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TSIA2 Math study materials
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TSIA2 Math practice questions

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Question 1Quantitative Reasoning

A recipe calls for 3 cups of flour for every 2 cups of sugar. If a cook uses 12 cups of flour and keeps the same ratio, how many cups of sugar are needed?

  1. 18 cups
  2. 6 cups
  3. 8 cups Correct answer.
  4. 4 cups

Explanation

Set up the proportion flour/sugar = 3/2 = 12/x. Solving gives x = 12 × 2 ÷ 3 = 8 cups of sugar. The ratio must be scaled by the same factor (here, 4) in both quantities.

Question 2Quantitative Reasoning

What is 15% of 240?

  1. 16
  2. 24
  3. 360
  4. 36 Correct answer.

Explanation

Convert the percent to a decimal and multiply: 0.15 × 240 = 36. A quick check is that 10% of 240 is 24 and 5% is 12, so 15% must be 24 + 12 = 36.

Question 3Quantitative Reasoning

A store sells a 5-pound bag of rice for $12.50. What is the price per pound?

  1. $2.25
  2. $3.00
  3. $2.00
  4. $2.50 Correct answer.

Explanation

A unit rate is found by dividing total cost by total quantity: $12.50 ÷ 5 = $2.50 per pound. Multiplying $2.50 by 5 returns the original $12.50, which confirms the rate.

Question 4Quantitative Reasoning

A student scored 78, 85, 90, 92, and 80 on five quizzes. What is the mean quiz score?

  1. 82
  2. 83
  3. 85 Correct answer.
  4. 84

Explanation

The mean is the sum of the values divided by the number of values. The sum is 78 + 85 + 90 + 92 + 80 = 425, and 425 ÷ 5 = 85.

Question 5Quantitative Reasoning

On a map, 1 inch represents 25 miles. A road measures 4.5 inches on the map. What is the actual length of the road?

  1. 87.5 miles
  2. 100 miles
  3. 125 miles
  4. 112.5 miles Correct answer.

Explanation

Multiply the map length by the scale factor: 4.5 × 25 = 112.5 miles. The scale gives a constant multiplier of 25 miles for every inch measured.

Question 6Quantitative Reasoning

Which of these values is the greatest?

  1. 5/8 Correct answer.
  2. 0.6
  3. 0.62
  4. 58%

Explanation

Rewrite each value as a decimal: 0.6, 0.625, 0.62, and 0.58. Comparing place values shows 0.625 is the largest, so 5/8 is the greatest value.

Question 7Quantitative Reasoning

Which value is the best estimate of 47.8 × 21.3?

  1. 10,000
  2. 1,000 Correct answer.
  3. 100
  4. 500

Explanation

Round each factor to a friendly number: about 48 × 21 = 1,008. The exact product is close to 1,000, so 1,000 is the best estimate.

Question 8Quantitative Reasoning

A jacket's price drops from $80 to $60. What is the percent decrease in price?

  1. 40%
  2. 25% Correct answer.
  3. 33%
  4. 20%

Explanation

Percent change equals the amount of change divided by the original value: (80 − 60) ÷ 80 = 20 ÷ 80 = 0.25, or 25%. The original price is the correct base for a percent decrease.

Question 9Quantitative Reasoning

A jacket is priced at $120 and is on sale for 25% off. Sales tax of 10% is then applied to the sale price. What is the final cost?

  1. $90
  2. $99 Correct answer.
  3. $96
  4. $108

Explanation

Apply the discount first: 120 × 0.75 = $90, the sale price. Then apply tax to that sale price: 90 × 1.10 = $99. The tax base must be the discounted price, not the original price.

Question 10Quantitative Reasoning

A student scored 80 on each of 3 tests and 95 on each of 2 tests. What is the student's mean score across all 5 tests?

  1. 88
  2. 86 Correct answer.
  3. 85
  4. 87.5

Explanation

A weighted mean multiplies each score by how many times it occurs: (80 × 3 + 95 × 2) ÷ 5 = (240 + 190) ÷ 5 = 430 ÷ 5 = 86. Simply averaging 80 and 95 ignores that 80 occurs more often.

