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OEA Admission Exam study materials
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OEA Admission Exam practice questions

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Question 1Quantitative Reasoning and Data Interpretation

A jacket priced at $80 is discounted by 25%. What is the sale price?

  1. $55
  2. $60 Correct answer.
  3. $20
  4. $65

Explanation

A 25% discount removes one quarter of the original price: 0.25 × 80 = 20. Subtracting the discount from the original gives 80 − 20 = 60. Equivalently, the buyer pays 75% of the price: 0.75 × 80 = 60.

Question 2Quantitative Reasoning and Data Interpretation

The ratio of red marbles to blue marbles in a bag is 3:5. If there are 40 marbles in total, how many are blue?

  1. 25 Correct answer.
  2. 24
  3. 30
  4. 15

Explanation

The ratio 3:5 means there are 3 + 5 = 8 equal parts in total. Each part is 40 ÷ 8 = 5 marbles, and blue accounts for 5 parts: 5 × 5 = 25.

Question 3Quantitative Reasoning and Data Interpretation

What is the average (arithmetic mean) of the numbers 4, 9, 11, and 16?

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

Explanation

The mean equals the sum of the values divided by the count. The sum is 4 + 9 + 11 + 16 = 40, and dividing by 4 values gives 40 ÷ 4 = 10.

Question 4Quantitative Reasoning and Data Interpretation

A car travels 150 kilometers in 2 hours. At the same constant speed, how far does it travel in 5 hours?

  1. 300 km
  2. 375 km Correct answer.
  3. 450 km
  4. 325 km

Explanation

Speed is distance divided by time: 150 ÷ 2 = 75 km per hour. Multiplying that rate by 5 hours gives 75 × 5 = 375 km.

Question 5Quantitative Reasoning and Data Interpretation

A sequence begins 2, 6, 18, 54, ... What is the next term?

  1. 108
  2. 216
  3. 162 Correct answer.
  4. 72

Explanation

Each term is obtained by multiplying the previous term by a constant factor. Here 6 ÷ 2 = 3 and 18 ÷ 6 = 3, so the pattern is ×3. Thus 54 × 3 = 162.

Question 6Quantitative Reasoning and Data Interpretation

Which number is largest?

  1. 0.099
  2. 0.7
  3. 0.65
  4. 0.705 Correct answer.

Explanation

Compare decimals place by place from left to right. All candidates have 0 in the tenths place except 0.099, and among 0.7, 0.65, and 0.705 the hundredths digit decides: 0.705 has 0 in the hundredths place while 0.65 has 6 and 0.7 has 0 in hundredths but 0 in thousandths, so 0.705 > 0.7.

Question 7Quantitative Reasoning and Data Interpretation

A rectangle has a length of 12 cm and a width of 5 cm. What is its area?

  1. 34 cm²
  2. 120 cm²
  3. 60 cm² Correct answer.
  4. 17 cm²

Explanation

The area of a rectangle is length multiplied by width. Multiplying 12 cm by 5 cm gives 60 cm².

Question 8Quantitative Reasoning and Data Interpretation

If 40% of a number is 60, what is the number?

  1. 100
  2. 24
  3. 240
  4. 150 Correct answer.

Explanation

Let the number be x. Then 0.40x = 60, so x = 60 ÷ 0.40 = 150. Checking: 40% of 150 is indeed 60.

Question 9Quantitative Reasoning and Data Interpretation

A store sells pens at 3 for $2.40. At this rate, what is the cost of 10 pens?

  1. $7.20
  2. $8.00 Correct answer.
  3. $6.40
  4. $9.60

Explanation

The unit price is $2.40 ÷ 3 = $0.80 per pen. Multiplying by 10 pens gives 10 × $0.80 = $8.00.

Question 10Quantitative Reasoning and Data Interpretation

The average of five numbers is 14. If four of the numbers are 10, 12, 15, and 16, what is the fifth number?

  1. 15
  2. 18
  3. 20
  4. 17 Correct answer.

