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OAR practice questions

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Question 1Mathematics (Math Skills content area)

What is the sum of 3/4 and 5/8?

  1. 11/8 Correct answer.
  2. 8/12
  3. 15/32
  4. 7/8

Explanation

Convert 3/4 to eighths by multiplying numerator and denominator by 2, giving 6/8. Adding 6/8 + 5/8 combines the numerators over the common denominator, producing 11/8, which is already in lowest terms.

Question 2Mathematics (Math Skills content area)

A jacket is priced at $80 and is marked down 25%. What is the sale price?

  1. $64
  2. $20
  3. $55
  4. $60 Correct answer.

Explanation

The discount equals 0.25 × 80 = $20, and subtracting that from the original price gives 80 − 20 = $60. Equivalently, paying 75% of $80 gives 0.75 × 80 = $60.

Question 3Mathematics (Math Skills content area)

What is the average of the numbers 4, 9, 11, and 16?

  1. 12
  2. 11
  3. 10 Correct answer.
  4. 9

Explanation

The sum of the four values is 4 + 9 + 11 + 16 = 40. Dividing the sum by the count of values gives 40 ÷ 4 = 10.

Question 4Mathematics (Math Skills content area)

Evaluate: 6 + 2 × 3² − 4

  1. 68
  2. 16
  3. 20 Correct answer.
  4. 24

Explanation

Order of operations requires exponents first, so 3² = 9. Then multiplication gives 2 × 9 = 18, and finally 6 + 18 − 4 = 20.

Question 5Mathematics (Math Skills content area)

Two numbers are in the ratio 3:5 and their sum is 40. What is the smaller number?

  1. 12
  2. 25
  3. 15 Correct answer.
  4. 24

Explanation

The ratio 3:5 divides the total into 3 + 5 = 8 equal parts, so each part is 40 ÷ 8 = 5. The smaller share is 3 × 5 = 15.

Question 6Mathematics (Math Skills content area)

How many minutes are in 2.5 hours?

  1. 150 Correct answer.
  2. 180
  3. 250
  4. 120

Explanation

There are 60 minutes in one hour, so multiply 2.5 by 60. That gives 2.5 × 60 = 150 minutes.

Question 7Mathematics (Math Skills content area)

Simplify the expression 2⁵ ÷ 2².

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

Explanation

When dividing powers with the same base, subtract the exponents: 2⁵ ÷ 2² = 2^(5−2) = 2³. Evaluating 2³ gives 8.

Question 8Mathematics (Math Skills content area)

A rectangle measures 8 inches by 5 inches. What is its perimeter?

  1. 40
  2. 26 Correct answer.
  3. 21
  4. 13

Explanation

Perimeter of a rectangle is 2(length + width). Substituting gives 2(8 + 5) = 2(13) = 26 inches.

Question 9Mathematics (Math Skills content area)

Solve for x: 5x − 7 = 3x + 9

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

Explanation

Subtract 3x from both sides to get 2x − 7 = 9, then add 7 to both sides to get 2x = 16. Dividing by 2 gives x = 8.

Question 10Mathematics (Math Skills content area)

A stock price rises from $40 to $50. What is the percent increase?

  1. 20%
  2. 80%
  3. 10%
  4. 25% Correct answer.

Explanation

Percent change is the amount of change divided by the original value. The change is $10, and 10 ÷ 40 = 0.25, which is a 25% increase.

Question 11Mathematics (Math Skills content area)

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

  1. 24
  2. 12
  3. 40
  4. 21 Correct answer.

Explanation

Adding the two equations eliminates y and gives 2x = 14, so x = 7. Substituting back gives y = 3, and the product is 7 × 3 = 21.

Question 12Mathematics (Math Skills content area)

A triangle has a base of 12 centimeters and a height of 7 centimeters. What is its area?

  1. 84
  2. 42 Correct answer.
  3. 19
  4. 21

Explanation

The area of a triangle is one-half the base times the height. Substituting gives (1/2)(12)(7) = 42 square centimeters.

Question 13Mathematics (Math Skills content area)

A bag contains 5 red, 3 blue, and 2 green marbles. If one marble is drawn at random, what is the probability that it is blue?

  1. 3/7
  2. 2/10
  3. 1/3
  4. 3/10 Correct answer.

Explanation

The bag holds 5 + 3 + 2 = 10 marbles in total, of which 3 are blue. Probability is favorable outcomes over total outcomes, so the probability is 3/10.

Question 14Mathematics (Math Skills content area)

A vehicle travels 180 miles at a constant speed of 45 miles per hour. How long does the trip take?

  1. 5 hours
  2. 3 hours
  3. 4 hours Correct answer.
  4. 4.5 hours

Explanation

Time equals distance divided by rate. Dividing 180 miles by 45 miles per hour gives 4 hours.

