1. You just wrapped up a contract project that paid $64,000 in gross income. Your state tax rate is 0%, and your federal tax rate is 25%. How much total income taxes will you owe from this contract?                   

Key: $16,000             

Rationale:                 

25% + 0% = 25%                 

25% * 64,000 = $16,000                   

2. You’ve made a great year from art commissions! Here's the financial breakdown:                       

•Gross earnings: $58,000                   

•State tax rate: 0%                 

•Federal tax rate: 12%           

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

Key: $6,960               

Rationale:                 

12% + 0% = 12%                 

12% * 58,000 = $6,960                     

3. A batch of 24 liters of cleaning solution was distributed into open containers across a warehouse. After a few hours, 25% had evaporated. What is the remaining volume of the solution?                     

Key:               

If 25% evaporated, then 75% is left.             

75% of 24 is 18                     

18 is the correct answer                     

4. An artist filled a tub with 38 liters of a specialty varnish. Later that day, she discovered that 2/8 of it had dried up from air exposure. How many liters of varnish remains in liquid form?                     

Key:               

If 25% dried up, then 75% is left.                 

75% of 38 is 28.5                   

28.5 is the correct answer                 

5. In her last 25 swim meets, 11 of Layla’s races resulted in personal bests. What decimal represents the proportion of meets in which she achieved a personal best?           

Key:             

11 out of 25 as a decimal is 0.44                   

0.44 is the correct answer                 

6. During a project delay, Nolan spent 4.25 hours troubleshooting a software issue. How many minutes did that take?                 

Key:             

4.25 hours = 4.25 * 60 minutes = 255 minutes                     

255 minutes is the correct answer                 

7. During a race, Sarah finished the 10K in 55.6 minutes. How many seconds did she take to complete the race?                 

Key:             

55.6 minutes = 55.6 minutes * 60 = 3336 seconds               

3336 seconds is the correct answer               

8. Quinn poured herself 1/5 of a pitcher of iced tea. Later, she drank another 3/4 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. 1/5 as a decimal is 0.2                   

3/4 as a decimal is 0.75                     

The total amount that was drank was 0.95               

100% - 95% = 5%                 

5% is the correct answer                   

9. A fruit tart was divided into 15 equal slices. Jordan had 6 slices after dinner and snuck 4 more later that night. What fraction of the tart is still uneaten?                 

Key:             

Basically, what is 15 – (6 + 4)?                     

15 – (10) = 5             

5 of the 15 pieces remain.                 

5/15 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 3 times, Lever X 3 times, and then read the final display: 13. What number was originally displayed?                 

Key: Since you are given the end result, 13, AND since you are given chronological instructions, use those chronological instructions backwards and invert each operation.                   

You started with 13               

you pulled Lever X 3 times, (3 * -5) = -15               

13-15 = -2                 

you pulled Lever W 3 times, (3 * +20) = +60                       

-2+60 = 58                 

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

58-2 = 56                   

56 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 44, then the player entered →1 9 times, entered ↑10 1 time, entered ←3 80 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, 44, use those chronological instructions to find the ending number.               

We started with 44                 

Player then increases the score by 1, 9 times, totaling 53                 

Player then multiplies the score by 10, 1 time, totaling 530             

Player then decreases the score by 3, 80 times, totaling 290           

the ending score is 290                     

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

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

12/120 = 0.1, which is 10%               

10% is the correct answer                 

13. A set of rare figurines was delivered in 6 crates. Each crate contained a different quantity: 39, 48, 36, 51, 32, and 64 figurines. If 22 total were found with defects, how many figurines are left in good condition?               

Key: We only need the sum of all figurines, minus 22.  39 + 48 + 36 + 51 + 32 + 64 = 270             

270 - 22 = 248. 248 is the correct answer                 

14. Each handcrafted table requires 4 and 1/4 liters of varnish. If a workshop is preparing 12 tables, how many liters of varnish are needed in total? Ignore simplification.                       