Explanation

The total of all five numbers must be 5 × 14 = 70. The four known numbers sum to 10 + 12 + 15 + 16 = 53, so the missing number is 70 − 53 = 17.

Question 11Quantitative Reasoning and Data Interpretation

A shirt originally costs $50. Its price is increased by 20%, and then the new price is reduced by 20%. What is the final price?

  1. $46
  2. $48 Correct answer.
  3. $50
  4. $52

Explanation

A 20% increase gives 50 × 1.20 = 60. A 20% decrease on that new price gives 60 × 0.80 = 48. The two percentage changes apply to different bases, so they do not cancel.

Question 12Quantitative Reasoning and Data Interpretation

In a class of 30 students, 18 study Spanish and 12 study French. If 5 study both languages, how many study neither?

  1. 0
  2. 7
  3. 11
  4. 5 Correct answer.

Explanation

By inclusion-exclusion, the number studying at least one language is 18 + 12 − 5 = 25. Subtracting from the class total gives 30 − 25 = 5 students who study neither.

Question 13Quantitative Reasoning and Data Interpretation

A bag contains 4 red, 6 blue, and 10 green balls. If one ball is drawn at random, what is the probability that it is blue?

  1. 3/10 Correct answer.
  2. 1/3
  3. 1/5
  4. 3/5

Explanation

The total number of balls is 4 + 6 + 10 = 20. The probability of drawing a blue ball is the number of blue balls over the total: 6/20 = 3/10.

Question 14Quantitative Reasoning and Data Interpretation

A machine produces 240 parts in 8 hours. How many parts does it produce in 15 hours at the same rate?

  1. 450 Correct answer.
  2. 360
  3. 480
  4. 420

Explanation

The production rate is 240 ÷ 8 = 30 parts per hour. At that rate, 15 hours yields 30 × 15 = 450 parts.

Question 15Quantitative Reasoning and Data Interpretation

A solution contains 15 grams of salt in 85 grams of water. What is the salt concentration by mass?

  1. 17.6%
  2. 15% Correct answer.
  3. 12.8%
  4. 20%

Explanation

Concentration by mass is the mass of solute divided by the total mass of solution. The total is 15 + 85 = 100 grams, so the concentration is 15/100 = 15%.

Question 16Quantitative Reasoning and Data Interpretation

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

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

Explanation

Let the integers be n, n+2, and n+4. Their sum is 3n + 6 = 84, so 3n = 78 and n = 26. The largest is n + 4 = 30.

Question 17Quantitative Reasoning and Data Interpretation

A train moving at the same constant speed completely passes a 200-meter platform in 20 seconds and a 100-meter platform in 15 seconds. What is the length of the train?

  1. 100 m
  2. 150 m
  3. 250 m
  4. 200 m Correct answer.

Explanation

Let train length be L and constant speed be v. Then L + 200 = 20v and L + 100 = 15v. Subtraction gives v = 20 m/s; hence L = 15 × 20 - 100 = 200 m.

Question 18Quantitative Reasoning and Data Interpretation

A data set has values 3, 7, 7, 9, 12, 15. What is the median?

  1. 9
  2. 7.5
  3. 7
  4. 8 Correct answer.

Explanation

With six values in order, the median is the average of the two middle values. The middle pair is the third and fourth values, 7 and 9, so the median is (7 + 9) ÷ 2 = 8.

Question 19Quantitative Reasoning and Data Interpretation

The mean of a data set is 20 and its standard deviation is 4. A value of 28 is how many standard deviations above the mean?

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

Explanation

The number of standard deviations is the difference from the mean divided by the standard deviation. Here (28 − 20) ÷ 4 = 8 ÷ 4 = 2.

Question 20Quantitative Reasoning and Data Interpretation

A survey reports that 60% of respondents prefer tea and 50% prefer coffee, with every respondent preferring at least one of the two. What percentage prefer both?

  1. 10% Correct answer.
  2. 5%
  3. 30%
  4. 20%

Explanation

Since everyone prefers at least one drink, the union is 100%. By inclusion-exclusion, both = tea + coffee − union = 60% + 50% − 100% = 10%.