Question 15Mathematics (Math Skills content area)

A circle has a radius of 7 units. What is its circumference?

  1. 7π
  2. 14π Correct answer.
  3. 28π
  4. 49π

Explanation

Circumference equals 2πr. Substituting r = 7 gives 2 × π × 7 = 14π units.

Question 16Mathematics (Math Skills content area)

What is the slope of the line passing through the points (2, 3) and (6, 11)?

  1. 4
  2. −2
  3. 1/2
  4. 2 Correct answer.

Explanation

Slope equals the change in y divided by the change in x. Here that is (11 − 3) divided by (6 − 2), which is 8/4 = 2.

Question 17Mathematics (Math Skills content area)

Pipe A can fill a tank in 6 hours and pipe B can fill the same tank in 12 hours. Working together, how long will they take to fill the tank?

  1. 9 hours
  2. 18 hours
  3. 4 hours Correct answer.
  4. 3 hours

Explanation

Rates add, so the combined rate is 1/6 + 1/12 = 3/12 = 1/4 of the tank per hour. Inverting that rate gives 4 hours to fill the tank.

Question 18Mathematics (Math Skills content area)

What are the solutions to x² − 5x + 6 = 0?

  1. −1 and −6
  2. 1 and 6
  3. −2 and −3
  4. 2 and 3 Correct answer.

Explanation

Factor the trinomial as (x − 2)(x − 3) = 0, since −2 and −3 multiply to 6 and add to −5. Setting each factor equal to zero gives x = 2 or x = 3.

Question 19Mathematics (Math Skills content area)

How much simple interest is earned on $2,000 invested at 4% annual interest for 3 years?

  1. $2,240
  2. $80
  3. $240 Correct answer.
  4. $120

Explanation

Simple interest is I = Prt. Substituting gives 2000 × 0.04 × 3 = $240.

Question 20Mathematics (Math Skills content area)

Solve for x: |x − 3| = 7

  1. 10 only
  2. −10 and 4
  3. 10 and −4 Correct answer.
  4. 4 and −4

Explanation

An absolute value equation splits into two cases: x − 3 = 7 or x − 3 = −7. Solving each gives x = 10 or x = −4, and both check in the original equation.

Question 21Mathematics (Math Skills content area)

A 20-liter solution is 10% acid. How many liters of pure acid must be added to raise the concentration to 25%?

  1. 2 liters
  2. 4 liters Correct answer.
  3. 10 liters
  4. 6 liters

Explanation

The solution starts with 0.10 × 20 = 2 liters of acid. Adding x liters of pure acid gives (2 + x)/(20 + x) = 0.25, which simplifies to 2 + x = 5 + 0.25x, so 0.75x = 3 and x = 4.

Question 22Mathematics (Math Skills content area)

How many different 3-person committees can be formed from a group of 7 people?

  1. 210
  2. 343
  3. 21
  4. 35 Correct answer.

Explanation

Because order within a committee does not matter, use combinations: 7!/(3!4!) = (7 × 6 × 5)/(3 × 2 × 1) = 35.

Question 23Mathematics (Math Skills content area)

If f(x) = 2x + 1 and g(x) = x² − 3, what is f(g(2))?

  1. 1
  2. 9
  3. 3 Correct answer.
  4. 22

Explanation

Work from the inside out: g(2) = 2² − 3 = 1, then f(1) = 2(1) + 1 = 3. Composition applies the inner function first.

Question 24Mathematics (Math Skills content area)

If 3^(x + 2) = 27^(x − 1), what is the value of x?

  1. 4
  2. 2.5 Correct answer.
  3. 1
  4. 0.5

Explanation

Rewrite 27 as 3³ so the right side becomes 3^(3x − 3). Since the bases match, set x + 2 = 3x − 3, giving 5 = 2x, so x = 2.5.

Question 25Mathematics (Math Skills content area)

A rectangular box has dimensions 3, 4, and 12. What is the length of the longest diagonal that fits inside the box?

  1. 13 Correct answer.
  2. 19
  3. 12
  4. 7

Explanation

The space diagonal of a box is the square root of the sum of the squares of its three dimensions. Here that is √(3² + 4² + 12²) = √(9 + 16 + 144) = √169 = 13.

Question 26Mathematics (Math Skills content area)

What is 3/4 + 2/3?

  1. 13/12
  2. 5/7
  3. 17/12 Correct answer.
  4. 6/7

Explanation

Rewrite both fractions with the least common denominator, 12: 3/4 = 9/12 and 2/3 = 8/12. Adding the numerators gives 9/12 + 8/12 = 17/12, which is already in lowest terms.

Question 27Mathematics (Math Skills content area)

Evaluate 4 + 3 × 2².