Key: 1 table needs 4 and 1/4 liters of varnish, so we multiply to get the varnish for 12 tables.           

Convert the 4 and 1/4 into a decimal (4.25)             

4.25 * 12 = 51           

51 is the correct answer                     

15. A furniture store advertises: Buy 2 sofas at full price, get the next for 30% off. If the total for all sofas is $1,640, which equation models the regular price of one sofa?                       

Key:             

If you look at the offer, it is buy 2, get the next 30% off.                 

This means the next sofas costs 70% of regular price, so 2.7 * (regular price) = total sales price.                 

2.7x = 1,640 is the correct answer                 

16. In a customer survey about car brands, 160 people were asked to pick their favorite. If 12 people chose Brand V, and there are only 5 brands, what percent of the people chose Brand W? (Round to the nearest percent.)                 

•1/8 chose Brand X               

•1/4 chose Brand Y               

•1/5 chose Brand Z               

If 12 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 = 12/160 (7.5%),                 

Brand X = 20/160 (12.5%),               

Brand Y = 40/160 (25%),                 

Brand Z = 32/160 (20%), and                       

Brand W is the remainder.                 

7.5% + 12.5% + 25% + 20% = 65%, which means Brand W was chosen by 35% of the customers.           

35% is the correct answer.                 

17. Devon managed to complete 1/8 of a report in 1.75 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)           

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.                     

1/8 (of a report) = 1.75 weeks     – now, question asks for days, so convert this too                       

1/8 (of a report) = 12.25 days           

To finish the report is to get from 1/8 to 1, which means we should multiply by 8/1 on both sides                   

1/8 (of a report) * 8/1 = 12.25 days * 8/1                 

1 (report) = 98 days               

Now, if you have already gone through 12.25 days and you have a total of 98 days,                       

just subtract the two (98 – 12.25 = 85.75, which is approximately 86 days)           

86 days is the correct answer             

18. Sofia has completed 4/20 of a project in 7 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.                     

4/20 (of a project) = 7 weeks     – now, the answer is in days, so convert this too             

4/20 (of a project) = 49 days             

To reach 60% is to get from 4/20 to 60%, so we can divide 0.6 by 0.2, which gives us                       

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

0.6 / 0.2 = 3, this means that 3 is your multiplier

               

4/20 (of a project) * 3 = 49 days * 3             

60% (of a project)        = 147 days               

Now, if you have already gone through 49 days and you have a total of 147 days ,           

just subtract the two (147 – 49 = 98)             

98 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: ((7 * 110) + (5 * 52) + (3 * 30)) =             

(770 + 260 + 90) = 1120                   

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

•Triceratops Skull: 720 ft                 

•Fossil wall panel: 650 ft                   

•Mini fossils (x8): 45 ft each             

What’s the total length of protective casing needed?           

Key: You can add all of the material together: (720 + 650 + (8 * 45)) =                 

(720 + 650 + 360) =               

1730 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 160 and the new output is 200     

If the new output is 200, and we need to find the increase, we use the       

(New – Old) / Old formula to calculate the increase

(200 – 160) / 160 will equal 40/160, which is 0.25, or 25% as a percentage.         

25% 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 30 minutes

•Worker C builds one shelf every 36 minutes

If they all begin cooperatively building at the same time, how many completed shelves will they build in 1 hour and 48 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 – 2 shelves/hour;   

C – 1.67 shelves/hour;           

Collectively, they can all clean 6.67 panels an hour. Make this an equation and find the     

multiplier that divides 1 hour and 48 minutes (108) by 1 hour (60 minutes),         

which gives us 1.8 (108/60) 

6.67 shelves (* 1.8) = 1 hour (* 1.8) 

12.006 shelves = 1.8 hours (108 minutes)   

12 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 25 minutes     

•Worker C assembles one furniture set every 30 minutes     

If they all work together, how many minutes will it take to complete 35% 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 – 2.4 sets/hour;       