Question 21Quantitative Reasoning and Data Interpretation

A cube has a surface area of 96 cm². What is its volume?

  1. 64 cm³ Correct answer.
  2. 48 cm³
  3. 216 cm³
  4. 96 cm³

Explanation

A cube has six congruent faces, so each face has area 96 ÷ 6 = 16 cm². The edge length is √16 = 4 cm, and the volume is 4³ = 64 cm³.

Question 22Quantitative Reasoning and Data Interpretation

Working alone, A can finish a job in 6 hours and B can finish it in 12 hours. Working together, how long will they take?

  1. 3 hours
  2. 9 hours
  3. 4.5 hours
  4. 4 hours Correct answer.

Explanation

Rates add when working together: A completes 1/6 of the job per hour and B completes 1/12. Combined rate is 1/6 + 1/12 = 3/12 = 1/4 job per hour, so the job takes 4 hours.

Question 23Quantitative Reasoning and Data Interpretation

A quantity increases by 50% and then decreases by 50%. The final value compared with the original is:

  1. the same
  2. 50% lower
  3. 25% lower Correct answer.
  4. 25% higher

Explanation

Start with 100: a 50% increase gives 150, and a 50% decrease on 150 gives 75. Comparing 75 with 100 shows a 25% decrease overall, because the decrease applies to the larger base.

Question 24Quantitative Reasoning and Data Interpretation

A sequence follows the rule aₙ = 2aₙ₋₁ + 1 with a₁ = 1. What is a₄?

  1. 23
  2. 11
  3. 7
  4. 15 Correct answer.

Explanation

Apply the recurrence step by step: a₂ = 2(1) + 1 = 3; a₃ = 2(3) + 1 = 7; a₄ = 2(7) + 1 = 15.

Question 25Quantitative Reasoning and Data Interpretation

In a group of 50 people, 30 own a car, 25 own a bicycle, and 10 own neither. How many own both a car and a bicycle?

  1. 20
  2. 10
  3. 15 Correct answer.
  4. 5

Explanation

Those owning at least one item number 50 − 10 = 40. By inclusion-exclusion, both = car + bicycle − at least one = 30 + 25 − 40 = 15.

Question 26Quantitative Reasoning and Data Interpretation

A recipe uses 2 cups of flour for every 3 cups of milk. If a cook uses 9 cups of milk, how many cups of flour are needed?

  1. 4.5
  2. 13.5
  3. 6 Correct answer.
  4. 8

Explanation

Set up the proportion 2/3 = x/9 and cross-multiply to get 3x = 18, so x = 6. The flour-to-milk ratio stays constant.

Question 27Quantitative Reasoning and Data Interpretation

What is 15% of 240?

  1. 3.6
  2. 24
  3. 16
  4. 36 Correct answer.

Explanation

Convert the percent to a decimal: 0.15 × 240 = 36. Percent-of problems multiply the rate by the base.

Question 28Quantitative Reasoning and Data Interpretation

A car travels 150 kilometers in 2.5 hours. What is its average speed in kilometers per hour?

  1. 60 Correct answer.
  2. 62.5
  3. 375
  4. 75

Explanation

Average speed equals distance divided by time: 150 ÷ 2.5 = 60 km/h. Dividing by 2.5 is the same as multiplying by 0.4.

Question 29Quantitative Reasoning and Data Interpretation

Which value is the median of the data set 4, 8, 6, 10, 12, 7?

  1. 8
  2. 7.5 Correct answer.
  3. 6
  4. 7

Explanation

Order the values: 4, 6, 7, 8, 10, 12. With an even count, the median is the mean of the two middle values, (7 + 8)/2 = 7.5.

Question 30Quantitative Reasoning and Data Interpretation

A number is increased from 80 to 100. What is the percent increase?

  1. 25% Correct answer.
  2. 20%
  3. 125%
  4. 80%

Explanation

Percent change is the change divided by the original value: (100 − 80)/80 = 20/80 = 0.25, or 25%. The original value is always the denominator.

