ACT WorkKeys Applied Math

34 questions/tasks. Use the approved directions below.

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Question 1

A loading dock receives 17 empty crates in the morning, 26 at midday, and 14 in the afternoon. How many crates does it receive altogether?

☐ A. 67 crates
☐ B. 61 crates
☐ C. 47 crates
☐ D. 57 crates
☐ E. 53 crates

Your response / working

Show answer and explanation

Response: D

Final answer: 57 crates

The dock receives three separate deliveries of empty crates, so add all three counts,

17 + 26 + 14 = 57

, to find how many crates arrive during the day. Altogether, that is 57 crates.

Question 2

A petty-cash envelope contains

$ 125.00

. A worker removes

$ 38.75

to buy supplies. How much remains?

☐ A. $$ 86.75$
☐ B. $$ 86.25$
☐ C. $$ 96.25$
☐ D. $$ 87.25$
☐ E. $$ 163.75$

Your response / working

Show answer and explanation

Response: B

Final answer:

$ 86.25

The supplies are an expense. Taking

$ 38.75

out of the original

$ 125.00

leaves

125.00 - 38.75 = 86.25

dollars in the envelope, rather than increasing the balance by the purchase amount.

Question 3

A laundry orders 8 cases of cleaning cloths at

$ 6.40

per case. With no additional charges, what is the total cost?

☐ A. $$ 48.40$
☐ B. $$ 6.48$
☐ C. $$ 51.20$
☐ D. $$ 56.40$
☐ E. $$ 50.80$

Your response / working

Show answer and explanation

Response: C

Final answer:

$ 51.20

Multiply the price per case by the number of cases:

6.40 \times 8 = 51.20

. The units are dollars per case times cases, leaving dollars for the total cost of the order. The laundry pays

$ 51.20

Question 4

A warehouse receives 212 totes and sends out 245 totes on the same day. What is the net change in its tote count?

☐ A. A decrease of 457 totes
☐ B. An increase of 33 totes
☐ C. A decrease of 23 totes
☐ D. A decrease of 33 totes
☐ E. An increase of 457 totes

Your response / working

Show answer and explanation

Response: D

Final answer: A decrease of 33 totes

Outgoing totes exceed incoming totes. Subtract the 245 dispatched totes from the 212 received totes,

212 - 245 = - 33

, because receipts increase the warehouse count and dispatches decrease it. The negative sign records a decrease of 33 totes.

Question 5

A supervisor divides a 240-minute block into 6 appointments of equal length, with no gaps. How long is each appointment?

☐ A. 60 minutes
☐ B. 46 minutes
☐ C. 30 minutes
☐ D. 40 minutes
☐ E. 36 minutes

Your response / working

Show answer and explanation

Response: D

Final answer: 40 minutes

Each appointment gets an equal share of the 240-minute block, so

240 \div 6 = 40

minutes, with all six appointments together filling the available time. There are no gaps.

Question 6

A maintenance log uses decimal notation. Which decimal should a worker enter to represent

\frac{1}{4}

of the stations?

☐ A. $0.75$
☐ B. $0.40$
☐ C. $0.50$
☐ D. $0.14$
☐ E. $0.25$

Your response / working

Show answer and explanation

Response: E

Final answer:

0.25

To convert the fraction in the log entry, divide its numerator by its denominator,

\frac{1}{4} = 1 \div 4 = 0.25

, expressing one quarter of the stations as a decimal share of the whole. Enter 0.25 in the log. The digits in a fraction are not copied side by side to write its decimal value.

Question 7

An equipment inspection is scheduled to last 3 hours. How many minutes should be reserved?

☐ A. 30 minutes
☐ B. 180 minutes
☐ C. 300 minutes
☐ D. 183 minutes
☐ E. 120 minutes

Your response / working

Show answer and explanation

Response: B

Final answer: 180 minutes

Use 60 minutes per hour. Three hours contain

3 \times 60 = 180

minutes, which is the amount of time to reserve for the inspection, regardless of how the hours are split across the schedule.

Question 8

A cafe starts with

$ 80.00

in its till. During the shift it receives

$ 185.00

in cash sales and pays

$ 27.50

from the till for an emergency purchase. What should the closing till balance be?