C – 2 sets/hour;         

Collectively, they can all build 7.4 sets an hour. Make this into an equation. Since

you’re needing to find the time to make 0.35 of a set, divide 0.35 by 7.4 to find your           

multiplier (0.0473)   

7.4 sets * (0.0473) = 60 minutes * (0.0473) 

0.35 (furniture set) = 2.838 minutes  

24. A subscription analytics tool offers two pricing tiers:   

•Plan A: $25 base + $0.006 per transaction for the first 10,000 transactions, then $0.004 per transaction after that       

•Plan B: $40 base + $0.005 per transaction (flat rate, no tiers)       

If a business averages 30,000 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 – (25 + (0.006 * 10,000) + (0.004 * 20,000) = 25 + 60 + 80, which is 165         

B – (40 + (0.005 * 30,000) = 40 + 150, which is 190

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

Therefore, $165 / 30000 = 0.006       

0.006 is the correct answer.   

25. A custom paint supplier prepares 30 gallons of wall paint for a client. Each gallon contains 3.6% 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 30 gallons into ounces by multiplying by 128 (3,840)

Next, convert 3.6% into a decimal by moving the decimal to the left twice (dividing           

by 100), which is 0.036         

Then, multiply 0.036 by 3,840 which is approximately 138 

138 is the correct answer.     

26. You’ve rented a car for a road trip that will last 10 nights, starting this Thursday night. The base rental rate is $42 per day, but on Fridays and Saturdays, the rate increases by $23 per day. During the last two days of the trip, there’s a special holiday surcharge that raises the rate by 15%, 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 @ 42, 2 nights @ 65, and 2 nights @ 74.75 

Thursday –     $42     

Friday –            $65   

Saturday –      $65     

Sunday –         $42   

Monday –        $42   

Tuesday –       $42     

Wednesday – $42       

Thursday –     $42     

Friday –            $74.75         

Saturday –      $74.75

42 + 65 + 65 + 42 + 42 + 42 + 42 + 42 + 74.75 + 74.75 = 531.5     

Total – $531.5, so the average is $531.5/10, which is $53.15           

$53.15 is the correct answer. 

27. A gym charges a special membership of 12 months in a promotion for new members: the standard rate is $360 per year, paid in equal monthly installments, but for the first 3 months, you pay only 40% of the cost of the installments; after 3 months, the regular monthly rate of $28per 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 $360 per year, monthly installments would be $30     

Half of 30 is 12 so the first 3 months are 12 each.   

First 3 months = (12 * 3), which is roughly $36     

Then, 9 months of $28 each is $252 

36 + 252 = 288 in 12 monthly payments     

Average = cost / month, which is 288 / 12 = 24       

$24 is the correct answer       

28. An HVAC company offers service plans for $150/year. With 3,400 customers, the company earns a steady annual profit of $200,000. Due to rising labor rates, total expenses rise by $69,000 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 = $69,000         

What you have = 3,400 customers   

Therefore $69,000 lost profit / 3,400 customers = $ per customer   

$20.29 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 6:15 PM, and the typical workweek lasts 41 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.

41 hours and 30 minutes = typical workweek

Lengthened workweek = 1.5 * typical workweek

Lengthened workweek = 1.5 * 41.5 hours

Lengthened workweek = 62.25 hours 

A lengthened workweek is still 5 days, so divide this by 5, which is 12.45 hours per lengthened day, which is 12 hours and 27 minutes. 

We are given an end time: 6:15 PM. 

Now, lets subtract the 27 minutes, which is 5:48 PM

Now, let’s subtract the hours, using the 24-hour metric. 17:48 – 12 hours = 5:48 AM

5:45 AM is the correct answer.