Question 31Quantitative Reasoning and Data Interpretation

A fair six-sided die is rolled once. What is the probability of rolling a number greater than 4?

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

Explanation

The outcomes greater than 4 are 5 and 6, giving 2 favorable outcomes out of 6. That simplifies to 2/6 = 1/3.

Question 32Quantitative Reasoning and Data Interpretation

Simplify the expression 3(2x + 4) − 5x.

  1. x + 4
  2. x + 12 Correct answer.
  3. 6x + 12
  4. 11x + 12

Explanation

Distribute the 3 to get 6x + 12, then subtract 5x to obtain x + 12. Combine like terms only after distributing.

Question 33Quantitative Reasoning and Data Interpretation

A data set contains the values 2, 4, 4, 5, 9. What is the mean?

  1. 4
  2. 5
  3. 4.5
  4. 4.8 Correct answer.

Explanation

The sum is 2 + 4 + 4 + 5 + 9 = 24, and there are 5 values, so the mean is 24 ÷ 5 = 4.8. The mean divides the total by the count.

Question 34Quantitative Reasoning and Data Interpretation

A store offers a 30% discount on an item priced at $80. What is the sale price?

  1. $56 Correct answer.
  2. $50
  3. $104
  4. $24

Explanation

The discount is 0.30 × 80 = $24, so the sale price is 80 − 24 = $56. Equivalently, pay 70% of the original: 0.70 × 80 = 56.

Question 35Quantitative Reasoning and Data Interpretation

If 5 machines produce 200 units in 4 hours, how many units will 8 machines produce in 6 hours at the same rate per machine?

  1. 600
  2. 240
  3. 320
  4. 480 Correct answer.

Explanation

Each machine makes 200 ÷ (5 × 4) = 10 units per hour. Then 8 machines × 6 hours × 10 = 480 units.

Question 36Quantitative Reasoning and Data Interpretation

A jar contains 5 red, 3 blue, and 2 yellow marbles. Two marbles are drawn without replacement. What is the probability that both are red?

  1. 5/10
  2. 1/9
  3. 2/9 Correct answer.
  4. 1/4

Explanation

The first red has probability 5/10 = 1/2, and the second red has probability 4/9. Multiplying gives (1/2)(4/9) = 2/9.

Question 37Quantitative Reasoning and Data Interpretation

A sum of money is invested at 8% simple interest per year. After 3 years the interest earned is $600. What was the principal?

  1. $2,500 Correct answer.
  2. $1,800
  3. $7,500
  4. $2,000

Explanation

Simple interest is I = P × r × t, so 600 = P × 0.08 × 3 = 0.24P. Solving gives P = 600 ÷ 0.24 = $2,500.

Question 38Quantitative Reasoning and Data Interpretation

The ratio of boys to girls in a class is 4:5. If there are 36 students in total, how many girls are there?

  1. 20 Correct answer.
  2. 16
  3. 24
  4. 18

Explanation

The ratio has 4 + 5 = 9 parts, so each part is 36 ÷ 9 = 4 students. Girls make up 5 parts, giving 5 × 4 = 20.

Question 39Quantitative Reasoning and Data Interpretation

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

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

Explanation

By the Pythagorean theorem, c² = 9² + 12² = 81 + 144 = 225, so c = 15. This is a 3-4-5 triangle scaled by 3.

Question 40Quantitative Reasoning and Data Interpretation

A sequence begins 3, 7, 15, 31, ... and each term after the first equals twice the previous term plus 1. What is the next term?

  1. 64
  2. 47
  3. 63 Correct answer.
  4. 62

Explanation

Apply the rule to the last term: 2 × 31 + 1 = 63. The pattern is consistent with the earlier terms.

Question 41Quantitative Reasoning and Data Interpretation

A box contains tickets numbered 1 through 20. One ticket is drawn at random. What is the probability that the number is a multiple of 3?

  1. 7/20
  2. 1/3
  3. 3/10 Correct answer.
  4. 1/5

Explanation

The multiples of 3 from 1 to 20 are 3, 6, 9, 12, 15, 18, giving 6 favorable outcomes. That is 6/20 = 3/10.

