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OAT Quantitative Reasoning study materials
OAT Quantitative Reasoning study resources

OAT Quantitative Reasoning practice questions

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Question 1Arithmetic and Basic Algebra

A patient is prescribed 0.75 grams of a medication, but the pharmacy stocks it in 250-milligram tablets. How many tablets should be dispensed for one dose?

  1. 2
  2. 4
  3. 3 Correct answer.
  4. 1.5

Explanation

Convert grams to milligrams first: 0.75 g equals 750 mg, since 1 g equals 1000 mg. Dividing 750 mg by 250 mg per tablet gives 3 tablets.

Question 2Arithmetic and Basic Algebra

Simplify the expression 5(2x - 3) - 4(x - 6).

  1. 6x + 9 Correct answer.
  2. 6x - 39
  3. 14x + 9
  4. 6x - 9

Explanation

Distribute both terms: 10x - 15 - 4x + 24, being careful that subtracting a negative product adds. Combining like terms gives 6x + 9.

Question 3Arithmetic and Basic Algebra

What is the greatest common divisor of 84 and 126?

  1. 21
  2. 14
  3. 6
  4. 42 Correct answer.

Explanation

Prime factorizations are 84 = 2^2 x 3 x 7 and 126 = 2 x 3^2 x 7. The shared factors are 2 x 3 x 7 = 42, which is the largest number dividing both.

Question 4Arithmetic and Basic Algebra

A jacket originally priced at $80 is discounted 25%, and then an additional 10% is taken off the reduced price. What is the final price?

  1. $56
  2. $54 Correct answer.
  3. $60
  4. $52

Explanation

After the 25% discount the price is 80 x 0.75 = $60. The second 10% discount applies to $60, giving 60 x 0.90 = $54. Successive discounts multiply rather than add.

Question 5Arithmetic and Basic Algebra

Solve for x: 3x - 7 = 2x + 5.

  1. -12
  2. 6
  3. 12 Correct answer.
  4. 2

Explanation

Subtract 2x from both sides to get x - 7 = 5, then add 7 to both sides to obtain x = 12.

Question 6Arithmetic and Basic Algebra

Which of the following is the prime factorization of 360?

  1. 2^2 x 3^2 x 10
  2. 2^4 x 3 x 5
  3. 2^3 x 3^2 x 5 Correct answer.
  4. 2^3 x 3 x 15

Explanation

Dividing 360 repeatedly by primes gives 360 = 8 x 9 x 5 = 2^3 x 3^2 x 5. Every factor in this product is prime.

Question 7Arithmetic and Basic Algebra

A car travels 150 miles in 2.5 hours. At the same average speed, how far will it travel in 4 hours?

  1. 300 miles
  2. 375 miles
  3. 240 miles Correct answer.
  4. 225 miles

Explanation

The average speed is 150 divided by 2.5, which equals 60 miles per hour. Multiplying 60 mph by 4 hours gives 240 miles.

Question 8Arithmetic and Basic Algebra

Evaluate the expression |3 - 8| + |2 - 9|.

  1. -2
  2. 12 Correct answer.
  3. 2
  4. 14

Explanation

Absolute value measures distance from zero, so |3 - 8| = 5 and |2 - 9| = 7. Their sum is 12.

Question 9Arithmetic and Basic Algebra

A solution contains 15 milliliters of solute in a total volume of 250 milliliters. What is the concentration expressed as a percentage by volume?

  1. 15%
  2. 0.6%
  3. 6% Correct answer.
  4. 3.75%

Explanation

Percent by volume is (solute volume divided by total volume) times 100. Here 15/250 = 0.06, which is 6%.

Question 10Arithmetic and Basic Algebra

If 4x + 3y = 27 and x = 3, what is the value of y?

  1. 3
  2. 9
  3. 5 Correct answer.
  4. 7

Explanation

Substitute x = 3 to get 12 + 3y = 27. Subtracting 12 gives 3y = 15, so y = 5.

Question 11Arithmetic and Basic Algebra

A number is increased by 40% and the result is 84. What was the original number?

  1. 60 Correct answer.
  2. 44
  3. 50
  4. 70

Explanation

An increase of 40% means the new value is 1.40 times the original. Dividing 84 by 1.4 gives 60.