☐ A. $$ 292.50$
☐ B. $$ 157.50$
☐ C. $$ 265.00$
☐ D. $$ 212.50$
☐ E. $$ 237.50$

Your response / working

Show answer and explanation

Response: E

Final answer:

$ 237.50

The till has both its starting cash and the money collected from sales before the emergency purchase is paid, giving

80 + 185 = 265

dollars available. Subtract the purchase next. The closing balance is

265 - 27.50 = 237.50

dollars.

Question 9

A worker has 96 parts. Inspection rejects 6 parts, and each shipping box holds 9 acceptable parts. How many full boxes can the worker pack?

☐ A. 11 boxes
☐ B. 90 boxes
☐ C. 9 boxes
☐ D. 10 boxes
☐ E. 12 boxes

Your response / working

Show answer and explanation

Response: D

Final answer: 10 boxes

Only acceptable parts can be shipped, so the 6 rejected parts leave

96 - 6 = 90

parts available, which fill

90 \div 9 = 10

boxes at 9 parts each. No parts remain unpacked.

Question 10

A trim strip is

\frac{15}{8}

yard long. A worker cuts off

\frac{5}{8}

yard. How much strip remains?

☐ A. $\frac{15}{8}$ yards
☐ B. $\frac{5}{8}$ yard
☐ C. $2 \frac{1}{2}$ yards
☐ D. $1 \frac{1}{4}$ yards
☐ E. $\frac{10}{16}$ yard

Your response / working

Show answer and explanation

Response: D

Final answer:

1 \frac{1}{4}

yards

Both measurements already use eighths. Removing five eighths from fifteen eighths leaves

\frac{15}{8} - \frac{5}{8} = \frac{10}{8}

yard, and simplifying that fraction gives

\frac{5}{4} = 1 \frac{1}{4}

yards of strip remaining.

Question 11

An installer needs four cable pieces, each

3 \frac{1}{4}

meters long. What total cable length is needed, ignoring cutting waste?

☐ A. $12 \frac{1}{4}$ meters
☐ B. 7 meters
☐ C. 13 meters
☐ D. $13 \frac{1}{4}$ meters
☐ E. 16 meters

Your response / working

Show answer and explanation

Response: C

Final answer: 13 meters

Four lengths must be combined. Four pieces require four copies of the specified length, so

4 \times 3 \frac{1}{4} = 4 \times \frac{13}{4} = 13

meters of cable, with no extra allowance for cutting waste. As a check, four 3-meter portions use 12 meters, and the four quarter-meter portions use the remaining meter of the required cable.

Question 12

A clerk processes 8 forms in 12 minutes. At that same constant rate, how long will 20 forms take?

☐ A. 32 minutes
☐ B. 18 minutes
☐ C. 40 minutes
☐ D. 24 minutes
☐ E. 30 minutes

Your response / working

Show answer and explanation

Response: E

Final answer: 30 minutes

Twenty forms are

20 \div 8 = 2.5

times the original workload. The rate stays constant. Allowing the same increase in processing time gives

12 \times 2.5 = 30

minutes for all 20 forms, rather than adding minutes for each additional form without using the given rate.

Question 13

A store receives 3, 7, 6, and 8 returned bins on four successive days. What is the average number of returned bins per day?

☐ A. 24 bins
☐ B. 7 bins
☐ C. 6 bins
☐ D. 8 bins
☐ E. 5 bins

Your response / working

Show answer and explanation

Response: C

Final answer: 6 bins

Add the returns from all four days,

3 + 7 + 6 + 8 = 24

bins, and divide by the number of days to find the daily mean,

24 \div 4 = 6

bins. The mean is 6 bins.

Question 14

A board is

4 \frac{1}{2}

feet long. The damaged end occupies

\frac{5}{6}

foot and must be cut off. Ignoring the saw-blade width, how much usable board remains?

☐ A. $3 \frac{2}{3}$ feet
☐ B. $4 \frac{1}{3}$ feet
☐ C. $3 \frac{1}{3}$ feet
☐ D. $5 \frac{1}{3}$ feet
☐ E. $3 \frac{5}{6}$ feet

Your response / working

Show answer and explanation

Response: A

Final answer:

3 \frac{2}{3}

feet

Use sixths for both lengths. Converting the original

4 \frac{1}{2}

feet to

\frac{27}{6}

feet lets you subtract the damaged

\frac{5}{6}

foot directly, giving

\frac{22}{6} = 3 \frac{2}{3}

feet of usable board. The stem excludes additional loss to the saw blade.