  1. 10
  2. 28
  3. 16 Correct answer.
  4. 11

Explanation

Order of operations requires exponents first, then multiplication, then addition. So 2² = 4, then 3 × 4 = 12, and finally 4 + 12 = 16.

Question 28Mathematics (Math Skills content area)

The decimal 0.045 written as a percent is:

  1. 0.45%
  2. 45%
  3. 4.5% Correct answer.
  4. 450%

Explanation

To convert a decimal to a percent, multiply by 100 and attach the percent sign. 0.045 × 100 = 4.5, so the result is 4.5%.

Question 29Mathematics (Math Skills content area)

How many inches are in 3 yards?

  1. 108 inches Correct answer.
  2. 72 inches
  3. 36 inches
  4. 96 inches

Explanation

One yard equals 3 feet, and each foot equals 12 inches, so one yard is 36 inches. Multiplying 3 yards by 36 inches per yard gives 108 inches.

Question 30Mathematics (Math Skills content area)

What is the arithmetic mean of 12, 18, 20, and 30?

  1. 22
  2. 20 Correct answer.
  3. 16
  4. 18

Explanation

The mean is the sum of the values divided by the count of values. The sum is 12 + 18 + 20 + 30 = 80, and 80 ÷ 4 = 20.

Question 31Mathematics (Math Skills content area)

Two angles are complementary. If one angle measures 37°, what is the measure of the other angle?

  1. 143°
  2. 43°
  3. 63°
  4. 53° Correct answer.

Explanation

Complementary angles are two angles whose measures add to 90°. Subtracting the known angle from 90° gives 90° − 37° = 53°.

Question 32Mathematics (Math Skills content area)

If 5 identical notebooks cost $3.50, what is the cost of 8 of the same notebooks?

  1. $5.20
  2. $4.80
  3. $5.60 Correct answer.
  4. $6.40

Explanation

Find the unit price first: $3.50 ÷ 5 = $0.70 per notebook. Multiplying by 8 gives $0.70 × 8 = $5.60.

Question 33Mathematics (Math Skills content area)

What is 15% of 240?

  1. 24
  2. 30
  3. 36 Correct answer.
  4. 32

Explanation

Convert the percent to a decimal and multiply: 0.15 × 240 = 36. Equivalently, 10% of 240 is 24 and 5% is 12, and 24 + 12 = 36.

Question 34Mathematics (Math Skills content area)

A trapezoid has parallel bases of length 6 and 10 and a height of 4. What is its area?

  1. 24
  2. 48
  3. 32 Correct answer.
  4. 64

Explanation

The area of a trapezoid is the average of the bases times the height: ((6 + 10) / 2) × 4. That equals 8 × 4 = 32.

Question 35Mathematics (Math Skills content area)

A right circular cylinder has a radius of 3 units and a height of 5 units. What is its volume?

  1. 15π
  2. 45π Correct answer.
  3. 90π
  4. 30π

Explanation

The volume of a cylinder is πr²h. Substituting r = 3 and h = 5 gives π × 9 × 5 = 45π cubic units.

Question 36Mathematics (Math Skills content area)

A right triangle has legs measuring 9 and 12. What is the length of its hypotenuse?

  1. 21
  2. 15 Correct answer.
  3. 14
  4. 13

Explanation

By the Pythagorean theorem, the hypotenuse is √(9² + 12²) = √(81 + 144) = √225 = 15.

Question 37Mathematics (Math Skills content area)

Triangle ABC is similar to triangle DEF. Side AB = 4 corresponds to side DE = 10, and side BC = 6 corresponds to side EF. What is the length of EF?

  1. 8
  2. 12
  3. 15 Correct answer.
  4. 20

Explanation

Corresponding sides of similar triangles are proportional, so 4/10 = 6/EF. Cross-multiplying gives 4 × EF = 60, so EF = 15.

Question 38Mathematics (Math Skills content area)

A jacket priced at $80 is marked down 25%, and then a 10% sales tax is applied to the reduced price. What is the final cost?

  1. $60.00
  2. $72.00
  3. $66.00 Correct answer.
  4. $64.00

Explanation

A 25% markdown leaves 75% of $80, which is $60. The 10% tax is applied to $60, adding $6, for a final cost of $66.

Question 39Mathematics (Math Skills content area)

Which expression is equivalent to (2x²y)³?

  1. 2x⁶y³
  2. 8x⁵y³
  3. 6x⁶y³
  4. 8x⁶y³ Correct answer.

Explanation

When a product is raised to a power, each factor is raised to that power: 2³ = 8, (x²)³ = x⁶, and y³ = y³. The result is 8x⁶y³.

Question 40Mathematics (Math Skills content area)

Which product is equal to x² − 9x + 20?

  1. (x + 4)(x + 5)
  2. (x − 1)(x − 20)
  3. (x − 2)(x − 10)
  4. (x − 4)(x − 5) Correct answer.