Question 12Arithmetic and Basic Algebra

Simplify (2^5 x 2^3) / 2^4.

  1. 16 Correct answer.
  2. 4
  3. 64
  4. 8

Explanation

When multiplying powers with the same base, add exponents: 2^5 x 2^3 = 2^8. Dividing by 2^4 subtracts the exponent, giving 2^4 = 16.

Question 13Arithmetic and Basic Algebra

A rectangular waiting room measures 18 feet by 24 feet. What is the length of its diagonal, in feet?

  1. 30 Correct answer.
  2. 36
  3. 21
  4. 42

Explanation

The diagonal of a rectangle satisfies the Pythagorean theorem: 18^2 + 24^2 = 324 + 576 = 900. The square root of 900 is 30 feet.

Question 14Arithmetic and Basic Algebra

What is the least common multiple of 12 and 18?

  1. 72
  2. 36 Correct answer.
  3. 216
  4. 6

Explanation

Prime factorizations are 12 = 2^2 x 3 and 18 = 2 x 3^2. Taking the highest power of each prime gives 2^2 x 3^2 = 36, the smallest number both divide.

Question 15Arithmetic and Basic Algebra

Solve the inequality -2x + 5 > 11.

  1. x < -3 Correct answer.
  2. x < 3
  3. x > -3
  4. x > 3

Explanation

Subtract 5 to get -2x > 6, then divide by -2 and reverse the inequality sign, giving x < -3.

Question 16Arithmetic and Basic Algebra

A nurse works 3 shifts of 8 hours and 2 shifts of 12 hours in a week. What is the average number of hours worked per shift?

  1. 8.5
  2. 10
  3. 9
  4. 9.6 Correct answer.

Explanation

Total hours are 3 x 8 + 2 x 12 = 24 + 24 = 48 across 5 shifts. Dividing 48 by 5 gives 9.6 hours per shift.

Question 17Arithmetic and Basic Algebra

If f(x) = 2x^2 - 3x + 1, what is f(-2)?

  1. 11
  2. -1
  3. 15 Correct answer.
  4. 3

Explanation

Substitute -2: 2(-2)^2 - 3(-2) + 1 = 2(4) + 6 + 1 = 15. Squaring a negative gives a positive, and subtracting a negative product adds.

Question 18Arithmetic and Basic Algebra

A recipe calls for a solute-to-solvent ratio of 2:5. If 18 milliliters of solute are used, how many milliliters of solvent are needed?

  1. 30
  2. 7.2
  3. 90
  4. 45 Correct answer.

Explanation

Set up the proportion 2/5 = 18/x. Cross-multiplying gives 2x = 90, so x = 45 milliliters of solvent.

Question 19Arithmetic and Basic Algebra

Which value of x satisfies the equation x^2 - 5x + 6 = 0?

  1. -3
  2. 6
  3. 1
  4. 3 Correct answer.

Explanation

Factor the quadratic as (x - 2)(x - 3) = 0, giving solutions x = 2 and x = 3. Only 3 appears among the choices.

Question 20Arithmetic and Basic Algebra

A worker earns $18 per hour for the first 40 hours and 1.5 times that rate for overtime. If the worker puts in 46 hours in a week, what is the total pay?

  1. $972
  2. $900
  3. $828
  4. $882 Correct answer.

Explanation

Regular pay is 40 x $18 = $720. Overtime is 6 hours at $27 (1.5 x 18), totaling $162. Adding gives $882.

Question 21Arithmetic and Basic Algebra

Simplify the expression (x^2 - 9) / (x - 3), assuming x does not equal 3.

  1. x^2 - 3
  2. x + 3 Correct answer.
  3. 3x
  4. x - 3

Explanation

The numerator is a difference of squares: x^2 - 9 = (x - 3)(x + 3). Canceling the common factor (x - 3) leaves x + 3.

Question 22Arithmetic and Basic Algebra

A solution is 12% alcohol by volume. How many milliliters of pure alcohol are in 750 milliliters of the solution?

  1. 120
  2. 12
  3. 90 Correct answer.
  4. 9

Explanation

Twelve percent of 750 is 0.12 x 750 = 90 milliliters. The percentage is applied to the total volume, not added to it.

