1. You just wrapped up a contract project that paid $50,000 in gross income. Your state tax rate is 3%, and your federal tax rate is 16%.

How much total income taxes will you owe from this contract?

Key: $9,500

Rationale:

16% + 3% = 19%

19% * 50,000 = $9,500

2. You’ve made a great year from art commissions!

Here's the financial breakdown:

•Gross earnings: $60,000

•State tax rate: 4%

•Federal tax rate: 12%

What is the total amount you’ll owe in taxes this year?

Key: $9,600

Rationale:

12% + 4% = 16%

16% * 60,000 = $9,600

3. A batch of 40 liters of cleaning solution was distributed into open containers across a warehouse. After a few hours, 35% had evaporated.

What is the remaining volume of the solution?

Key:

If 35% evaporated, then 65% is left.

65% of 40 is 26

26 is the correct answer

4. An artist filled a tub with 40 liters of a specialty varnish. Later that day, she discovered that 2/5 of it had dried up from air exposure.

How many liters of varnish remain in liquid form?

Key:

If 40% dried up, then 60% is left.

60% of 40 is 24

24 is the correct answer

5. In her last 15 swim meets, 6 of Layla’s races resulted in personal bests. What decimal represents the proportion of meets in which she achieved a personal best?

Key: 

6 out of 15 as a decimal is 0.4

0.4 is the correct answer

6. During a project delay, Nolan spent 4.75 hours troubleshooting a software issue. How many minutes did that take?

Key: 

4.75 hours = 4.75 * 60 minutes = 285 minutes

285 minutes is the correct answer

7. During a race, Sarah finished the 10K in 53.2 minutes. How many seconds did she take to complete the race?

Key: 

53.2 minutes = 53.2 minutes * 60 = 3192 seconds

3192 seconds is the correct answer

8. Quinn poured herself 1/8 of a pitcher of iced tea. Later, she drank another 2/10 of the pitcher. What percentage of the iced tea in the pitcher still remains?

Key: 

It's best to convert each fraction into a decimal. 1/8 as a decimal is 0.125

2/10 as a decimal is 0.2

The total amount that was drank was 0.325

100% - 32.5% = 67.5%

67.5% is the correct answer

9. A fruit tart was divided into 20 equal slices. Jordan had 8 slices after dinner and snuck 6 more later that night. What fraction of the tart is still uneaten?

Key: 

Basically, what is 20 – (8 + 6)?

20 – (14) = 6

6 of the 20 pieces remain.

6/20 is the correct answer

10. You’re solving a puzzle box for a number that changes its display based on levers. Lever X increases the number by 5, Lever Y increases it by 1, Lever Z decreases it by 2, and Lever W decreases it by 20.

You pulled Lever Y 2 times, Lever W 2 times, Lever X 2 times, and then read the final display: 100.

 What number was originally displayed?

Key: Since you are given the end result, 100, AND since you are given chronological instructions, use those chronological instructions backwards and invert each operation.

You started with 100

you pulled Lever X 2 times, (2 * -5) = -10

100-10 = 90

you pulled Lever W 2 times, (2 * +20) = +40

90+40 = 130

you pulled Lever Y 2 times, (2 * -1) = -2

130-2 = 128

128 is the correct answer

11. In a retro-style video game, you control a terminal with four commands. ↑10 multiplies score by 10, ↓5 divides score by 5, →1 increases score by 1, and ←3 decreases score by 3.

The player started with 100, then the player entered →1 2 times, entered ↑10 2 times, entered ←3 2 times, and looked at the screen.

What was the ending score? (Round to the nearest whole number.)

Key: Since you are given the starting number, 100, use those chronological instructions to find the ending number.

We started with 100

Player then increases the score by 1, 2 times, totaling 102

Player then multiplies the score by 10, 2 times, totaling 10200

Player then decreases the score by 3, 2 times, totaling 10194

the ending score is 10194

12. A shipment of 20 cartons arrived at a ceramics studio, each containing 6 mugs. After sorting, it was found that 42 mugs were cracked.

What percentage of the shipment was cracked?

Key: 20 cartons of 6 mugs in each carton = 20 * 6, which is 120 total mugs

42 of the 120 mugs were cracked, which means we should divide.

42/120 = 0.35, which is 35%

35% is the correct answer

13. A set of rare figurines was delivered in 6 crates. Each crate contained a different quantity: 52, 11, 26, 58, 20, and 23 figurines.

