Answer Key for Practice Test 13

1. You just wrapped up a contract project that paid $52,000 in gross income. Your state tax rate is 3%, and your federal tax rate is 21%.

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

Key: $12,480

Rationale:

21% + 3% = 24%

24% * 52,000 = $12,480

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

Here's the financial breakdown:

•Gross earnings: $49,000

•State tax rate: 0%

•Federal tax rate: 20%

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

Key: $9,800

Rationale:

20% + 0% = 20%

20% * 49,000 = $9,800

3. A batch of 80 liters of cleaning solution was distributed into open containers across a warehouse. After a few hours, 20% had evaporated.

What is the remaining volume of the solution?

Key:

If 20% evaporated, then 80% is left.

80% of 80 is 64

64 is the correct answer

4. An artist filled a tub with 60 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 60 is 36

36 is the correct answer

5. In her last 5 swim meets, 1 of Layla’s races resulted in personal bests. What decimal represents the proportion of meets in which she achieved a personal best?

Key: 

1 out of 5 as a decimal is 0.2

0.2 is the correct answer

6. During a project delay, Nolan spent 3.75 hours troubleshooting a software issue. How many minutes did that take?

Key: 

3.75 hours = 3.75 * 60 minutes = 225 minutes

225 minutes is the correct answer

7. During a race, Sarah finished the 10K in 56.8 minutes. How many seconds did she take to complete the race?

Key: 

56.8 minutes = 56.8 minutes * 60 = 3408 seconds

3408 seconds is the correct answer

8. Quinn poured herself 2/5 of a pitcher of iced tea. Later, she drank another 1/8 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. 2/5 as a decimal is 0.4

1/8 as a decimal is 0.125

The total amount that was drank was 0.525

100% - 52.5% = 47.5%

47.5% is the correct answer

9. A fruit tart was divided into 30 equal slices. Jordan had 6 slices after dinner and snuck 9 more later that night. What fraction of the tart is still uneaten?

Key: 

Basically, what is 30 – (6 + 9)?

30 – (15) = 15

15 of the 30 pieces remain.

15/30 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 1 time, Lever W 2 times, Lever X 3 times, and then read the final display: 220.

What number was originally displayed?

Key: Since you are given the end result, 220, AND since you are given chronological instructions, use those chronological instructions backwards and invert each operation.

You started with 220

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

220-15 = 205

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

205+40 = 245

you pulled Lever Y 1 time, (1 * -1) = -1

245-1 = 244

244 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 45, then the player entered →1 1 time, entered ↑10 2 times, entered ↓5 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, 45, use those chronological instructions to find the ending number.

We started with 45

Player then increases the score by 1, 1 time, totaling 46

Player then multiplies the score by 10, 2 times, totaling 4600

Player then divides the score by 5, 2 times, totaling 184

the ending score is 184

12. A shipment of 20 cartons arrived at a ceramics studio, each containing 7 mugs. After sorting, it was found that 35 mugs were cracked.

What percentage of the shipment was cracked?

Key: 20 cartons of 7 mugs in each carton = 20 * 7, which is 140 total mugs

35 of the 140 mugs were cracked, which means we should divide.

35/140 = 0.25, which is 25%

25% is the correct answer

13. A set of rare figurines was delivered in 6 crates. Each crate contained a different quantity: 64, 28, 55, 51, 35, and 17 figurines.

If 40 total were found with defects, how many figurines are left in good condition?

Key: We only need the sum of all figurines, minus 40.  64 + 28 + 55 + 51 + 35 + 17 = 250

250 - 40 = 210. 210 is the correct answer

14. Each handcrafted table requires 2 and 4/5 liters of varnish. If a workshop is preparing 50 tables, how many liters of varnish are needed in total? Ignore simplification.

Key: 1 table needs 2 and 4/5 liters of varnish, so we multiply to get the varnish for 50 tables.