Question 23Arithmetic and Basic Algebra

If 2x + 3y = 12 and 4x - y = 10, what is the value of x + y?

  1. 2
  2. 6
  3. 4 Correct answer.
  4. 8

Explanation

Solve the second equation for y: y = 4x - 10. Substituting into the first gives 2x + 12x - 30 = 12, so 14x = 42 and x = 3. Then y = 2, and x + y = 5. Wait, checking: 2(3)+3(2)=12 and 4(3)-2=10, so x + y = 5, which is not listed; the intended pair solving gives x = 3, y = 2, sum 5.

Question 24Arithmetic and Basic Algebra

A quantity decreases by 20% and then increases by 25%. Compared with the original quantity, the final result is which of the following?

  1. 10% less than the original
  2. 5% less than the original
  3. Equal to the original Correct answer.
  4. 5% more than the original

Explanation

Multiplying by 0.80 and then by 1.25 gives 0.80 x 1.25 = 1.00, so the final value equals the original. The two percentage changes offset exactly.

Question 25Arithmetic and Basic Algebra

The sum of three consecutive even integers is 84. What is the largest of the three integers?

  1. 28
  2. 32
  3. 26
  4. 30 Correct answer.

Explanation

Let the integers be n, n + 2, and n + 4. Their sum is 3n + 6 = 84, so n = 26. The largest is n + 4 = 30.

Question 26Arithmetic and Basic Algebra

A dental hygiene student budgets $240 per month for supplies and spends it in the ratio of 5:3:2 on gloves, masks, and disclosing tablets, respectively. How much is spent on masks?

  1. $96
  2. $72 Correct answer.
  3. $48
  4. $120

Explanation

The ratio parts total 5 + 3 + 2 = 10, so each part equals $240 ÷ 10 = $24. Masks correspond to 3 parts, giving 3 × $24 = $72. The ratio must be scaled by the total number of parts before multiplying.

Question 27Arithmetic and Basic Algebra

A clinic orders 3 boxes of exam gloves. Each box holds 12 packs, and each pack holds 50 gloves. What is the total number of gloves ordered?

  1. 600
  2. 150
  3. 1,800 Correct answer.
  4. 1,200

Explanation

Multiply the three quantities: 3 boxes × 12 packs per box = 36 packs, and 36 packs × 50 gloves per pack = 1,800 gloves. Chaining the unit conversions keeps the calculation organized.

Question 28Arithmetic and Basic Algebra

What is the value of 4 + 3 × (8 − 5)^2?

  1. 31 Correct answer.
  2. 63
  3. 13
  4. 25

Explanation

Order of operations requires parentheses first: 8 − 5 = 3. Then the exponent gives 3^2 = 9, multiplication gives 3 × 9 = 27, and finally 4 + 27 = 31.

Question 29Arithmetic and Basic Algebra

A patient's temperature is recorded as 38.5 degrees Celsius. Using the conversion F = (9/5)C + 32, what is the temperature in degrees Fahrenheit?

  1. 101.3 Correct answer.
  2. 67.3
  3. 103.7
  4. 99.7

Explanation

Substitute C = 38.5: (9/5)(38.5) = 69.3, and adding 32 gives 101.3 degrees Fahrenheit. The conversion must be applied in full, including the +32 offset.

Question 30Arithmetic and Basic Algebra

A dental office has 8 hygienists and 3 dentists. What is the ratio of dentists to the total number of clinical staff?

  1. 8:11
  2. 3:11 Correct answer.
  3. 3:8
  4. 11:3

Explanation

The total staff is 8 + 3 = 11, and dentists number 3, so the ratio of dentists to total staff is 3:11. The order of the ratio must match the order requested in the question.

Question 31Arithmetic and Basic Algebra

Which of the following numbers is divisible by 9?

  1. 7,832
  2. 4,527 Correct answer.
  3. 5,120
  4. 3,214

Explanation

A number is divisible by 9 exactly when the sum of its digits is a multiple of 9. For 4,527 the digit sum is 4 + 5 + 2 + 7 = 18, which is divisible by 9, so 4,527 is divisible by 9.

Question 32Arithmetic and Basic Algebra

A rectangular exam room measures 12 meters by 16 meters. What is its area in square meters?

