All practice questions

Question 3441Question →

Which term serves as the precise synonym for the word INTRANSIGENT?

compliant

transient

unyielding

transparent

Show answer & explanation

Answer: unyielding

Answer

unyielding

The word 'unyielding' is the exact synonym for 'intransigent', as both terms describe a person, stance, or attitude that firmly refuses to compromise or surrender.

Step-by-Step Solution

1

Analyze the meaning and part of speech of the target word.

The adjective INTRANSIGENT characterizes someone who is uncompromising, completely stubborn, and refusing to agree or yield.

Defining the target word sets the exact criteria required for identifying a true synonym.

2

Evaluate candidate options to find the direct semantic match.

The adjective 'unyielding' directly mirrors the meaning of being firmly resolute and refusing to compromise.

Synonyms must align in both part of speech and core semantic definition.

Key Concept

Isolated Word Synonyms

Estimated Time:35s

Question 3442Question →

Read each sentence and examine the surrounding context clues. Match each bolded word on the left with its correct contextual synonym on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The technician's 'candid' assessment matches 'Frank and truthful'; the 'fatigued' crew matches 'Exhausted and worn out'; the decision to 'terminate' the inspection matches 'End or halt'; and the 'abundant' water supply matches 'Plentiful and ample'.

Each target word is paired with its precise synonym based on explicit contextual evidence: 'candid' is supported by 'speaking honestly', 'fatigued' by the 'grueling twelve-hour' shift, 'terminate' by stopping the hazardous outdoor work, and 'abundant' by the supply 'exceeding daily requirements'.

Step-by-Step Solution

1

Analyze the context clues in the first sentence for the target word 'candid'.

The phrase 'speaking honestly without hiding' directly defines 'candid' as truthful and frank.

Restatement and descriptive clues clarify the meaning of unfamiliar or descriptive terms.

2

Analyze the context clues in the second sentence for the target word 'fatigued'.

The mention of a 'grueling twelve-hour maintenance shift' and needing rest shows the physical state of being exhausted.

Cause-and-effect clues indicate the physical outcome of prolonged labor.

3

Analyze the context clues in the third sentence for the target word 'terminate'.

Halting an outdoor inspection due to safety hazards means ending the activity.

Action-based context reveals the functional meaning of the verb.

4

Analyze the context clues in the fourth sentence for the target word 'abundant'.

A supply that 'easily exceeds daily requirements' is plentiful and ample.

Degree and quantity descriptions provide direct clues for adjectives of measure.

Key Concept

Identifying Synonyms Using Sentence Context Clues

Estimated Time:50s

Question 3443Question →

A cyclist travels from her home to a nearby town, a distance of $15$ miles, at an average speed of $12$ mph. On the return trip along the same route, her average speed is $20$ mph. What is her average speed, in mph, for the entire round trip?

Show answer & explanation

Answer: 15

Answer

15

The correct average speed is found by dividing the total round-trip distance (

30

miles) by the total travel time (

2

hours), resulting in

15

mph.

Step-by-Step Solution

1

Calculate the time for the outbound trip.

1.25 hours

Time equals distance divided by speed (

15 \text{ miles} / 12 \text{ mph} = 1.25 \text{ hours}

).

2

Calculate the time for the return trip.

0.75 hours

Time equals distance divided by speed (

15 \text{ miles} / 20 \text{ mph} = 0.75 \text{ hours}

).

3

Determine the total time and total distance for the entire round trip.

Total time = 2 hours, Total distance = 30 miles

Adding the outbound and return times (

1.25 + 0.75

) gives 2 hours. The round trip is twice the one-way distance (

15 \times 2

).

4

Calculate the average speed for the entire round trip.

15 mph

Average speed is total distance divided by total time (

30 \text{ miles} / 2 \text{ hours} = 15 \text{ mph}

).