Question 15

A workshop buys three tools at

$ 125

each and two cases at

$ 50

each. Sales tax is

6 %

of the merchandise subtotal, with no delivery charge. What is the total bill?

☐ A. $$ 475.00$
☐ B. $$ 500.00$
☐ C. $$ 528.00$
☐ D. $$ 485.50$
☐ E. $$ 503.50$

Your response / working

Show answer and explanation

Response: E

Final answer:

$ 503.50

The merchandise subtotal includes three tools and two cases,

3 (125) + 2 (50) = 475

dollars, and the sales tax applies to that entire subtotal. Tax increases the subtotal. Calculating

0.06 (475) = 28.50

dollars in tax and adding it to the purchase price gives a final bill of

475 + 28.50 = 503.50

dollars.

Question 16

A drawing specifies a 36-millimeter fastener. A supplier lists fastener lengths in inches. Using 1 inch = 25.4 millimeters, what inch length matches the drawing, rounded to the nearest hundredth?

☐ A. 914.40 inches
☐ B. 1.40 inches
☐ C. 0.71 inch
☐ D. 1.42 inches
☐ E. 9.14 inches

Your response / working

Show answer and explanation

Response: D

Final answer: 1.42 inches

An inch contains 25.4 millimeters. Dividing the 36-millimeter length by 25.4 gives

36 \div 25.4 \approx 1.4173

inches, which rounds to 1.42 inches because the thousandths digit is 7. Keep the hundredths place.

Question 17

A shift lasts 7 hours 30 minutes, including 1.25 hours of unpaid breaks. How much paid work time does the shift contain?

☐ A. 6 hours 15 minutes
☐ B. 8 hours 45 minutes
☐ C. 6 hours 45 minutes
☐ D. 6 hours 25 minutes
☐ E. 6 hours 5 minutes

Your response / working

Show answer and explanation

Response: A

Final answer: 6 hours 15 minutes

The shift is 7.5 hours long, so subtracting the 1.25 unpaid hours leaves

7.5 - 1.25 = 6.25

paid hours, with the decimal portion still expressed in hours. A quarter hour is 15 minutes. Paid work therefore lasts 6 hours 15 minutes, and adding back the 1 hour 15 minutes of breaks accounts for the entire shift.

Question 18

A crew marks a rectangular work area 7 meters long and 4 meters wide. Rope follows the boundary except for a 2-meter entrance gap. How many meters of rope are needed?

☐ A. 22 meters
☐ B. 28 meters
☐ C. 26 meters
☐ D. 18 meters
☐ E. 20 meters

Your response / working

Show answer and explanation

Response: E

Final answer: 20 meters

The rope follows the perimeter. The rectangle has two 7-meter sides and two 4-meter sides, for

2 (7 + 4) = 22

meters of boundary, including the entrance gap. Leaving that 2-meter gap uncovered reduces the rope needed to

22 - 2 = 20

meters.

Question 19

A print shop can buy clips in three pack sizes. Pack A has 24 clips for

$ 15.60

, Pack B has 30 for

$ 18.90

, and Pack C has 40 for

$ 27.20

. With no delivery charges, which pack has the lowest cost per clip?

☐ A. Pack A at 65 cents per clip
☐ B. Pack B at 63 cents per clip
☐ C. Pack C at 68 cents per clip
☐ D. Pack B at 67 cents per clip
☐ E. Pack A at 60 cents per clip

Your response / working

Show answer and explanation

Response: B

Final answer: Pack B at 63 cents per clip

Find the price of one clip in each pack by dividing price by clip count: A costs

15.60 \div 24 = 0.65

, B costs

18.90 \div 30 = 0.63

, and C costs

27.20 \div 40 = 0.68

dollars. Pack B costs least per clip. Its unit price is 63 cents, even though its full pack costs more than Pack A.

Question 20

An inventory clerk prepares the calculation below. There are 10 bins with 12 items in each, and 5 damaged items are removed. Which calculation line contains the first error?