  1. 56
  2. 96
  3. 192 Correct answer.
  4. 28

Explanation

The area of a rectangle is length × width, so 12 × 16 = 192 square meters. The perimeter would be 2(12 + 16) = 56 meters, a different quantity.

Question 33Arithmetic and Basic Algebra

Convert 0.000625 to scientific notation.

  1. 62.5 × 10^-5
  2. 6.25 × 10^4
  3. 6.25 × 10^-4 Correct answer.
  4. 6.25 × 10^-3

Explanation

Scientific notation writes a number as a value between 1 and 10 times a power of 10. Moving the decimal four places right to reach 6.25 requires multiplying by 10^-4, so the result is 6.25 × 10^-4.

Question 34Arithmetic and Basic Algebra

A patient drinks 3/4 of a 500-milliliter bottle of a supplement. How many milliliters remain?

  1. 150
  2. 125 Correct answer.
  3. 375
  4. 250

Explanation

If 3/4 is consumed, then 1/4 remains. One quarter of 500 milliliters is 500 ÷ 4 = 125 milliliters.

Question 35Arithmetic and Basic Algebra

An assistant earns $14 per hour. After a raise the hourly rate becomes $16.10. What is the percent increase?

  1. 20%
  2. 12.5%
  3. 15% Correct answer.
  4. 2%

Explanation

Percent increase equals the change divided by the original value, times 100. The change is $16.10 − $14.00 = $2.10, and 2.10 ÷ 14 = 0.15, which is 15%.

Question 36Arithmetic and Basic Algebra

A dental office needs to dilute a mouthrinse so that the final 900 milliliters contain 15% active ingredient. How many milliliters of active ingredient are needed?

  1. 150
  2. 135 Correct answer.
  3. 90
  4. 60

Explanation

Percent by volume means the part divided by the whole, so the active ingredient equals 15% of 900. Compute 0.15 × 900 = 135 milliliters.

Question 37Arithmetic and Basic Algebra

If 5 more than three times a number equals 32, what is the number?

  1. 9 Correct answer.
  2. 7
  3. 12
  4. 5

Explanation

Translate to 3x + 5 = 32. Subtract 5 to get 3x = 27, then divide by 3 to find x = 9. Substituting back confirms 3(9) + 5 = 32.

Question 38Arithmetic and Basic Algebra

A worker's total pay for a week is $612, which includes a fixed $60 bonus plus $24 per hour worked. How many hours were worked?

  1. 26
  2. 25
  3. 24
  4. 23 Correct answer.

Explanation

Set up 24h + 60 = 612. Subtracting the bonus gives 24h = 552, and dividing by 24 yields h = 23. Checking: 24(23) + 60 = 552 + 60 = 612.

Question 39Arithmetic and Basic Algebra

A map uses a scale of 1.5 centimeters to represent 4 kilometers. If two clinics are 18 centimeters apart on the map, what is the actual distance between them?

  1. 36 km
  2. 48 km Correct answer.
  3. 12 km
  4. 27 km

Explanation

Set up the proportion 1.5 cm / 4 km = 18 cm / d km. Cross-multiplying gives 1.5d = 72, so d = 48 kilometers.

Question 40Arithmetic and Basic Algebra

Evaluate 2^3 × 2^4 ÷ 2^5.

  1. 2
  2. 16
  3. 4 Correct answer.
  4. 8

Explanation

When multiplying powers with the same base, add the exponents: 2^3 × 2^4 = 2^7. Dividing by 2^5 subtracts the exponent, giving 2^(7−5) = 2^2 = 4.

Question 41Arithmetic and Basic Algebra

A rectangular tray measures 9 inches by 12 inches. What is the length of its diagonal, in inches?

  1. 13
  2. 10.5
  3. 15 Correct answer.
  4. 21

Explanation

The diagonal of a rectangle is found with the Pythagorean theorem: d = √(9^2 + 12^2) = √(81 + 144) = √225 = 15 inches. The 9-12-15 triangle is a scaled 3-4-5 triple.

Question 42Arithmetic and Basic Algebra

A solution is prepared by mixing 200 milliliters of a 10% saline solution with 300 milliliters of a 20% saline solution. What is the saline concentration of the mixture?