Question 42Quantitative Reasoning and Data Interpretation

The mean of a data set is 50 and the standard deviation is 5. A value of 42 lies how many standard deviations from the mean, and in which direction?

  1. 1.6 below the mean Correct answer.
  2. 1.6 above the mean
  3. 0.16 below the mean
  4. 8 below the mean

Explanation

The z-score is (42 − 50)/5 = −8/5 = −1.6, which is 1.6 standard deviations below the mean.

Question 43Quantitative Reasoning and Data Interpretation

A pipe fills a tank in 12 minutes, and a drain empties it in 20 minutes. If both are open, how long will it take to fill the empty tank?

  1. 8 minutes
  2. 32 minutes
  3. 30 minutes Correct answer.
  4. 7.5 minutes

Explanation

The net rate is 1/12 − 1/20 = 5/60 − 3/60 = 2/60 = 1/30 tank per minute. Filling one tank therefore takes 30 minutes.

Question 44Quantitative Reasoning and Data Interpretation

A shirt is marked up 25% from its wholesale cost and then sold at a 20% discount off the marked price. The final selling price compared with the wholesale cost is:

  1. 5% lower
  2. 5% higher
  3. 45% higher
  4. Equal to the wholesale cost Correct answer.

Explanation

The marked price is 1.25 times cost, and the discount multiplies it by 0.80. Since 1.25 × 0.80 = 1.00, the final price equals the wholesale cost.

Question 45Quantitative Reasoning and Data Interpretation

A survey of 200 people found that 120 read newspaper A, 90 read newspaper B, and 40 read both. How many read exactly one of the two newspapers?

  1. 170
  2. 90
  3. 130 Correct answer.
  4. 80

Explanation

Those reading exactly one are (120 − 40) + (90 − 40) = 80 + 50 = 130. This removes the double-counted overlap.

Question 46Quantitative Reasoning and Data Interpretation

A data set has 7 values. The mean is 12, and the median is 10. If the smallest value is increased by 7 while all other values stay the same, what happens to the mean?

  1. It increases by 7
  2. It increases by 7/12
  3. It increases by 1 Correct answer.
  4. It stays the same

Explanation

Increasing one value by 7 raises the total by 7, and dividing by 7 values adds 1 to the mean. The new mean is 13.

Question 47Quantitative Reasoning and Data Interpretation

Two fair coins are flipped. Given that at least one flip shows heads, what is the probability that both flips show heads?

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

Explanation

Conditioning on at least one head leaves three equally likely outcomes: HT, TH, HH. Only HH has two heads, so the probability is 1/3.

Question 48Quantitative Reasoning and Data Interpretation

A sum doubles under compound interest in 8 years. In how many years will it become eight times the original amount, assuming the same annual rate?

  1. 24 years Correct answer.
  2. 64 years
  3. 32 years
  4. 16 years

Explanation

Each doubling multiplies the amount by 2 and takes 8 years. Reaching 8 times requires three doublings (2³ = 8), so 3 × 8 = 24 years.

Question 49Quantitative Reasoning and Data Interpretation

A set of five numbers has a mean of 10 and a standard deviation of 0. If one number is changed from 10 to 14, what is the new mean?

  1. 10.8 Correct answer.
  2. 10
  3. 11.2
  4. 12

Explanation

A standard deviation of 0 means all five values equal the mean, so each is 10 and the total is 50. Changing one value to 14 gives a total of 54, and 54 ÷ 5 = 10.8.

Question 50Quantitative Reasoning and Data Interpretation

A mixture contains milk and water in the ratio 3:2. If 10 liters of water are added, the ratio becomes 3:4. How many liters of milk are in the mixture?

  1. 10 liters
  2. 12 liters
  3. 15 liters Correct answer.
  4. 20 liters

Explanation

Let milk be 3k and water 2k. After adding 10 liters, 3k/(2k + 10) = 3/4, so 12k = 6k + 30 and k = 5. Milk is 3k = 15 liters.