Key Concept

Average Speed for a Round Trip

Question 3444Question →

Examine the following tactical and logistical statements. Using the structural and semantic clues within each sentence, match the bolded vocabulary word to its most accurate contextual definition.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The correct matches are: 'obviate' pairs with 'To render completely unnecessary', 'enervate' pairs with 'To systematically drain of physical vitality', 'apposite' pairs with 'Strikingly appropriate', and 'exigency' pairs with 'An immediate crisis'.

Each bolded term's meaning is uniquely constrained by its surrounding sentence. 'Obviate' is defined by a technological replacement eliminating a task. 'Enervate' is defined by the debilitating consequences of harsh weather. 'Apposite' is defined by its contrast with 'generic' and its alignment with providing a perfect solution. 'Exigency' is defined by the rule-breaking, rapid response required by a sudden rupture.

Step-by-Step Solution

1

Analyze the cause-and-effect relationship in the first sentence.

Determine that the new sensor array removes the need for manual patrols, leading to the definition 'to render completely unnecessary'.

Identifying the logical substitution of technology for manual labor isolates the meaning of 'obviate'.

2

Evaluate the descriptive modifiers in the second sentence.

Connect 'oppressive humidity' and 'without respite' to a negative physical impact, aligning with 'to systematically drain of physical or operational vitality'.

Students must bypass the false morphological cue (sounding like 'energize') and rely strictly on the negative contextual environment to define 'enervate'.

3

Identify the contrast clue in the third sentence.

Recognize that 'Rather than... generic' sets up an antonymous relationship, pointing to 'Strikingly appropriate, relevant, or closely applicable'.

This prevents the common error of assuming 'apposite' means 'opposite' due to phonetic similarity.

4

Assess the narrative urgency in the fourth sentence.

Link the 'sudden supply line rupture' and bypassed protocols to 'An immediate crisis, pressing demand, or urgent need'.

The severe reaction described requires a word that signifies extreme urgency.

Key Concept

Deducing advanced vocabulary meanings by synthesizing embedded syntactic contrasts, cause-and-effect indicators, and descriptive situational clues.

Question 3445Question →

Fill in the blank with a precise direct synonym for the capitalized term: What single word has the same meaning as COMMENCE?

Fill in the blanks below

A direct synonym for the word COMMENCE is .

Show answer & explanation

Answer

begin (or start / initiate)

The word COMMENCE is a verb meaning to start or set in motion. Therefore, common equivalent terms like 'begin' and 'start' correctly complete the sentence.

Step-by-Step Solution

1

Determine the part of speech and primary definition of the target term COMMENCE.

COMMENCE is a verb meaning to start, begin, or enter upon an action.

Establishing the precise definition and grammatical form is essential for identifying an equivalent isolated synonym.

2

Select a direct, interchangeable vocabulary term that shares the exact semantic meaning.

Terms such as 'begin' and 'start' are direct, common equivalents of COMMENCE.

Direct synonyms match the denotation and part of speech of the target word without requiring contextual clues.

Key Concept

Isolated Word Synonyms

Question 3446Question →

The mountain guide warned the hikers that the trail was impassable after the heavy snowfall. In this sentence, what does the word impassable most nearly mean?

Impressive

Uncrossable

Clear

Temporary

Show answer & explanation

Answer: Uncrossable

Answer

Uncrossable

The prefix 'im-' means 'not', the root 'pass' refers to traveling across, and the suffix '-able' means 'capable of being'. Together, 'impassable' describes something that cannot be traversed, matching 'uncrossable'.

Step-by-Step Solution

1

Break down the target word into its prefix, root, and suffix.

The word consists of the prefix 'im-' (not), the base word 'pass' (to traverse or travel across), and the suffix '-able' (capable of).

Morphological analysis reveals the component meanings of the derived word.

2

Synthesize the component definitions to find the synonym.

'Not capable of being passed through' directly corresponds to 'uncrossable'.

Matching the combined affix definition to the choices confirms the correct synonym.

