Question 1
For x ≠ 3, consider the equation (x² - 9)/(x - 3) = 6. What is the solution set?
Show answer & explanation
Correct answer: B - No real solution
10 exam-style questions with answers and explanations, straight from our 1,030-question bank. Tap an answer to check yourself. When you're ready, take the scored version in the free practice test.
The OAT-QR exam has 40 questions and runs 45 minutes.
These 10 free OAT-QR questions are organized by exam domain, so you can see how each part of the Optometry Admission Test Quantitative Reasoning (OAT) blueprint is tested. Reveal the answer and explanation under each question.
For x ≠ 3, consider the equation (x² - 9)/(x - 3) = 6. What is the solution set?
Correct answer: B - No real solution
For any function f, let g(x) = f(x + 4) - 3. Relative to the graph of y = f(x), how is the graph of y = g(x) obtained?
Correct answer: D - Shift left 4 and down 3
A report combines 20 observations with mean 72 and 80 observations with mean 84. An analyst averages the two reported means and obtains 78. Which correction is accurate?
Correct answer: A - 81.6, using the group sizes as weights
A test-preparation company emails all users an optional survey. Among the 18% who respond, 82% say their scores improved. Which statement is justified by these data?
Correct answer: B - Among respondents, 82% reported improvement; the result may not represent all users.
The sum of two real numbers x and y is 12, and their product is 35. Which additional fact makes the value of x unique?
Correct answer: D - x is greater than y
A laboratory rinse tank holds 8 L of solution that is 15% concentrate. To meet a safety rule, the final concentration must be below 12%. Pure water can be added only in whole liters. What is the smallest amount to add?
Correct answer: C - 3 L
A quality-control tray contains 4 flagged samples and 6 unflagged samples. Two samples are selected at random without replacement. Which probability correctly accounts for the changed composition after the first draw?
Correct answer: A - 2/15, because the second probability becomes 3/9
The equation 3x + 2y = 14 is known. Which second equation supplies enough independent information to determine a unique ordered pair (x, y)?
Correct answer: C - 2x - 3y = 1
A courier drives the same distance at 40 mph and at 60 mph. Which method gives the average speed for the entire trip?
Correct answer: B - Use total distance divided by total time: 2(40)(60)/(40 + 60).
Let x be positive. Quantity A = (x + 1)² and Quantity B = x² + 1. Determine their relationship.
Correct answer: A - Quantity A is greater.
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