Convert the 2 and 4/5 into a decimal (2.8)

2.8 * 50 = 140

140 is the correct answer

15. A furniture store advertises: Buy 3 sofas at full price, get the next for 75% off. If the total for all sofas is $1,655, which equation models the regular price of one sofa?

Key: 

If you look at the offer, it is buy 3, get the next 75% off.

This means the next sofas costs 25% of regular price, so 3.25 * (regular price) = total sales price.

3.25x = 1,655 is the correct answer

16. In a customer survey about car brands, 160 people were asked to pick their favorite.

If 32 people chose Brand V, and there are only 5 brands, what percent of the people chose Brand W? (Round to the nearest percent.)

•1/5 chose Brand X

•1/4 chose Brand Y

•1/8 chose Brand Z

If 32 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 = 32/160 (20%),

Brand X = 32/160 (20%),

Brand Y = 40/160 (25%),

Brand Z = 20/160 (12.5%), and

Brand W is the remainder.

20% + 20% + 25% + 12.5% = 77.5%, which means Brand W was chosen by 23% of the customers.

23% is the correct answer.

17. Devon managed to complete 1/5 of a report in 4.5 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) = 4.5 weeks     – now, question asks for days, so convert this too

1/5 (of a report) = 31.5 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 = 31.5 days * 5/1

1 (report) = 157.5 days

Now, if you have already gone through 31.5 days and you have a total of 157.5 days,

just subtract the two (157.5 – 31.5 = 126, which is approximately 126 days)

126 days is the correct answer

18. Sofia has completed 1/4 of a project in 3 weeks. If she maintains the same progress rate, how many additional days will she need to reach approximately 75% completion? Round to the nearest whole number.

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

1/4 (of a project) = 3 weeks    – now, the answer is in days, so convert this too

1/4 (of a project) = 21 days

To reach 75% is to get from 1/4 to 75%, so we can divide 0.75 by 0.25, which gives us

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

0.75 / 0.25 = 3, this means that 3 is your multiplier

1/4 (of a project) * 3 = 21 days * 3

75% (of a project)        = 63 days

Now, if you have already gone through 21 days and you have a total of 63 days, just subtract the two (63 – 21 = 42)

42 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: ((6 * 25) + (4 * 20) + (7 * 16)) = 

(150 + 80 + 112) = 342

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

•Triceratops Skull: 620 ft

•Fossil wall panel: 530 ft

•Mini fossils (x15): 50 ft each

What’s the total length of protective casing needed?

Key: You can add all of the material together: (620 + 530 + (15 * 50)) =

(620 + 530 + 750) =

1900 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 120 and the new output is 144

If the new output is 144, and we need to find the increase, we use the

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

(144 – 120) / 120 will equal 24/120, which is 0.2, or 20% as a percentage.

20% is the correct answer

22. Three workers build shelves at different speeds:

•Worker A builds one shelf every 30 minutes

•Worker B builds one shelf every 15 minutes

•Worker C builds one shelf every 40 minutes

If they all begin cooperatively building at the same time, how many completed shelves will they build in 4 hours and 45 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 – 2 shelves/hour;

B – 4 shelves/hour;

C – 1.5 shelves/hour;

Collectively, they can all clean 7.5 panels an hour. Make this an equation and find the

multiplier that divides 4 hours and 45 minutes (285) by 1 hour (60 minutes),

which gives us 4.75 (285/60)

7.5 shelves (* 4.75) = 1 hour (* 4.75)

35.625 shelves = 4.75 hours (285 minutes)

35 is the correct answer.