Key Concept

Prefix and suffix analysis with negative prefixes and capability suffixes

Estimated Time:30s

Question 3447Question →

What word is the closest in meaning to CONCEAL?

Reveal

Concede

Hide

Protect

Show answer & explanation

Answer: Hide

Answer

Hide

The word 'conceal' means to prevent something from being seen, known, or discovered. The choice 'Hide' carries the exact same meaning.

Step-by-Step Solution

1

Determine the precise definition of the target word.

The verb 'conceal' means to place out of sight, disguise, or prevent the disclosure of something.

Establishing the core meaning of the isolated word is required to identify its exact synonym.

2

Evaluate the choices to locate the equivalent meaning.

'Hide' matches the exact definition of keeping something out of sight or secret.

Direct synonym selection requires choosing the word with identical semantic value.

Key Concept

Identifying direct synonyms for isolated vocabulary words.

Estimated Time:30s

Question 3448Question →

Identify an exact one-word synonym for the designated term to complete the statement below.

Fill in the blanks below

An accurate synonym for the isolated term NEBULOUS is .

Show answer & explanation

Answer

vague (or unclear, hazy, indistinct, obscure)

The word 'nebulous' originates from the Latin root 'nebula' (mist or cloud) and means lacking clear form or limits, indefinite, or vague. Therefore, words such as 'vague', 'unclear', and 'hazy' serve as direct synonyms.

Step-by-Step Solution

1

Define the target word

The adjective 'nebulous' describes something that is hazy, vague, indistinct, or lacking definite form.

Establishing the precise denotation identifies the exact semantic meaning required.

2

Identify direct equivalent terms

Terms such as 'vague', 'unclear', 'hazy', or 'indistinct' share the identical meaning and adjective form.

A valid synonym must accurately substitute for the target word without altering the part of speech or meaning.

Key Concept

Direct synonym identification for isolated descriptive adjectives

Estimated Time:35s

Question 3449Question →

During the quarterly safety review, the inspector's remarks were entirely desultory, jumping haphazardly from storage protocols to vehicle maintenance without following a coherent plan.

In this sentence, the word desultory most nearly means which of the following?

methodical

gloomy

unfocused

urgent

Show answer & explanation

Answer: unfocused

Answer

The word desultory most nearly means unfocused.

The sentence explicitly restates the behavior characterized by the word desultory: the inspector was 'jumping haphazardly from storage protocols to vehicle maintenance' and acting 'without following a coherent plan.' These details describe an erratic, scattered, and unfocused delivery.

Step-by-Step Solution

1

Analyze the sentence for descriptive modifiers and context clues surrounding the target word.

Identified the descriptive phrases 'jumping haphazardly' and 'without following a coherent plan.'

Contextual definitions in Word Knowledge questions are directly established by supporting clauses in the sentence.

2

Determine the semantic relationship and synthesize the intended meaning of desultory.

The target word describes something lacking purpose, direction, or order (erratic and unfocused).

Connecting 'jumping haphazardly' to the description of the remarks shows that the presentation lacked focus.

3

Evaluate the answer choices to identify the option that matches this synthesized meaning.

Matched 'unfocused' as the direct contextual synonym for 'desultory'.

Unfocused precisely mirrors the lack of coherent structure indicated by the context clues.

Key Concept

Context Clues for Synonyms

Question 3450Question →

Complete the statement by applying your knowledge of word parts. Which word formed by adding the suffix '-less' to the root word 'fear' correctly completes the sentence?

Fill in the blanks below

A firefighter who demonstrates exceptional courage and acts without fear in dangerous situations is described as .

Show answer & explanation

Answer

fearless

The root word 'fear' joined with the suffix '-less' (which means 'without' or 'lacking') yields 'fearless.' In the given context, 'fearless' accurately describes someone who acts with courage and without fear during dangerous emergencies.

Step-by-Step Solution

1

Identify the base root word and the required meaning from the sentence context.