Question 11Quantitative Reasoning

A car travels at a speed of 45 miles per hour. What is this speed in feet per second? (1 mile = 5,280 feet)

  1. 88 ft/s
  2. 45 ft/s
  3. 30 ft/s
  4. 66 ft/s Correct answer.

Explanation

Multiply by the conversion factors so that units cancel: 45 mi/h × 5,280 ft/1 mi × 1 h/3,600 s = 66 ft/s. Dimensional analysis ensures miles and hours cancel, leaving feet per second.

Question 12Quantitative Reasoning

One pipe can fill a tank in 6 hours, and a second pipe can fill it in 3 hours. Working together at these rates, how long will it take to fill the tank?

  1. 2 hours Correct answer.
  2. 9 hours
  3. 2.5 hours
  4. 4.5 hours

Explanation

Add the rates: 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 tank per hour. The reciprocal of the combined rate gives the time: 2 hours. Rates are added, not the times.

Question 13Quantitative Reasoning

A savings account earns 4% simple interest per year. How much interest is earned on $500 after 3 years?

  1. $560
  2. $60 Correct answer.
  3. $120
  4. $20

Explanation

Simple interest is I = Prt = 500 × 0.04 × 3 = $60. Simple interest is computed on the original principal only, so it does not compound.

Question 14Quantitative Reasoning

A container holds 2 liters of a solution that is 50% acid. How many liters of water must be added to make the solution 20% acid?

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

Explanation

The acid amount stays fixed at 0.50 × 2 = 1 liter. If the new total volume is 2 + w, then 1 ÷ (2 + w) = 0.20, so 2 + w = 5 and w = 3 liters. Only water is added, so the acid quantity is unchanged.

Question 15Quantitative Reasoning

A 12-ounce box of cereal costs $3.60, and a 20-ounce box costs $5.60. Which package is the better buy based on price per ounce?

  1. The 20-ounce box Correct answer.
  2. The 12-ounce box
  3. They cost the same per ounce
  4. It cannot be determined from the prices given

Explanation

Compare unit prices: $3.60 ÷ 12 = $0.30 per ounce and $5.60 ÷ 20 = $0.28 per ounce. The lower price per ounce is the better buy, so the 20-ounce box wins.

Question 16Quantitative Reasoning

A city has a population of 84,000 people spread evenly over 30 square miles. What is the population density?

  1. 25,200 people per square mile
  2. 280 people per square mile
  3. 2,520 people per square mile
  4. 2,800 people per square mile Correct answer.

Explanation

Density is population divided by area: 84,000 ÷ 30 = 2,800 people per square mile. Checking by multiplication, 2,800 × 30 = 84,000.

Question 17Quantitative Reasoning

If 6 workers can complete a job in 10 days, how many days will 4 workers take, assuming they work at the same rate?

  1. 8 days
  2. 15 days Correct answer.
  3. 6.7 days
  4. 12 days

Explanation

The job requires 6 × 10 = 60 worker-days of labor. Dividing that fixed amount of work among 4 workers gives 60 ÷ 4 = 15 days. Fewer workers means more days, so the quantities are inversely proportional.

Question 18Quantitative Reasoning

An amount of $450 is divided among three people in the ratio 2:3:4. What is the largest share?

  1. $200 Correct answer.
  2. $150
  3. $225
  4. $100

Explanation

The ratio has 2 + 3 + 4 = 9 equal parts, so each part is $450 ÷ 9 = $50. The largest share is 4 parts, or 4 × $50 = $200.

Question 19Quantitative Reasoning

Which decimal is equal to 3.6 × 10⁻⁴?

  1. 0.000036
  2. 0.00036 Correct answer.
  3. 0.036
  4. 0.0036

Explanation

A negative exponent of −4 moves the decimal point 4 places to the left: 3.6 becomes 0.00036. Writing it in scientific notation again confirms 3.6 × 10⁻⁴.

Question 20Quantitative Reasoning

If 18% of a number is 45, what is the number?

  1. 200
  2. 8.1
  3. 250 Correct answer.
  4. 81

Explanation

Let x be the number, so 0.18x = 45. Dividing both sides by 0.18 gives x = 45 ÷ 0.18 = 250. Checking, 0.18 × 250 = 45.