If 35 total were found with defects, how many figurines are left in good condition?

Key: We only need the sum of all figurines, minus 35.  52 + 11 + 26 + 58 + 20 + 23 = 190

190 - 35 = 155. 155 is the correct answer

14. Each handcrafted table requires 2 and 3/4 liters of varnish. If a workshop is preparing 90 tables, how many liters of varnish are needed in total? Ignore simplification.

Key: 1 table needs 2 and 3/4 liters of varnish, so we multiply to get the varnish for 90 tables.

Convert the 2 and 3/4 into a decimal (2.75)

2.75 * 90 = 247.5. Rewritten as a mixed number, this is 247 and 2/4.

247 and 2/4 is the correct answer

15. A furniture store advertises: Buy 3 sofas at full price, get the next for 40% off. If the total for all sofas is $1,785, which equation models the regular price of one sofa?

Key: 

If you look at the offer, it is buy 3, get the next 40% off.

This means the next sofas costs 60% of regular price, so 3.6 * (regular price) = total sales price.

3.6x = 1,785 is the correct answer

16. In a customer survey about car brands, 500 people were asked to pick their favorite.

If 2 people chose Brand V, and there are only 5 brands, what percent of the people chose Brand W? (Round to the nearest percent.)

•7/20 chose Brand X

•1/5 chose Brand Y

•2/5 chose Brand Z

If 2 people chose Brand V, and there are only 5 brands, what percent of the people chose Brand W? (Round to the nearest percent.)

Key: 

Since the answer choices are represented as percentages, let’s translate into percentages.

Brand V = 2/500 (0.4%),

Brand X = 175/500 (35%),

Brand Y = 100/500 (20%),

Brand Z = 200/500 (40%), and

Brand W is the remainder.

0.4% + 35% + 20% + 40% = 95.4%, which means Brand W was chosen by 5% of the customers.

5% is the correct answer.

17. Devon managed to complete 1/5 of a report in 2.75 weeks. Assuming he works at the same pace, approximately how many more days will he need to finish the report? (Round to the nearest whole number)

Key: You can treat this problem like an equation. Convert both sides into sensible formats.

1/5 (of a report) = 2.75 weeks     – now, question asks for days, so convert this too

1/5 (of a report) = 19.25 days

To finish the report is to get from 1/5 to 1, which means we should multiply by 5/1 on both sides

1/5 (of a report) * 5/1 = 19.25 days * 5/1

1 (report) = 96.25 days

Now, if you have already gone through 19.25 days and you have a total of 96.25 days,

just subtract the two (96.25 – 19.25 = 77, which is approximately 77 days)

77 days is the correct answer

18. Sofia has completed 1/10 of a project in 4 weeks. If she maintains the same progress rate, how many additional days will she need to reach approximately 60% completion? Round to the nearest whole number.

Key: You can treat this problem like an equation. Convert both sides into sensible formats.

1/10 (of a project) = 4 weeks    – now, the answer is in days, so convert this too

1/10 (of a project) = 28 days

To reach 60% is to get from 1/10 to 60%, so we can divide 0.6 by 0.1, which gives us

the multiplier that we can use on both sides of the equation

0.6 / 0.1 = 6, this means that 6 is your multiplier.

1/10 (of a project) * 6 = 28 days * 6

60% (of a project)        = 168 days

Now, if you have already gone through 28 days and you have a total of 168 days ,

just subtract the two (168 – 28 = 140)

140 is the correct answer               

19. You work in logistics and calculate total protective padding needed for shipping tech equipment:           

How many total feet of padding are required?

Key: You can add all of the material together: ((8 * 60) + (4 * 40) + (3 * 12)) =

(480 + 160 + 36) = 676

20. You’re helping install a traveling dinosaur exhibit. Each display requires the following protective casing:

•Triceratops Skull: 1250 ft

•Fossil wall panel: 650 ft

•Mini fossils (x6): 120 ft each

What’s the total length of protective casing needed?

Key: You can add all of the material together: (1250 + 650 + (6 * 120)) =

(1250 + 650 + 720) =

2620 is the correct answer.

21. You're reporting results from a literacy improvement program.  

By what percentage did the group’s total reading output increase? (Round to the nearest percentage)

Formula: ((New – Old) / Old)

Key: The initial output is 300 and the new output is 390

If the new output is 390, and we need to find the increase, we use the (New – Old) / Old formula to calculate the increase

(390 – 300) / 300 will equal 90/300, which is 0.3, or 30% as a percentage.