23. Three workers assemble furniture:

•Worker A assembles one furniture set every 30 minutes 

•Worker B assembles one furniture set every 20 minutes 

•Worker C assembles one furniture set every 80 minutes 

If they all work together, how many minutes will it take to complete 60% 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 – 2 sets/hour; 

B – 3 sets/hour; 

C – 0.75 sets/hour; 

Collectively, they can all build 5.75 sets an hour. Make this into an equation. Since

you’re needing to find the time to make 0.6 of a set, divide 0.6 by 5.75 to find your

multiplier (0.10435)

5.75 sets * (0.10435) = 60 minutes * (0.10435)

0.6 (furniture set) = 6.261 minutes 

24. A subscription analytics tool offers two pricing tiers:

•Plan A: $50 base + $0.0048 per transaction for the first 10,000 transactions, then $0.003 per transaction after that

•Plan B: $65 base + $0.0031 per transaction (flat rate, no tiers)

If a business averages 30,500 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 – (50 + (0.0048 * 10,000) + (0.003 * 20,500) = 50 + 48 + 61.5, which is 159.5

B – (65 + (0.0031 * 30,500) = 65 + 94.55, which is 159.55

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

Therefore, $159.5 / 30,500 = 0.005

0.005 is the correct answer.

25. A custom paint supplier prepares 52 gallons of wall paint for a client. Each gallon contains 5% 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 52 gallons into ounces by multiplying by 128 (6,656)

Next, convert 5% into a decimal by moving the decimal to the left twice (dividing

by 100), which is 0.05

Then, multiply 0.05 by 6,656 which is approximately 333

333 is the correct answer.

26. You’ve rented a car for a road trip that will last 10 nights, starting this Tuesday night. The base rental rate is $42 per day, but on Fridays and Saturdays, the rate increases by $12 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 @ 42, 2 nights @ 54, and 2 nights @ 54.6

Tuesday –    $42

Wednesday – $42

Thursday –   $42

Friday –       $54

Saturday –    $54

Sunday –     $42

Monday –     $42

Tuesday –    $42

Wednesday – $54.6

Thursday –   $54.6

42 + 42 + 42 + 54 + 54 + 42 + 42 + 42 + 54.6 + 54.6 = 469.2

Total – $469.2, so the average is $469.2/10, which is $46.92

$46.92 is the correct answer.

27. A gym charges a special membership of 12 months in a promotion for new members: the standard rate is $150 per year, paid in equal monthly installments, but for the first 3 months, you pay only 50% of the cost of the installments; after 3 months, the regular monthly rate of $10 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 $150 per year, monthly installments would be $12.5

Half of 12.5 is 6.25 so the first 3 months are 6.25 each.

First 3 months = (6.25 * 3), which is roughly $19

Then, 9 months of $10 each is $90

19 + 90 = 109 in 12 monthly payments

Average = cost / month, which is 109 / 12 = 9.08

$9.08 is the correct answer

28. An HVAC company offers service plans for $150/year. With 3,000 customers, the company earns a steady annual profit of $200,000. Due to rising labor rates, total expenses rise by $51,000 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 = $51,000

What you have = 3,000 customers

Therefore $51,000 lost profit / 3,000 customers = $ per customer

$17 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 1.1 times the hours worked during the typical 5-day workweek. On this lengthened week, the office closes at 7:00 PM, and the typical workweek lasts 44 hours and 0 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.

44 hours = typical workweek

Lengthened workweek = 1.1 * typical workweek

Lengthened workweek = 1.1 * 44 hours

Lengthened workweek = 48.4 hours 

A lengthened workweek is still 5 days, so divide this by 5, which is 9.68 hours per lengthened day, which is 9 hours and 41 minutes. 

We are given an end time: 7:00 PM. 

Now, lets subtract the 41 minutes, which is 6:19 PM

Now, let’s subtract the hours, using the 24-hour metric. 18:19 – 9 hours = 9:19 AM

9:15 AM is the correct answer.