Question 21Quantitative Reasoning

A price is increased by 20% and then the new price is decreased by 20%. What is the overall effect on the original price?

  1. A 4% decrease Correct answer.
  2. A 4% increase
  3. A 40% decrease
  4. No change at all

Explanation

Multiplying by 1.20 and then by 0.80 gives 0.96 times the original price, which is a 4% decrease. The second percent is taken from a larger base, so the decrease outweighs the increase.

Question 22Quantitative Reasoning

A cyclist rides 60 miles at 30 miles per hour and then returns the same 60 miles at 60 miles per hour. What is the average speed for the entire round trip?

  1. 50 miles per hour
  2. 45 miles per hour
  3. 42 miles per hour
  4. 40 miles per hour Correct answer.

Explanation

Average speed is total distance divided by total time. The outbound trip takes 2 hours and the return takes 1 hour, so 120 miles ÷ 3 hours = 40 miles per hour. It is not the simple average of the two speeds.

Question 23Quantitative Reasoning

A company has annual revenue of 2.4 × 10⁷ dollars and 5 × 10⁴ customers. What is the revenue per customer?

  1. $480 Correct answer.
  2. $4.80
  3. $4,800
  4. $48

Explanation

Divide the coefficients and the powers of ten separately: (2.4 ÷ 5) × 10^(7−4) = 0.48 × 10³ = 480. So the revenue is $480 per customer.

Question 24Quantitative Reasoning

A coffee shop blends 3 pounds of coffee costing $4 per pound with 2 pounds costing $9 per pound. What is the cost per pound of the blend?

  1. $6.50 per pound
  2. $6.25 per pound
  3. $6.00 per pound Correct answer.
  4. $5.50 per pound

Explanation

Total cost is 3 × $4 + 2 × $9 = $12 + $18 = $30, and total weight is 5 pounds. Dividing gives $30 ÷ 5 = $6.00 per pound. The blend price is a weighted average, not a simple average.

Question 25Quantitative Reasoning

A jar contains only red and blue marbles in the ratio 3:5. After 10 red marbles are added, the ratio of red to blue becomes 4:5. How many red marbles were in the jar originally?

  1. 50
  2. 20
  3. 40
  4. 30 Correct answer.

Explanation

Let red = 3k and blue = 5k. Adding 10 red gives (3k + 10)/5k = 4/5, so 15k + 50 = 20k and k = 10. The original number of red marbles is 3 × 10 = 30, which checks: 40 red to 50 blue is 4:5.

Question 26Quantitative Reasoning

A recipe calls for 3 cups of flour for every 2 cups of sugar. If a baker uses 15 cups of flour and keeps the same ratio, how many cups of sugar are needed?

  1. 8 cups
  2. 12 cups
  3. 22.5 cups
  4. 10 cups Correct answer.

Explanation

Set up a proportion comparing flour to sugar: 3/2 = 15/x. Cross-multiplying gives 3x = 30, so x = 10 cups. Equivalently, the flour is scaled by a factor of 15 ÷ 3 = 5, so the sugar is 2 × 5 = 10.

Question 27Quantitative Reasoning

What is 35% of 240?

  1. 72
  2. 84 Correct answer.
  3. 96
  4. 60

Explanation

To find a percent of a number, convert the percent to a decimal and multiply: 35% = 0.35, and 0.35 × 240 = 84. A quick check is that 10% of 240 is 24, and three and a half of those is 84.

Question 28Quantitative Reasoning

A printer produces 84 pages in 3 minutes. Working at the same rate, how many pages does it produce in 7 minutes?

  1. 189
  2. 196 Correct answer.
  3. 210
  4. 168

Explanation

First find the unit rate: 84 ÷ 3 = 28 pages per minute. Then multiply by the new time: 28 × 7 = 196 pages.

Question 29Quantitative Reasoning

Which fraction is equal to 0.375?

  1. 3/8 Correct answer.
  2. 5/8
  3. 3/4
  4. 7/16

Explanation

Write the decimal as a fraction over 1000: 0.375 = 375/1000. Dividing the numerator and denominator by 125 gives 3/8.

Question 30Quantitative Reasoning

A crate holds 24 bottles. How many bottles are in 15 crates?