30% is the correct answer

22. Three workers build shelves at different speeds:

•Worker A builds one shelf every 20 minutes

•Worker B builds one shelf every 15 minutes

•Worker C builds one shelf every 25 minutes

If they all begin cooperatively building at the same time, how many completed shelves will they build in 3 hours and 15 minutes ?

Key: This represents a “work rate”, so we need to translate their work into a common unit

     of measurement, which is “per-hour”.

A – 3 shelves/hour;

B – 4 shelves/hour;

C – 2.4 shelves/hour;

Collectively, they can all clean 9.4 panels an hour. Make this an equation and find the multiplier that divides 3 hours and 15 minutes (195) by 1 hour (60 minutes), which gives us 3.25 (195/60)

9.4 shelves (* 3.25) = 1 hour (* 3.25)

30.55 shelves = 3.25 hours (195 minutes)

30 is the correct answer.

23. Three workers assemble furniture:

•Worker A assembles one furniture set every 20 minutes

•Worker B assembles one furniture set every 30 minutes

•Worker C assembles one furniture set every 40 minutes

If they all work together, how many minutes will it take to complete 40% of a furniture set?

Key: This represents a “work rate”, so we need to translate their work into a common unit of measurement, which is “per-hour”.

A – 3 sets/hour;

B – 2 sets/hour;

C – 1.5 sets/hour;

Collectively, they can all build 6.5 sets an hour. Make this into an equation. Since you’re needing to find the time to make 0.4 of a set, divide 0.4 by 6.5 to find your multiplier (0.06154)

6.5 sets * (0.06154) = 60 minutes * (0.06154)

0.4 (furniture set) = 3.6924 minutes

24. A subscription analytics tool offers two pricing tiers:

•Plan A: $20 base + $0.012 per transaction for the first 10,000 transactions, then $0.009 per transaction after that

•Plan B: $35 base + $0.011 per transaction (flat rate, no tiers)

If a business averages 20,000 transactions per month, what is the average unit transaction cost under the more cost-effective plan? Round to the nearest thousandth. (Formula: Total Cost / Total Transactions)

Key: This represents a “best priced plan” question. Figure out which is cheaper.

A – (20 + (0.012 * 10,000) + (0.009 * 10,000) = 20 + 120 + 90, which is 230

B – (35 + (0.011 * 20,000) = 35 + 220, which is 255

Since A is cheaper, calculate the average unit cost: (formula: total cost / total transactions)

Therefore, $230 / 20000 = 0.012

0.012 is the correct answer.

25. A custom paint supplier prepares 25 gallons of wall paint for a client. Each gallon contains 4.2% titanium dioxide by volume.

How many fluid ounces of titanium dioxide are in the entire batch? Round to the nearest whole number. (1 gallon = 128 fluid ounces)

Key: This represents a “unit conversion” question.

First, convert 25 gallons into ounces by multiplying by 128 (3,200)

Next, convert 4.2% into a decimal by moving the decimal to the left twice (dividing by 100), which is 0.042

Then, multiply 0.042 by 3,200 which is approximately 134

134 is the correct answer.

26. You’ve rented a car for a road trip that will last 10 nights, starting this Sunday night. The base rental rate is $40 per day, but on Fridays and Saturdays, the rate increases by $17 per day.

During the last two days of the trip, there’s a special holiday surcharge that raises the rate by 30%, even over the usual weekend price.

What is the average daily cost for your entire rental?

Key: This represents a “tiered/dynamic pricing” question that usually focuses on averages.

First, carefully figure out the total costs: 6 nights @ 40, 2 nights @ 57, and 2 nights @ 52

Sunday –         $40

Monday –        $40

Tuesday –       $40

Wednesday – $40

Thursday –     $40

Friday –            $57

Saturday –      $57

Sunday –         $40

Monday –        $52

Tuesday –       $52

40 + 40 + 40 + 40 + 40 + 57 + 57 + 40 + 52 + 52 = 458

Total – $458, so the average is $458/10, which is $45.8

$45.8 is the correct answer.

27. A gym charges a special membership of 12 months in a promotion for new members: the standard rate is $500 per year, paid in equal monthly installments, but for the first 4 months, you pay only 60% of the cost of the installments; after 4 months, the regular monthly rate of $34 per month applies.

