, Geometry, and Trigonometry.
Test Name  OAT Practice Test 2023 
Test Purpose  Admission into optometry schools 
Subject  Quantitative Reasoning 
Sub Test  Quantitative Reasoning 
Sample Questions  40 
Time Limit  N/A 
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OAT Quantitative Reasoning Test
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Question 1 of 40
1. Question
1 pointsA car rental company charges for mileage as follows: x dollars per mile for the first n miles and x + 1 dollars per mile for each mile over n miles. How much will the mileage charge be, in dollars, for a journey of d miles, where d > n ?

Question 2 of 40
2. Question
1 pointsThe manufacturer of SleepEZ mattresses is offering a 10% discount on the price of its king size mattress. Some retailers are offering additional discounts. If a retailer offers an additional 20% discount, then what is the total discount available at that retailer?

Question 3 of 40
3. Question
1 pointsIf 2 is the remainder when m is divided by 5, what is the remainder when 3 m is divided by 5?

Question 4 of 40
4. Question
1 pointsRon begins reading a book at 4:30 p.m. and reads at a steady pace of 30 pages per hour. Michelle begins reading a copy of the same book at 6:00 p.m. If Michelle started 5 pages behind the page that Ron started on and reads at an average pace of 50 pages per hour, at what time would Ron and Michelle be reading the same page?

Question 5 of 40
5. Question
1 points²²Each writer for the local newspaper is paid as follows: a dollars for each of the first n stories each month and a +b dollars for each story thereafter, where a > b. How many more dollars will a writer who submits n + a stories in a month earn than a writer who submits n + b stories?

Question 6 of 40
6. Question
1 pointsA crate of apples contains 1 bruised apple for every 30 apples in the crate. Three out of every four bruised apples are considered not fit to sell, and every apple that is not fit to sell is bruised. If there are 12 apples not fit to sell in the crate, then how many total apples are there in the crate?

Question 7 of 40
7. Question
1 pointsQuantity A
x² + 2 x − 2
Quantity B
x² + 2 x − 1

Question 8 of 40
8. Question
1 pointsFor all shows except those on Sunday afternoons, a local theater sells tickets at one price for adults and a reduced price for children. On Sunday afternoons, all tickets are sold at a discount of 20%.
Quantity A
Quantity B
The amount of money
collected for 120
adults and 100
children on a
Saturday nightThe amount of money
collected for 150
adults and 120
children on a Sunday
afternoon 
Question 9 of 40
9. Question
1 pointsApproximately how much did total revenues increase from 2004 to 2007?

Question 10 of 40
10. Question
1 pointsFor the year in which profits from foodrelated operations increased over the previous year, total revenues were approximately:

Question 11 of 40
11. Question
1 pointsIn 2008, total profits represented approximately what percent of total revenues?

Question 12 of 40
12. Question
1 pointsFor which of the years was the unemployment rate in Country Y more than 5 percentage points greater than that of Country X ?

Question 13 of 40
13. Question
1 pointsWhich of the following is closest to the average (arithmetic mean) of the 9 changes in the percentage of unemployed workers in Country X between consecutive years from 2000 to 2009?

Question 14 of 40
14. Question
1 pointsThe average of 3, 15, 18, and 8 is

Question 15 of 40
15. Question
1 pointsWhich of the following fractions is the largest?

Question 16 of 40
16. Question
1 pointsWhich of the following numbers is smallest?

Question 17 of 40
17. Question
1 points16 + 0.267 + 36.78 =

Question 18 of 40
18. Question
1 pointsWhat is the cost of a blouse that is priced at $50.00 with a tax of 7%?

Question 19 of 40
19. Question
1 pointsWhat is the value of 2,886 ÷ 37?

Question 20 of 40
20. Question
1 pointsIf x = 3 − y2 and y = −2, what is the value of x ?

Question 21 of 40
21. Question
1 pointsWhen 3x³ − 7 x + 7 is divided by x + 2, the remainder is:

Question 22 of 40
22. Question
1 pointsIf 4 x + ky = 15 and x − ky = −25, which of the following could be the values of x and y?

Question 23 of 40
23. Question
1 pointsHow many integers are in the solution set of 4 x + 3 < 8?

Question 24 of 40
24. Question
1 pointsA certain school has 50 students assigned to five distinct classes so that the numbers of students in the classes are consecutive and each student is assigned to only one class. What is the probability that a student selected at random from the 50 students is in one of the two largest classes?

Question 25 of 40
25. Question
1 pointsA certain machine produces toy cars in a repeating cycle of blue, red, green, yellow, and black. If a string of six consecutively produced cars is selected at random from all the possible strings of six consecutively produced cars, what is the probability that, in the string selected, two of the cars are red?

Question 26 of 40
26. Question
1 pointsAmanda goes to the toy store to buy 1 ball and 3 different board games. If the toy store is stocked with 3 types of balls and 6 types of board games, how many different selections of the 4 items can Amanda make?

Question 27 of 40
27. Question
1 pointsA code is to be made by arranging 7 letters. Three of the letters used will be the letter A, two of the letters used will be the letter B, one of the letters used will be the letter C, and one of the letters used will be the letter D. If there is only one way to present each letter, how many different codes are possible?

Question 28 of 40
28. Question
1 pointsIn the figure below, what is the value of cos θ?

Question 29 of 40
29. Question
1 points 
Question 30 of 40
30. Question
1 pointsIf θ is an acute angle for which tan²θ = 6 tan θ − 9, what is the approximate measure of θ?

Question 31 of 40
31. Question
1 pointsWhat is the ycoordinate of the point at which the graph of y = 2 sin x − cos 2 x intersects the yaxis?

Question 32 of 40
32. Question
1 pointsWhat is 0.09356 – 0.003784?

Question 33 of 40
33. Question
1 pointsWhat is the product of (4)(2)(6)?

Question 34 of 40
34. Question
1 pointsHow many cubic inches are in a box 10” wide, 3” deep and 14” long?

Question 35 of 40
35. Question
1 pointsWhat is the perimeter of a park that is 300 yards long and 640 yards wide?

Question 36 of 40
36. Question
1 pointsIf my local grocery store last year had a total income of $7,056,238 and expenses of $3,998,100, how much profit did it make (profit is income minus expenses)?

Question 37 of 40
37. Question
1 pointsThe five events hosted last year by the event company, “We Plan It,” drew crowds of 175, 320, 417, 533, and 210 people. What is their average attendance for those events?

Question 38 of 40
38. Question
1 pointsA pizza dough recipe calls for 2 cups of flour and 1 1/2 teaspoons of salt. How much salt would you need if you wanted to triple the recipe?

Question 39 of 40
39. Question
1 pointsLex’s mom buys 3 of each kind of cookie for a picnic. If the store gives a 10% discount for purchase of a dozen cookies, how much did she spend?

Question 40 of 40
40. Question
1 pointsLex’s favorite cookie store sells the following cookies:
Sugar: $2.00
Macaroons: $1.50
Chocolate chip: $2.50
Peanut butter: $2.00If Lex buys 3 cookies, what is the least amount he could have spent?