  1. 380
  2. 420
  3. 360 Correct answer.
  4. 340

Explanation

Multiply the bottles per crate by the number of crates: 24 × 15 = 360. Breaking it apart confirms this: 24 × 10 = 240 and 24 × 5 = 120, and 240 + 120 = 360.

Question 31Quantitative Reasoning

What is the median of the data set 4, 9, 2, 7, 11?

  1. 7 Correct answer.
  2. 4
  3. 6
  4. 9

Explanation

The median is the middle value once the data are arranged in order: 2, 4, 7, 9, 11. With five values, the third value in order, 7, is the median.

Question 32Quantitative Reasoning

Which decimal is equal to 0.2%?

  1. 0.2
  2. 0.0002
  3. 0.02
  4. 0.002 Correct answer.

Explanation

Percent means per hundred, so 0.2% = 0.2/100 = 0.002. Moving the decimal point two places to the left converts any percent to a decimal.

Question 33Quantitative Reasoning

On a map, 1 inch represents 25 miles. Two towns are 3.5 inches apart on the map. How many miles apart are they in reality?

  1. 87.5 Correct answer.
  2. 75
  3. 105
  4. 90

Explanation

Multiply the map distance by the scale: 3.5 × 25 = 87.5 miles. Setting up the proportion 1/25 = 3.5/x gives the same result.

Question 34Quantitative Reasoning

After a 15% discount, a table costs $68. What was the original price before the discount?

  1. $78.20
  2. $90
  3. $80 Correct answer.
  4. $83

Explanation

The sale price equals the original price times (1 − 0.15) = 0.85. So the original price is 68 ÷ 0.85 = $80, which checks because 15% of $80 is $12 and $80 − $12 = $68.

Question 35Quantitative Reasoning

At a school, the ratio of boys to girls is 4:5. If there are 180 students in all, how many are girls?

  1. 108
  2. 90
  3. 100 Correct answer.
  4. 80

Explanation

A ratio of 4:5 splits the total into 4 + 5 = 9 equal parts, so each part is 180 ÷ 9 = 20 students. Girls account for 5 parts: 5 × 20 = 100 students.

Question 36Quantitative Reasoning

A car uses 3 gallons of gas to travel 96 miles. At this rate, how many gallons are needed to travel 320 miles?

  1. 7
  2. 10 Correct answer.
  3. 11
  4. 8

Explanation

The fuel efficiency is 96 ÷ 3 = 32 miles per gallon. Dividing the trip distance by the rate gives 320 ÷ 32 = 10 gallons.

Question 37Quantitative Reasoning

A salesperson earns a 6% commission on total sales. What is the commission on sales of $4,500?

  1. $450
  2. $2,700
  3. $270 Correct answer.
  4. $750

Explanation

Commission is a percent of sales: 0.06 × $4,500 = $270. A quick check is that 1% of $4,500 is $45, and 6 × $45 = $270.

Question 38Quantitative Reasoning

Evaluate 3 + 2(8 − 5)² ÷ 6.

  1. 6 Correct answer.
  2. 21
  3. 4.5
  4. 12

Explanation

Following the order of operations, first compute inside the parentheses: 8 − 5 = 3. Then square: 3² = 9, then multiply and divide left to right: 2 × 9 = 18 and 18 ÷ 6 = 3. Finally 3 + 3 = 6.

Question 39Quantitative Reasoning

A worker earns $14.50 per hour and is paid time-and-a-half for overtime. In one week she works 40 regular hours plus 6 overtime hours. What is her total pay for the week?

  1. $580.00
  2. $667.00
  3. $710.50 Correct answer.
  4. $696.00

Explanation

Regular pay is 40 × $14.50 = $580.00. The overtime rate is 1.5 × $14.50 = $21.75, so overtime pay is 6 × $21.75 = $130.50, giving $580.00 + $130.50 = $710.50.

Question 40Quantitative Reasoning

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 not blue?

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

Explanation

There are 5 + 3 + 2 = 10 marbles in all, and 5 + 2 = 7 of them are not blue. Probability equals favorable outcomes divided by total outcomes, so the probability is 7/10.

Question 41Quantitative Reasoning

What is the product (4 × 10⁵)(3 × 10⁻⁸) expressed in scientific notation?