If you’re joining for 12 months, what is the average monthly cost of the membership? (Round to the nearest hundredth)

Key: This represents a “tiered/dynamic pricing” question that usually focuses on averages

First, carefully figure out the total costs:

If the rate is usually $500 per year, monthly installments would be $41.67

Half of 41.67 is 25 so the first 4 months are 25 each.

First 4 months = (25 * 4), which is roughly $100

Then, 8 months of $34 each is $272

100 + 272 = 372 in 12 monthly payments

Average = cost / month, which is 372 / 12 = 31

$31 is the correct answer

28. An HVAC company offers service plans for $110/year. With 4,000 customers, the company earns a steady annual profit of $220,000. Due to rising labor rates, total expenses rise by $37,000 per year.

To maintain the same profit, what is the minimum increase required to the annual service plan? Round to the nearest hundredth.

Key: This represents a “profitability” question that can be simple if you focus.

The question asks about “an extra charge per plan” to recover profit, so figure out what profit you lost and divide by what you have.

What profit you lost = $37,000

What you have = 4,000 customers

Therefore $37,000 lost profit / 4,000 customers = $ per customer

$9.25 is the correct answer.

29. A company has a special project in which employees work a specific number of hours during a lengthened workweek, which is 1.5 times the hours worked during the typical 5-day workweek. On this lengthened week, the office closes at 7:15 PM, and the typical workweek lasts 37 hours and 30 minutes. 

About what time do employees begin work on the lengthened week? (Answer with the nearest 15-minute increment: 9:11 should be rounded to 9:15 and 8:07 should be rounded to 8:00.)

Key: This represents a “time calculation” question, so you must be ready to view 1 hour as 60 minutes, put time into fractions and percentages, and get a little abstract.

37 hours and 30 minutes = typical workweek

Lengthened workweek = 1.5 * typical workweek

Lengthened workweek = 1.5 * 37.5 hours

Lengthened workweek = 56.25 hours 

A lengthened workweek is still 5 days, so divide this by 5, which is 11.25 hours per lengthened day, which is 11 hours and 15 minutes. 

We are given an end time: 7:15 PM. 

Now, lets subtract the 15 minutes, which is 7:00 PM

Now, let’s subtract the hours, using the 24-hour metric. 19:00 – 11 hours = 8:00 AM

8:00 AM is the correct answer.

30. A company produces a special cocktail mix that uses three ingredients in a specific ratio:

•5 parts Pineapple Juice

•2 parts Mango Juice

•3 parts Coconut Water

They prepare 20 liters of the mix for a party. However, to adjust the flavor profile, they decide to add 3 liters of Coconut Water. To restore the original flavor balance, how many liters of Mango Juice should they add after the additional correct amount of Pineapple Juice is added? Round to the nearest hundredth.

Key: This represents a “measures-per-part” question, so focus on ratios and relationships.

It starts by stating a balanced mix was already made.

The relationship between Coconut Water : Mango Juice is 3 : 2

Use this ratio to divide 3 by 1 to get 3

Now if we divide the 2 by 1, we get 2

2 is the correct answer

31. A paint factory blends pigments to create a custom shade. The color mix requires these proportions:

•4 parts Red Pigment

•6 parts Blue Pigment

•5 parts Yellow Pigment

The factory creates 15 liters of paint. The production manager decides to enhance the shade by adding 3 liters of Blue Pigment to the batch. What is the total amount of Red Pigment needed to maintain the original color ratio after the additional correct amount of Yellow Pigment is added? Round your answer to the nearest hundredth.

Key: This represents a “measures-per-part” question, so focus on ratios and relationships.

It starts by stating a balanced mix was already made and you are looking for the total amount of Red Pigment, not the

additional amount.

Initial amount = (4/15) * 15L = 4L

Additional amount is derived from the ratio of Blue : Red, which is 6 : 4, then 3 : 2

Additional amount to balance = 2L

4 + 2 = 6. 6L is the correct answer.

32. You’re organizing floral arrangements for a high-profile gala event. A total of 200 centerpieces are required.

•30% of them must be orchid-based, priced at $27 each.

The rest are split evenly between 2 varieties of seasonal flowers:

•1 type of exotic tropical flowers priced at $50 each,

•and 1 type of local blooms priced at $52 each.

What will be the total cost of all the centerpieces?

Key: This represents a “variable cost” question.

Figure out the cost of each sector.