Line	Calculation	Recorded result
1: Items per bin	Given count	12 items
2: Beginning inventory	$10 + 12$	22 items
3: Usable inventory	$22 - 5$	17 items

☐ A. Line 3: usable inventory
☐ B. Line 2: beginning inventory
☐ C. Both Lines 1 and 3
☐ D. Line 1: items per bin
☐ E. No calculation line

Your response / working

Show answer and explanation

Response: B

Final answer: Line 2: beginning inventory

Each of the 10 bins contains 12 items, so beginning inventory is

10 \times 12 = 120

items, while Line 2 adds these quantities to get 22. Line 2 is wrong first. Line 3 uses the correct subtraction operation on the incorrect input, and Line 1 correctly states 12 items per bin.

Question 21

An inspection rejects 18 items from a shipment of 240 items. What percentage of the shipment is rejected?

☐ A. $7.0 %$
☐ B. $0.075 %$
☐ C. $75 %$
☐ D. $13.3 %$
☐ E. $7.5 %$

Your response / working

Show answer and explanation

Response: E

Final answer:

7.5 %

The rejected share is

18 \div 240 = 0.075

of the shipment, and multiplying this fraction by 100 expresses the same share as a percentage,

7.5 %

. That is the rejection percentage. Keeping 0.075 and adding a percent sign would report a quantity one hundredth as large as the actual rejected share.

Question 22

A repair service discounts its regular charge by

20 %

, then adds a fixed

$ 12

call-out fee. The final bill is

$ 204

, with no tax or other charge. What was the regular charge before the discount?

☐ A. $$ 240$
☐ B. $$ 192$
☐ C. $$ 230.40$
☐ D. $$ 244.80$
☐ E. $$ 255$

Your response / working

Show answer and explanation

Response: A

Final answer:

$ 240

Remove the fixed fee first. Subtracting

$ 12

from the

$ 204

bill leaves

$ 192

as the discounted service charge, which is

80 %

of the original charge after a

20 %

discount. Divide

192 \div 0.80 = 240

to recover the regular charge of

$ 240

Question 23

A machine makes 84 parts in 42 minutes while running. It runs at this constant rate during a 7.5-hour shift except for one 45-minute shutdown. How many parts does it make during the shift?

☐ A. 810 parts
☐ B. 630 parts
☐ C. 900 parts
☐ D. 840 parts
☐ E. 855 parts

Your response / working

Show answer and explanation

Response: A

Final answer: 810 parts

The machine produces

84 \div 42 = 2

parts per minute while running, and its 7.5-hour shift contains

7.5 (60) = 450

minutes before deducting downtime. The shutdown lasts 45 minutes. That leaves 405 running minutes and

405 (2) = 810

completed parts.

Question 24

A survey records a cable route as 2.5 miles. The cable supplier bills by the yard. Using 1 mile = 5,280 feet and 1 yard = 3 feet, how many yards is the route?

☐ A. 4,400 yards
☐ B. 39,600 yards
☐ C. 13,200 yards
☐ D. 1,760 yards
☐ E. 880 yards

Your response / working

Show answer and explanation

Response: A

Final answer: 4,400 yards

First express the route in feet,

2.5 (5, 280) = 13, 200

, then divide that result by 3 because each yard contains three feet. The route is 4,400 yards. A count in yards must be smaller than the count in feet for the same length.

Question 25

A rectangular crate has inside dimensions of 24 inches by 18 inches by 16 inches. Packing material fills the bottom to a depth of 10 inches. How many cubic feet of material are in the crate?

☐ A. 25 cubic feet
☐ B. 360 cubic feet
☐ C. 4 cubic feet
☐ D. 30 cubic feet
☐ E. 2.5 cubic feet

Your response / working

Show answer and explanation

Response: E

Final answer: 2.5 cubic feet

Use the material's filled depth. Its volume is

24 (18) (10) = 4, 320

cubic inches, since the unfilled space above the bottom 10 inches contains no packing material. A cubic foot contains

12^{3} = 1, 728

cubic inches, so

4, 320 \div 1, 728 = 2.5

cubic feet of material are present.