  1. 1.2 × 10⁻¹
  2. 12 × 10⁻²
  3. 1.2 × 10⁻² Correct answer.
  4. 1.2 × 10³

Explanation

Multiply the coefficients and add the exponents: 4 × 3 = 12 and 5 + (−8) = −3, giving 12 × 10⁻³. Rewriting with a coefficient between 1 and 10 gives 1.2 × 10⁻².

Question 42Quantitative Reasoning

A rectangular room measures 12 feet by 15 feet. Carpet costs $4.25 per square yard. What is the cost to carpet the room?

  1. $85.00 Correct answer.
  2. $127.50
  3. $765.00
  4. $76.50

Explanation

The area is 12 × 15 = 180 square feet. Since 9 square feet make 1 square yard, the area is 180 ÷ 9 = 20 square yards, and 20 × $4.25 = $85.00.

Question 43Quantitative Reasoning

The mean of six numbers is 14. Five of the numbers are 10, 12, 15, 18, and 9. What is the sixth number?

  1. 22
  2. 16
  3. 24
  4. 20 Correct answer.

Explanation

A mean of 14 across six values means the total is 6 × 14 = 84. The five known numbers add to 64, so the missing number is 84 − 64 = 20.

Question 44Quantitative Reasoning

If 5 machines produce 400 parts in 8 hours, how many parts do 3 machines produce in 12 hours at the same rate per machine-hour?

  1. 240
  2. 360 Correct answer.
  3. 300
  4. 450

Explanation

Each machine produces 400 ÷ (5 × 8) = 10 parts per hour. With 3 machines running 12 hours, the output is 3 × 12 × 10 = 360 parts.

Question 45Quantitative Reasoning

A faucet drips 3 drops every second. If 20 drops make 1 milliliter, how many liters does the faucet drip in one hour?

  1. 5.4
  2. 0.054
  3. 0.54 Correct answer.
  4. 54

Explanation

In one hour there are 3 × 3,600 = 10,800 drops. At 20 drops per milliliter this is 10,800 ÷ 20 = 540 milliliters, and dividing by 1,000 gives 0.54 liters.

Question 46Quantitative Reasoning

A savings account pays 5% interest compounded annually. If $2,000 is deposited and no other transactions occur, what is the balance after 2 years?

  1. $2,200.00
  2. $2,100.00
  3. $2,205.00 Correct answer.
  4. $2,300.00

Explanation

Compounding applies interest to the new balance each year: $2,000 × 1.05 = $2,100 after one year. The second year is $2,100 × 1.05 = $2,205.00.

Question 47Quantitative Reasoning

In a survey of 60 people, 35 like tea, 28 like coffee, and 12 like both. How many people like neither tea nor coffee?

  1. 23
  2. 16
  3. 9 Correct answer.
  4. 12

Explanation

By inclusion–exclusion, the number who like at least one drink is 35 + 28 − 12 = 51. Of the 60 people surveyed, 60 − 51 = 9 like neither.

Question 48Quantitative Reasoning

The side length of a square is increased by 30%. By what percent does the area of the square increase?

  1. 90%
  2. 69% Correct answer.
  3. 60%
  4. 30%

Explanation

If the side becomes 1.3 times as long, the area becomes 1.3² = 1.69 times as large. That means the area grows by 0.69, or 69%.

Question 49Quantitative Reasoning

If x:y = 3:4 and y:z = 6:5, what is the ratio x:z?

  1. 9:10 Correct answer.
  2. 2:3
  3. 5:6
  4. 3:5

Explanation

Rewrite both ratios so the y-terms match: x:y = 3:4 = 9:12 and y:z = 6:5 = 12:10. Since y is 12 in both, x:z = 9:10.

Question 50Quantitative Reasoning

A store marks up an item 40% above its wholesale cost and later sells it at 25% off the marked price. What is the profit as a percent of the wholesale cost?

  1. 15%
  2. 10%
  3. 0%
  4. 5% Correct answer.

Explanation

A 40% markup multiplies the wholesale cost by 1.40, and a 25% discount multiplies that price by 0.75. The combined factor is 1.40 × 0.75 = 1.05, a net gain of 5% over cost.