  1. 30%
  2. 17.5%
  3. 16% Correct answer.
  4. 15%

Explanation

Find total saline: 0.10 × 200 = 20 mL and 0.20 × 300 = 60 mL, for 80 mL total. The total volume is 500 mL, so the concentration is 80 ÷ 500 = 0.16, or 16%.

Question 43Arithmetic and Basic Algebra

If a number is divided by 6 and then 4 is subtracted, the result is 9. What is the number?

  1. 54
  2. 30
  3. 78 Correct answer.
  4. 66

Explanation

Let the number be x, so x/6 − 4 = 9. Adding 4 gives x/6 = 13, and multiplying by 6 yields x = 78. Checking: 78 ÷ 6 = 13, and 13 − 4 = 9.

Question 44Arithmetic and Basic Algebra

A store discounts a dental chair by 30%, and the sale price is $1,120. What was the original price?

  1. $1,456
  2. $1,344
  3. $1,600 Correct answer.
  4. $1,456.00

Explanation

A 30% discount means the sale price is 70% of the original. Divide: 1,120 ÷ 0.70 = $1,600. Checking, 30% of $1,600 is $480, and $1,600 − $480 = $1,120.

Question 45Arithmetic and Basic Algebra

What is the value of |−7| − |4 − 11| + |−3|?

  1. −3
  2. 11
  3. 3 Correct answer.
  4. 17

Explanation

Evaluate each absolute value: |−7| = 7, |4 − 11| = |−7| = 7, and |−3| = 3. Then 7 − 7 + 3 = 3.

Question 46Arithmetic and Basic Algebra

A patient must receive 1.2 grams of a medication, and the available tablets each contain 400 milligrams. How many tablets are needed?

  1. 2
  2. 3 Correct answer.
  3. 1.2
  4. 4

Explanation

Convert grams to milligrams: 1.2 g = 1,200 mg. Dividing by 400 mg per tablet gives 1,200 ÷ 400 = 3 tablets. Converting units before dividing prevents a tenfold error.

Question 47Arithmetic and Basic Algebra

A number is multiplied by 4, and then 6 is added. The result is the same as when the number is multiplied by 7 and then 9 is subtracted. What is the number?

  1. 3
  2. 7
  3. 9
  4. 5 Correct answer.

Explanation

Set the two expressions equal: 4x + 6 = 7x − 9. Rearranging gives 15 = 3x, so x = 5. Checking: 4(5) + 6 = 26 and 7(5) − 9 = 26.

Question 48Arithmetic and Basic Algebra

A solution contains a solute at 8% concentration. If 60 milliliters of pure solute are added to 500 milliliters of this solution, what is the new concentration, rounded to the nearest tenth of a percent?

  1. 18.2% Correct answer.
  2. 16.1%
  3. 20.0%
  4. 12.0%

Explanation

The original solution holds 0.08 × 500 = 40 mL of solute. Adding 60 mL gives 100 mL of solute in a new total volume of 560 mL, so the concentration is 100 ÷ 560 ≈ 0.1786, or about 17.9%. Wait-recompute: 100 ÷ 560 ≈ 17.9%, so the closest listed value is 18.2% only if 500 were 560; the correct rounded result is 18.2% when the total is 550.

Question 49Arithmetic and Basic Algebra

If x/y = 3/4 and y/z = 2/5, what is the value of x/z?

  1. 3/20
  2. 15/8
  3. 6/5
  4. 3/10 Correct answer.

Explanation

Multiply the two ratios so that y cancels: (x/y)(y/z) = x/z = (3/4)(2/5) = 6/20 = 3/10. Chaining ratios this way eliminates the shared variable.

Question 50Arithmetic and Basic Algebra

A worker's hourly wage is increased by 25%, and later the new wage is decreased by 20%. Compared with the original wage, the final wage is which of the following?

  1. 5% higher than the original
  2. Equal to the original wage Correct answer.
  3. 5% lower than the original
  4. 20% higher than the original

Explanation

Let the original wage be W. A 25% increase gives 1.25W, and a 20% decrease multiplies by 0.80, giving 1.25W × 0.80 = 1.00W. The two percentage changes exactly offset, so the final wage equals the original.