Question 26

A courier offers Plan A at

$ 20

per trip plus

$ 1.80

per mile, or Plan B at

$ 42

per trip plus

$ 1.20

per mile. A business needs fifteen identical 50-mile trips. It chooses the cheaper plan and has

$ 2, 000

available. How much money remains after these trips?

☐ A. $$ 980$
☐ B. $$ 1, 530$
☐ C. $$ 470$
☐ D. $$ 350$
☐ E. $$ 458$

Your response / working

Show answer and explanation

Response: C

Final answer:

$ 470

For one 50-mile trip, A charges

20 + 1.80 (50) = 110

dollars and B charges

42 + 1.20 (50) = 102

dollars, so the mileage charge makes B cheaper despite its higher fixed fee. Use B for all fifteen trips. Each trip carries its own fixed and mileage charges, so multiplying the full trip cost by fifteen gives

15 (102) = 1, 530

dollars spent and

2, 000 - 1, 530 = 470

dollars left in the budget.

Question 27

Three workers each pack n crates. Packing one crate requires 12 worker-minutes. The crew also uses a total of 45 worker-minutes for setup, counted once for the entire job. The completed job used exactly 333 worker-minutes, including setup. Which equation determines n?

☐ A. $3 (12 n + 45) = 333$
☐ B. $3 (12 + n) + 45 = 333$
☐ C. $3 (12 n) + 45 = 333$
☐ D. $12 n + 45 = 333$
☐ E. $3 (12 n) - 45 = 333$

Your response / working

Show answer and explanation

Response: C

Final answer:

3 (12 n) + 45 = 333

Each worker packs n crates. At 12 worker-minutes per crate, all three workers use

3 (12 n)

worker-minutes for packing, plus the single 45-worker-minute setup allocation for the crew. The equation is

3 (12 n) + 45 = 333

. It gives

n = 8

, or 24 crates altogether.

Question 28

A contractor processes

2 \frac{1}{2}

pallets in

\frac{3}{4}

hour at a constant rate. A 5-hour booking includes a half-hour break with no processing. How many pallets can be processed during the booking?

☐ A. 15 pallets
☐ B. $16 \frac{2}{3}$ pallets
☐ C. 12 pallets
☐ D. 18 pallets
☐ E. $13 \frac{1}{2}$ pallets

Your response / working

Show answer and explanation

Response: A

Final answer: 15 pallets

The half-hour break leaves

5 - \frac{1}{2} = 4 \frac{1}{2}

hours of processing, and dividing that time by

\frac{3}{4}

hour gives six complete intervals at the stated production rate. Each interval yields

2 \frac{1}{2}

pallets. Multiply

6 \times \frac{5}{2} = 15

pallets for the booking.

Question 29

A job uses

60 %

of a

12 \frac{1}{2}

-pound bag of resin. Use 1 pound = 453.592 grams and 1 kilogram = 1,000 grams. How many kilograms of resin does the job use, rounded to the nearest hundredth?

☐ A. 34.02 kilograms
☐ B. 5.67 kilograms
☐ C. 2.27 kilograms
☐ D. 3.75 kilograms
☐ E. 3.40 kilograms

Your response / working

Show answer and explanation

Response: E

Final answer: 3.40 kilograms

The job uses

0.60 (12.5) = 7.5

pounds of resin, which converts to

7.5 (453.592) = 3, 401.94

grams and then

3, 401.94 \div 1, 000 = 3.40194

kilograms. Round only the final result. The third decimal digit is 1, leaving 3.40 kilograms to the nearest hundredth.

Question 30

A conical container has an inside diameter of 4 feet and an inside height of 6 feet. It is filled completely with material weighing 55 pounds per cubic foot. Using pi = 3.14, approximately how many pounds of material does it hold, rounded to the nearest pound?

☐ A. 5,526 pounds
☐ B. 1,036 pounds
☐ C. 1,382 pounds
☐ D. 4,145 pounds
☐ E. 461 pounds

Your response / working

Show answer and explanation

Response: C

Final answer: 1,382 pounds

The diameter is 4 feet. Halve it to get the 2-foot radius, then use cone volume

\frac{1}{3} π r^{2} h = \frac{1}{3} (3.14) (2^{2}) (6) = 25.12

cubic feet before applying the material's weight per cubic foot. The weight is

25.12 (55) = 1, 381.6

pounds, or 1,382 pounds rounded to the nearest pound.