The context describes a firefighter showing courage and acting 'without fear,' indicating the root word 'fear.'

Contextual clues establish the specific emotional state and quality being described.

2

Attach the derivational suffix '-less' to the base noun 'fear.'

Combining 'fear' + '-less' creates the adjective 'fearless.'

The suffix '-less' means 'without' or 'lacking,' forming a word that directly means 'without fear' or courageous.

Key Concept

Suffix Analysis: Using the suffix '-less' to denote the absence or lack of a quality

Estimated Time:30s

Question 3451Question →

A logistics convoy leaves a supply depot and travels at a steady speed of 40 miles per hour for 2 hours and 15 minutes. After a 45-minute halt to refuel, the convoy resumes its route at a speed that is 20% faster than its initial speed. It travels at this new speed for 1 hour and 40 minutes until reaching the forward operating base. What is the total distance traveled by the convoy, in miles?

Show answer & explanation

Answer: 170; 170 miles; 170 mi

Answer

170

The correct answer is found by breaking the journey into two separate legs of movement, converting all times to hours, calculating the distance for each leg independently using their respective speeds, and summing the results.

Step-by-Step Solution

1

Calculate the time traveled during the first leg in hours.

2 hours and 15 minutes is equivalent to 2.25 hours.

Since the speed is given in miles per hour, time must be expressed in hours.

2

Calculate the distance covered during the first leg.

40 mph × 2.25 hours = 90 miles.

Using the distance formula

d = r \times t

.

3

Determine the speed of the convoy for the second leg.

40 mph + (0.20 × 40 mph) = 40 + 8 = 48 mph.

The problem states the convoy travels 20% faster after the halt.

4

Calculate the time traveled during the second leg in hours.

1 hour and 40 minutes is equivalent to

1 \frac{40}{60}

hours, which simplifies to

\frac{5}{3}

hours.

Converting mixed time units to a single fraction of hours is necessary for accurate calculation.

5

Calculate the distance covered during the second leg.

48 mph ×

\frac{5}{3}

hours = 80 miles.

Using the distance formula

d = r \times t

.

6

Calculate the total distance traveled.

90 miles + 80 miles = 170 miles.

The total distance is the sum of the distances from the two active travel legs. The 45-minute halt added 0 miles.

Key Concept

Calculating distance across multiple legs with varying speeds and mixed time units.

Question 3452Question →

A pilot flies a cargo plane from Airport A to Airport B at an average speed of $240$ mph. The pilot returns along the exact same route, but due to a strong headwind, the return flight averages only $160$ mph. If the total flying time for the entire round trip was exactly $5$ hours, what is the one-way distance between Airport A and Airport B, in miles?

Show answer & explanation

Answer: 480

Answer

480

By setting up an algebraic equation representing the total time taken for both legs of the trip (using Time = Distance / Speed), we get

d/240 + d/160 = 5

. Solving this equation by finding a common denominator of

480

yields

5d/480 = 5

, which simplifies to

d = 480

miles.

Step-by-Step Solution

1

Define a variable for the unknown distance.

Let

d

be the one-way distance in miles.

We need to find the one-way distance and relate it to the given times and speeds.

2

Express the time for each leg of the trip using the formula Time = Distance / Speed.

Outbound time =

\frac{d}{240}

, Return time =

\frac{d}{160}

.

The total time is given, so we need mathematical expressions for the time of each individual leg.

3

Set up an equation for the total time.

\frac{d}{240} + \frac{d}{160} = 5

The sum of the outbound flight time and the return flight time equals the total round-trip flight time.

4

Find a common denominator to add the fractions.

The least common multiple of

240

and

160

is

480

. The equation becomes

\frac{2d}{480} + \frac{3d}{480} = 5

.

To solve for

d

, we must combine the fractional terms into a single term.

5

Solve the equation for

d

.

\frac{5d}{480} = 5 \Rightarrow 5d = 2400 \Rightarrow d = 480

.

Isolating

d

gives the final one-way distance.