Orchid: 60 flowers * $27 = 1,620, (140/2 = 70),

Let's determine the number of other flowers: (200 - (30% * 200))

(30% * 200) = 60

200 - 60 = 140

(140/2 = 70), which means each type has 70 flowers

Exotic: 70 flowers * $50 = 3,500,

Blooms: 70 flowers * $52 = 3,640,

$1,620 + $3,500 + $3,640 = $8,760

$8,760 is the correct answer.              

33. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 65 feet long. The width of the rectangle is 48 feet long. Circle A is equivalent to Circle C, and the difference between r and s is 2. If the area of circle B is 251.67% of the area of circle A, what is the area of circle A, rounded to the nearest hundredth? 

Area of circle = 3.14 * radius²

Key: Honestly, most of the information given is irrelevant.

Area of circle = 3.14 * radius²

the width of the rectangle is the diameter of circle B, which is 48. Half of this is the radius of Circle B.

Area of circle B = 3.14 * 24² , which calculates to 1808.64. 

1808.64 = area of circle A * 251.67% (divide both sides by 2.5167)

718.66 = area of circle A

718.66 is the correct answer.

34. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 65 feet long. The width of the rectangle is 48 feet long. Circle A is equivalent to Circle C, and the difference between r and s is 2. If the area of circle B is 251.67% of the area of circle A, what is the length of the diagonal line, rounded to the nearest hundredth?

Pythagorean Theorem = A² + B² = C²

Key: Honestly, most of the information given is irrelevant.

You are given the length and width of the rectangle, and the diagonal line creates a right triangle. We use Pythagorean Theorem to figure out the length of this side.

A² + B² = C²

48² + 65² = C²

2304 + 4225 = C²

6529 = C²   *find the square root of both sides*

80.8 = C

35. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 72 feet long. The width of the rectangle is 48 feet long. Circle A is equivalent to Circle C, and the difference between r and s is 2. If the area of circle B is 251.67% of the area of circle A, what is the area, in square feet, of the unshaded area of the rectangle, rounded to the nearest whole number?

Area of circle = 3.14 * radius²

Key: Honestly, you need to subtract the area of the circles from the rectangle.

Area of rectangle – areas of circles

The rectangle has a length of 72ft and a width of 48ft.

Area of rectangle = 72 * 48, which is 3,456 sq ft.

Area of circle B = pi * radius², and the width of the rectangle is the diameter of circle B, which is 48. Half of this is the radius of Circle B.

Area of circle B = 3.14 * 24² , which calculates to 1808.64

1808.64 = area of circle A * 251.67% (rewritten as a decimal is 2.5167)

*Divide both sides by 2.5167*

718.66 = area of circle A

Area of rectangle (3,456) – Areas of circles (379.94 + 153.865 + 153.865)

3,456 – 3245.96 is approximately 210 sq ft.

210 sq ft is the correct answer.



36. Determine the diameter of the cylinder’s face above that would have a volume of approximately 41,034 cubic cm and a height of 12 cm. Round to the nearest hundredth.

Volume of cylinder = 3.14 * radius² * height

Key: Volume of cylinder = (3.14 * radius² * height)

41,034 = (3.14 * radius² * 12cm) (You should divide both sides by 12)

3419.5 = (3.14 * radius^²) (You should divide both sides by 3.14)

1089.01 = (radius²) (Use the “square root button” to get the root)

33 = (radius) (You have a radius. You need the diameter. Multiply by 2)

66 = (diameter)

66 is the correct answer

37. Determine the height of the cylinder above that would have a volume of approximately 42,690 cubic cm and a radius of 40 cm. Round to the nearest hundredth.

Volume of cylinder = 3.14 * radius² * height

Key: Volume of cylinder = (3.14 * radius² * height)

42,690 = (3.14 * 40² * height) (Find 40^2)

42,690 = (3.14 * 1,600 * height) (You should divide both sides by 1,600)

26.681 = (3.14 * height) (You should divide both sides by 3.14)

8.5 = height

8.5 is the correct answer

38. Determine the radius of the cylinder’s face above that would have a volume of approximately 68,960 cubic cm and a height of 16 cm. Round to the nearest hundredth.

Volume of cylinder = 3.14 * radius² * height

Key: Volume of cylinder = (3.14 * radius² * height)

68,960 = (3.14 * radius² * 16cm) (You should divide both sides by 16)

4310 = (3.14 * radius²) (You should divide both sides by 3.14)

1372.61 = (radius^2) (Use the “square root button” to get the root)

37.0487516658794 = (radius)

37.05 is the correct answer.