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

•8 parts Pineapple Juice         

•6 parts Mango Juice 

•5 parts Coconut Water         

They prepare 8 liters of the mix for a party. However, to adjust the flavor profile, they decide to add 3 liters of Mango Juice. To restore the original flavor balance, how many liters of Coconut Water 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 Mango Juice : Coconut Water is 6 : 5     

Use this ratio to divide 6 by 2 to get 3         

Now if we divide the 5 by 2, we get 2.5       

2.5 is the correct answer       

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

•6 parts Red Pigment 

•4 parts Blue Pigment

•2 parts Yellow Pigment       

The factory creates 6 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 = (6/12) * 6L = 3L     

Additional amount is derived from the ratio of Blue : Red, which is 4 : 6, then 3 : 4.5           

Additional amount to balance = 4.5L

3 + 4.5 = 7.5. 7.5L is the correct answer.     

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

•15% of them must be orchid-based, priced at $42 each.     

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

•1 type of exotic tropical flowers priced at $42 each,

•and 1 type of local blooms priced at $50 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: 30 flowers * $36 = 1,080, (170/2 = 85),     

Let's determine the number of other flowers: (200 - (15% * 200)) 

(15% * 200) = 30       

200 - 30 = 170

(170/2 = 85), which means each type has 85 flowers

Exotic: 85 flowers * $42 = 3,570,     

Blooms: 85 flowers * $50 = 4,250,   

$1,080 + $3,570 + $4,250 = $8,900 

$8,900 is the correct answer. 

33. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 76 feet long. The width of the rectangle is 25 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 189.36% 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 25. Half of this is the radius of Circle B.     

Area of circle B = 3.14 * 12.5² , which calculates to 490.63.           

490.63 = area of circle A * 189.36% (divide both sides by 1.8936) 

259.1 = area of circle A         

259.1 is the correct answer.   

34. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 76 feet long. The width of the rectangle is 25 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 167.84% 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 

252 + 762 = C²

625 + 5776 = C²       

6401 = C²    *find the square root of both sides*     

80.01 = C       

35. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 76 feet long. The width of the rectangle is 25 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 167.84% 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 76ft and a width of 25ft.         

Area of rectangle = 76 * 25, which is 1,900 sq ft.   

Area of circle B = pi * radius2, and the width of the rectangle is the diameter of circle B, which is 25. Half of this is the radius of Circle B.

Area of circle B = 3.14 * 12.5² , which calculates to 490.63

490.63 = area of circle A * 167.84% (rewritten as a decimal is 1.6784)     

*Divide both sides by 1.6784*         

292.32 = area of circle A       

Area of rectangle (1,900) – Areas of circles (379.94 + 153.865 + 153.865)

1,900 – 1075.27 is approximately 825 sq ft. 

825 sq ft is the correct answer.         

36. Determine the diameter of the cylinder’s face above that would have a volume of approximately 42,390 cubic cm and a height of 15 cm. Round to the nearest hundredth.     

Volume of cylinder = (3.14 * radius² * height)         

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

42,390 = (3.14 * radius² * 15cm) (You should divide both sides by 15)     

2826 = (3.14 * radius²) (You should divide both sides by 3.14)       

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

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

60 = (diameter)         

60 is the correct answer         

37. Determine the height of the cylinder above that would have a volume of approximately 36,480 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)

36,480 = (3.14 * 40² * height) (Find 40^2)   

36,480 = (3.14 * 1,600 * height) (You should divide both sides by 1,600) 

22.8 = (3.14 * height) (You should divide both sides by 3.14)         

7.26 = height 

7.26 is the correct answer     

38. Determine the radius of the cylinder’s face above that would have a volume of approximately 37,420 cubic cm and a height of 10 cm. Round to the nearest hundredth.     

Volume of cylinder = (3.14 * radius² * height)         

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

37,420 = (3.14 * radius² * 10cm) (You should divide both sides by 10)     

3742 = (3.14 * radius²) (You should divide both sides by 3.14)       

1191.72 = (radius²) (Use the “square root button” to get the root)   

34.521297773983 = (radius) 

34.52 is the correct answer.