Key Concept

Solving round trip scenarios by setting up a total time equation:

\frac{d}{v_1} + \frac{d}{v_2} = t_{total}

Estimated Time:2m 0s

Question 3453Question →

A city planner is designing a rectangular park that features a central grassy area measuring $150 \text{ feet}$ long and $90 \text{ feet}$ wide. A uniform concrete walkway that is $6 \text{ feet}$ wide will be constructed around the entire outer perimeter of the grassy area. If the concrete paving costs $\$12.50$ per square yard, what is the total cost, in dollars, of the paving material required for the walkway?

Show answer & explanation

Answer: 4200

Answer

4200

The correct cost is found by determining the total area of the walkway by subtracting the inner grass area from the outer total area (

16,524 - 13,500 = 3,024 \text{ sq ft}

), converting to square yards by dividing by 9 (

336 \text{ sq yd}

), and multiplying by the price of

\$12.50

per square yard.

Step-by-Step Solution

1

Determine the outer dimensions of the total area.

Outer length = 162 ft, Outer width = 102 ft.

The walkway is 6 feet wide and borders all sides. Therefore, 6 feet must be added to both ends of the length (

150 + 6 + 6 = 162

) and both sides of the width (

90 + 6 + 6 = 102

).

2

Calculate the area of the outer rectangle.

16,524 sq ft

Area is length multiplied by width:

162 \times 102 = 16,524

.

3

Calculate the area of the inner grassy rectangle.

13,500 sq ft

Using the given inner dimensions:

150 \times 90 = 13,500

.

4

Find the area of the walkway.

3,024 sq ft

Subtract the inner area from the outer area:

16,524 - 13,500 = 3,024

.

5

Convert the walkway area from square feet to square yards.

336 sq yd

There are

3 \times 3 = 9

square feet in one square yard. Divide the area by 9:

3,024 \div 9 = 336

.

6

Calculate the total cost.

$4,200

Multiply the area in square yards by the cost per square yard:

336 \times 12.50 = 4,200

.

Key Concept

Calculating subtractive rectangular area and converting square units for cost analysis.

Question 3454Question →

Type a single word into the blank that represents the closest synonym to the bold, capitalized term.

Fill in the blanks below

INIMICAL =

Show answer & explanation

Answer

A valid synonym is 'hostile', 'harmful', or 'antagonistic'.

The word 'inimical' means tending to obstruct or harm, or being unfriendly and hostile. Therefore, words like 'hostile', 'harmful', and 'antagonistic' are accurate, direct synonyms that match both the exact definition and the grammatical form of the target word.

Step-by-Step Solution

1

Analyze the target word 'INIMICAL'.

Identify it as an advanced adjective often used in formal or academic contexts.

Understanding the grammatical form and context helps filter potential synonyms.

2

Determine the definition based on root structure or vocabulary knowledge.

Recall that it derives from the Latin 'inimicus' (enemy), giving it the meaning of being adverse, harmful, or tending to obstruct.

An exact definition is critical to distinguish it from visually similar words.

3

Select a direct, single-word synonym.

Words like 'hostile', 'harmful', or 'antagonistic' perfectly match.

These terms align precisely with both the meaning and the adjective part of speech.

Key Concept

Advanced vocabulary comprehension and precise synonym identification.

Estimated Time:45s

Question 3455Question →

Read each sentence below and analyze the surrounding context clues. Match each bolded word from the left column to its correct contextual meaning in the right column.

Click a left item, then click its matching right item

Show answer & explanation

Answer

The sentence with 'pragmatic' matches 'Practical and focused on real-world application rather than theory'; the sentence with 'precarious' matches 'Unstable, insecure, and dangerously positioned'; the sentence with 'augment' matches 'To increase, enlarge, or supplement existing resources'; and the sentence with 'terse' matches 'Brief, concise, and stripped of excess words'.