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

•6 parts Pineapple Juice

•2 parts Mango Juice

•8 parts Coconut Water

They prepare 10 liters of the mix for a party. However, to adjust the flavor profile, they decide to add 3 liters of Pineapple Juice. To restore the original flavor balance, how many liters of Mango Juice should they add after the additional correct amount of Coconut Water 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 Pineapple Juice : Mango Juice is 6 : 2

Use this ratio to divide 6 by 2 to get 3

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

1 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

•2 parts Blue Pigment

•8 parts Yellow Pigment

The factory creates 20 liters of paint. The production manager decides to enhance the shade by adding 4 liters of Yellow 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 Blue 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 = (6/16) * 20L = 7.5L

Additional amount is derived from the ratio of Yellow : Red, which is 8 : 6, then 4 : 3

Additional amount to balance = 3L

7.5 + 3 = 10.5. 10.5L is the correct answer.

32. You’re organizing floral arrangements for a high-profile gala event. A total of 320 centerpieces are required.

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

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

•1 type of exotic tropical flowers priced at $34 each,

•and 1 type of local blooms priced at $32 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: 96 flowers * $30 = 2,880, (224/2 = 112), 

Let's determine the number of other flowers: (320 - (30% * 320))

(30% * 320) = 96

320 - 96 = 224

(224/2 = 112), which means each type has 112 flowers

Exotic: 112 flowers * $34 = 3,808, 

Blooms: 112 flowers * $32 = 3,584, 

$2,880 + $3,808 + $3,584 = $10,272

$10,272 is the correct answer.

33. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 95 feet long. The width of the rectangle is 45 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 312.5% 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 45. Half of this is the radius of Circle B.

Area of circle B = 3.14 * 22.5² , which calculates to 1589.63. 

1589.63 = area of circle A * 312.5% (divide both sides by 3.125)

508.68 = area of circle A

508.68 is the correct answer.

34. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 95 feet long. The width of the rectangle is 45 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 312.5% 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

45^2 + 95^2 = C²

2025 + 9025 = C²

11050 = C²   *find the square root of both sides*

105.12 = C

35. The diagram above represents tables A, B, & C. The length of the rectangle, the longer side, is 95 feet long. The width of the rectangle is 45 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 312.5% 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 95ft and a width of 45ft.

Area of rectangle = 95 * 45, which is 4,275 sq ft.

Area of circle B = pi * radius², and the width of the rectangle is the diameter of circle B, which is 45. Half of this is the radius of Circle B.

Area of circle B = 3.14 * 22.5² , which calculates to 1589.63

1589.63 = area of circle A * 312.5% (rewritten as a decimal is 3.125)

*Divide both sides by 3.125*

508.68 = area of circle A

Area of rectangle (4,275) – Areas of circles (379.94 + 153.865 + 153.865)

4,275 – 2606.99 is approximately 1668 sq ft.

1668 sq ft is the correct answer.

36. Determine the diameter of the cylinder’s face above that would have a volume of approximately 83,084 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)

83,084 = (3.14 * radius² * 15cm) (You should divide both sides by 15)

5538.93 = (3.14 * radius²) (You should divide both sides by 3.14)

1763.99 = (radius²) (Use the “square root button” to get the root)

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

84 = (diameter)

84 is the correct answer

37. Determine the height of the cylinder above that would have a volume of approximately 52,640 cubic cm and a radius of 37 cm. Round to the nearest hundredth.

Volume of cylinder = 3.14 * radius² * height

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

52,640 = (3.14 * 37² * height) (Find 37²)

52,640 = (3.14 * 1,369 * height) (You should divide both sides by 1,369)

38.451 = (3.14 * height) (You should divide both sides by 3.14)

12.25 = height

12.25 is the correct answer

38. Determine the radius of the cylinder’s face above that would have a volume of approximately 63,500 cubic cm and a height of 20 cm. Round to the nearest hundredth.

Volume of cylinder = 3.14 * radius² * height

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

63,500 = (3.14 * radius² * 20cm) (You should divide both sides by 20)

3175 = (3.14 * radius²) (You should divide both sides by 3.14)

1011.15 = (radius²) (Use the “square root button” to get the root)

31.7985848741733 = (radius)

31.8 is the correct answer.