Question 31

A supplier inspects 50 crates of Type R, averaging 4 damaged items per crate, and 20 crates of Type S, averaging 1.2 damaged items per crate. What is the average number of damaged items per crate across all 70 inspected crates?

☐ A. 5.2 damaged items
☐ B. 3.2 damaged items
☐ C. 2.8 damaged items
☐ D. 4.0 damaged items
☐ E. 2.6 damaged items

Your response / working

Show answer and explanation

Response: B

Final answer: 3.2 damaged items

Count the damaged items represented by each group's average,

50 (4) = 200

for Type R and

20 (1.2) = 24

for Type S, before combining all 70 crates. Together they contain 224 damaged items. Dividing

224 \div 70 = 3.2

gives the overall average, with the larger group receiving its proper weight.

Question 32

A workshop needs at least 300 usable sheets. Packs cannot be split. The usable yields shown are guaranteed, and delivery is charged once per order. Which listed order meets the need at the lowest total cost?

Supplier	Sheets/pack	Pack price	Usable yield	Delivery
A	100	$$ 80$	$80 %$	$$ 12$
B	120	$$ 96$	$90 %$	$$ 8$
C	75	$$ 65$	$100 %$	$$ 0$

☐ A. 3 packs from A, costing $$ 252$
☐ B. 2 packs from B, costing $$ 200$
☐ C. 5 packs from C, costing $$ 325$
☐ D. 4 packs from C, costing $$ 260$
☐ E. 3 packs from B, costing $$ 296$

Your response / working

Show answer and explanation

Response: D

Final answer: 4 packs from C, costing

$ 260

Check whether each listed order supplies 300 usable sheets before comparing its price, because three A packs supply only 240 and two B packs supply only 216. Those orders do not qualify. Four C packs provide exactly 300 sheets for

$ 260

, whereas three B packs cost

$ 296

and five C packs cost

$ 325

. Choose four packs from C.

Question 33

For this job, profit margin means profit as a percentage of selling price. A worker prices an item costing

$ 150

$ 180

and claims a

20 %

profit margin because

(180 - 150) \div 150 = 0.20

. What is the reason the claimed margin is wrong?

☐ A. The calculation should divide cost by selling price.
☐ B. The calculation should subtract selling price from cost.
☐ C. The profit should include both cost and selling price.
☐ D. The calculation divides profit by cost instead of selling price.
☐ E. The selling price should be divided by profit.

Your response / working

Show answer and explanation

Response: D

Final answer: The calculation divides profit by cost instead of selling price.

The profit is

180 - 150 = 30

dollars, and the stem defines margin using selling price, so the required denominator is 180, giving

30 \div 180 \approx 16.7 %

. The worker divided by cost. That

30 \div 150 = 20 %

calculation gives markup on cost instead of the defined profit margin.

Question 34

A 180-liter tank initially contains 45 liters. Three nozzles each add

2 \frac{1}{2}

liters per minute, while one drain continuously removes 3 liters per minute. All nozzles and the drain operate throughout. Which equation determines the number of minutes t needed to reach

80 %

of the tank's capacity?

☐ A. $(3 \times 2.5 - 3) t = 180 - 45$
☐ B. $(3 \times 2.5 + 3) t = 0.80 (180) - 45$
☐ C. $(3 \times 2.5 - 3) t = 0.80 (180) - 45$
☐ D. $(3 \times 2.5 - 3) t = 0.80 (180) + 45$
☐ E. $(2.5 - 3) t = 0.80 (180) - 45$

Your response / working

Show answer and explanation

Response: C

Final answer:

(3 \times 2.5 - 3) t = 0.80 (180) - 45

All three nozzles contribute flow. Their combined rate is

3 \times 2.5 = 7.5

liters per minute, and subtracting the drain's 3 liters per minute leaves a net rate of 4.5 liters per minute. The target volume is

0.80 (180) = 144

liters. Subtract the initial 45 liters to obtain the required increase, giving

(3 \times 2.5 - 3) t = 0.80 (180) - 45

, which reaches the target in 22 minutes.