Each pairing is determined by explicit clues in the sentences: 'pragmatic' contrasts directly with 'theoretical ideas'; 'precarious' is supported by 'washed away foundation' and 'near the ledge'; 'augment' is demonstrated by adding commercial vehicles during a surge; and 'terse' is defined by 'cutting out all unnecessary chatter'.

Step-by-Step Solution

1

Analyze each sentence's context clues (contrast, cause-effect, restatement) to deduce the definition of each bolded word.

Identified 'pragmatic' as practical (contrasting theoretical), 'precarious' as unstable/dangerous (washed-away foundation), 'augment' as supplement/increase (adding vehicles for a surge), and 'terse' as brief/concise (cutting unnecessary chatter).

Contextual clues provide structural evidence of meaning without relying on isolated memorization.

2

Correlate each identified contextual meaning to the matching definition item.

Formed accurate one-to-one matches for all four vocabulary terms.

Each definition corresponds directly to the grammatical category and semantic role of the target term.

Key Concept

Deducing vocabulary definitions using contextual contrast, cause-and-effect, and descriptive cues

Question 3456Question →

The commanding officer made it clear that while candid feedback was welcome during planning sessions, leadership would not countenance blatant insubordination during live drills. In this context, "countenance" most nearly means

facial appearance

tolerate

penalize

prohibit

Show answer & explanation

Answer: tolerate

Answer

tolerate

In this sentence, the target word functions as a verb modified by 'would not' to convey that leadership will not accept or permit insubordinate behavior. The contrast with 'welcome' in the preceding clause confirms that the verb means to tolerate or approve.

Step-by-Step Solution

1

Analyze the grammatical function of the target word within the sentence

The target word follows the auxiliary construction 'would not' and takes the direct object 'blatant insubordination', indicating it functions as a transitive verb rather than a noun.

Identifying the part of speech prevents confusing the contextual meaning with the primary noun definition.

2

Examine the contrast context clue introduced by the subordinate clause

The introductory conjunction 'while' sets up a direct contrast between what is permitted ('welcome') and what leadership will refuse to accept ('would not countenance').

Contrast clues establish the relationship between acceptable and unacceptable conduct.

3

Substitute the synonym candidates into the original sentence

Replacing the target word with 'tolerate' produces 'would not tolerate blatant insubordination', preserving the intended syntax and semantic meaning.

Direct substitution confirms semantic accuracy and grammatical agreement.

Key Concept

Using syntactic role and contrast context clues to determine the contextual synonym of a polysemous word

Question 3457Question →

Prefixes alter the fundamental meaning of base words to form specific terms. Which definition correctly matches each prefixed word based on its morphological structure?

Click a left item, then click its matching right item

Show answer & explanation

Answer

Autobiography pairs with 'An account of a person's life written by oneself'; Multipurpose pairs with 'Having many different applications or functions'; Semicircle pairs with 'One half of a circle'; Telescope pairs with 'An instrument designed for viewing distant objects'.

Each pair is correctly matched by identifying its Greek or Latin prefix: 'auto-' indicates self, 'multi-' indicates many, 'semi-' indicates half, and 'tele-' indicates distance.

Step-by-Step Solution

1

Analyze the prefix of each given term to deduce its primary meaning.

Identified 'auto-' (self), 'multi-' (many), 'semi-' (half), and 'tele-' (distant).

Prefixes systematically modify root words to create predictable definitions.

2

Pair each prefixed word with its corresponding definition based on the established morphological meanings.

Autobiography matches self-written history, multipurpose matches multiple uses, semicircle matches half-circle, and telescope matches viewing at a distance.

Direct morphological matching connects each prefix to its correct functional definition.

Key Concept

Prefix and Suffix Analysis

Estimated Time:45s

Question 3458Question →

The engineer explained that adding heavy insulation would counteract the heat loss during winter. In this context, what does the word counteract most nearly mean?