Explanation

The two numbers must multiply to +20 and add to −9, which are −4 and −5. Therefore x² − 9x + 20 factors as (x − 4)(x − 5).

Question 41Mathematics (Math Skills content area)

For which values of x is the inequality −2x + 5 > 11 true?

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

Explanation

Subtract 5 from both sides to get −2x > 6, then divide both sides by −2. Dividing by a negative number reverses the inequality sign, giving x < −3.

Question 42Mathematics (Math Skills content area)

An arithmetic sequence begins 3, 7, 11, 15, ... What is the 20th term?

  1. 75
  2. 80
  3. 79 Correct answer.
  4. 83

Explanation

The first term is 3 and the common difference is 4. Using aₙ = a₁ + (n − 1)d gives 3 + 19 × 4 = 3 + 76 = 79.

Question 43Mathematics (Math Skills content area)

A box contains 4 white socks and 6 black socks. Two socks are drawn at random one after another without replacement. What is the probability that both socks are black?

  1. 3/5
  2. 1/2
  3. 1/3 Correct answer.
  4. 2/5

Explanation

The probability the first sock is black is 6/10, and with one black sock removed the probability the second is black is 5/9. Multiplying gives (6/10)(5/9) = 30/90 = 1/3.

Question 44Mathematics (Math Skills content area)

A theater sells 200 tickets in one night. Adult tickets cost $8 each and child tickets cost $5 each, and total revenue is $1,330. How many adult tickets were sold?

  1. 110 Correct answer.
  2. 100
  3. 90
  4. 120

Explanation

Let a be adult tickets and c be child tickets, so a + c = 200 and 8a + 5c = 1330. Substituting c = 200 − a gives 8a + 1000 − 5a = 1330, so 3a = 330 and a = 110.

Question 45Mathematics (Math Skills content area)

A driver travels to a destination at an average speed of 30 miles per hour and returns along the same route at an average speed of 60 miles per hour. What is the average speed for the entire round trip?

  1. 45 mph
  2. 40 mph Correct answer.
  3. 50 mph
  4. 36 mph

Explanation

For equal distances at two speeds, the average speed is 2uv/(u + v) = (2 × 30 × 60)/(90) = 3600/90 = 40 mph. The slower leg takes twice as long, so it dominates the average.

Question 46Mathematics (Math Skills content area)

What are the solutions to 2x² − 4x − 3 = 0?

  1. (2 ± √10)/2 Correct answer.
  2. (2 ± √40)/2
  3. (−2 ± √10)/2
  4. (4 ± √10)/4

Explanation

Apply the quadratic formula with a = 2, b = −4, and c = −3: x = (4 ± √(16 + 24))/4 = (4 ± √40)/4. Since √40 = 2√10, this simplifies to (4 ± 2√10)/4 = (2 ± √10)/2.

Question 47Mathematics (Math Skills content area)

$1,000 is deposited in an account that earns 5% interest compounded annually. What is the balance after 2 years, assuming no other deposits or withdrawals?

  1. $1,100.00
  2. $1,102.50 Correct answer.
  3. $1,125.00
  4. $1,050.00

Explanation

The compound interest formula is A = P(1 + r)ᵗ. Here A = 1000(1.05)² = 1000 × 1.1025 = $1,102.50, which includes interest earned on the first year's interest.

Question 48Mathematics (Math Skills content area)

Two trains are 240 miles apart on the same track and leave at the same time traveling toward each other. One travels at 50 miles per hour and the other at 70 miles per hour. In how many hours will they meet?

  1. 2 hours Correct answer.
  2. 2.5 hours
  3. 4 hours
  4. 1.5 hours

Explanation

When two objects move toward each other, their closing speed is the sum of their speeds: 50 + 70 = 120 miles per hour. Dividing the 240-mile gap by 120 mph gives 2 hours.

Question 49Mathematics (Math Skills content area)

Which values of x satisfy |2x − 5| ≤ 9?

  1. x ≤ 7
  2. −2 ≤ x ≤ 7 Correct answer.
  3. −7 ≤ x ≤ 2
  4. x ≥ −2

Explanation

An absolute value less than or equal to a positive number becomes a compound inequality: −9 ≤ 2x − 5 ≤ 9. Adding 5 throughout gives −4 ≤ 2x ≤ 14, and dividing by 2 gives −2 ≤ x ≤ 7.

Question 50Mathematics (Math Skills content area)

A fair six-sided die is rolled twice. What is the probability of getting at least one 6?

  1. 1/6
  2. 1/3
  3. 25/36
  4. 11/36 Correct answer.

Explanation

It is easier to use the complement: the probability of no 6 on either roll is (5/6)(5/6) = 25/36. Therefore the probability of at least one 6 is 1 − 25/36 = 11/36.