Encounter

Neutralize

Accelerate

Calculate

Show answer & explanation

Answer: Neutralize

Answer

Neutralize

The prefix 'counter-' means 'against' or 'in opposition to', and the base 'act' means 'to do' or 'to operate'. Therefore, 'counteract' means to act against something to reduce its effect, making 'Neutralize' the precise synonym.

Step-by-Step Solution

1

Analyze the prefix and root components of the target word.

The word 'counteract' is composed of the prefix 'counter-' (meaning 'against', 'opposite', or 'in return') and the base verb 'act' (meaning 'to perform an action or exert energy').

Morphological decomposition isolates the core meaning of the word's building blocks.

2

Synthesize the morphological meaning with the sentence context.

Acting against heat loss means working to offset, balance out, or neutralize its effect.

Contextual integration verifies which synonym best captures the combined affix meaning.

Key Concept

Analyzing directional and oppositional prefixes like 'counter-' to determine word meanings

Estimated Time:45s

Question 3459Question →

Because the automated inventory database now logs incoming supply crates in real time, filling out handwritten tally sheets has become superfluous.

In this sentence, the word superfluous most nearly means which of the following?

essential

superficial

unnecessary

complicated

Show answer & explanation

Answer: unnecessary

Answer

unnecessary

In this context, 'superfluous' means exceeding what is sufficient or necessary. The sentence establishes a cause-and-effect relationship: because a digital database tracks supplies automatically in real time, doing the same task manually on paper is extra and unneeded. Therefore, 'unnecessary' is the exact contextual synonym.

Step-by-Step Solution

1

Analyze the sentence structure and context clues

The cause-and-effect clue introduced by 'Because' explains that the automated system tracks everything in real time, making the manual paper records redundant.

Identifying semantic and logical relationships in the sentence clarifies the functional role of the target word.

2

Substitute candidate words into the sentence frame

Replacing 'superfluous' with 'unnecessary' preserves the logical flow: since automated logging is active, manual paper sheets are unnecessary.

Substitution confirms that the chosen synonym maintains correct tone, part of speech, and intended meaning.

Key Concept

Context Clues for Synonyms (Cause-and-Effect Relationship)

Estimated Time:45s

Question 3460Question →

A commercial painting crew is hired to paint the four exterior walls of a rectangular warehouse. The warehouse has a length of $120\text{ ft}$ , a width of $80\text{ ft}$ , and a height of $24\text{ ft}$ . The building features $2$ identical loading doors, each measuring $16\text{ ft}$ wide by $15\text{ ft}$ high, and $4$ identical windows, each measuring $6\text{ ft}$ wide by $5\text{ ft}$ high. The doors and windows will not be painted. The crew must apply exactly $2$ coats of paint to all paintable exterior wall surfaces. If one gallon of paint covers exactly $400\text{ square feet}$ , how many total gallons of paint are required for this project?

Show answer & explanation

Answer: 45

Answer

45

The total area of the four exterior walls is 9,600 sq ft. The doors and windows have a combined area of 600 sq ft, leaving a net paintable area of 9,000 sq ft per coat. Since two coats are required, the total area to cover is 18,000 sq ft. With each gallon covering 400 sq ft, dividing 18,000 by 400 gives exactly 45 gallons.

Step-by-Step Solution

1

Calculate the gross area of the four exterior walls.

9,600 sq ft

To find the total surface area before accounting for doors and windows.

2

Calculate the total area of the unpainted cutouts.

600 sq ft

The doors and windows will not be painted and must be subtracted.

3

Determine the net paintable area for a single coat.

9,000 sq ft

Subtracting the cutout area from the gross area gives the actual area to paint.

4

Calculate the total area to be covered for two coats.

18,000 sq ft

The problem specifies that exactly two coats of paint must be applied.

5

Determine the total gallons of paint required.

45

Divide the total area to be painted by the coverage rate of 400 sq ft per gallon.

Key Concept

Calculating net rectangular area by subtracting cutouts and applying a rate for multiple layers.

Answer

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