All practice questions

Question 4061Question →

Complete the statement describing the standard double-entry accounting procedure required when a bad debt previously written off is subsequently recovered.

Fill in the blanks below

To properly record the recovery of a debt previously written off as irrecoverable, the customer's account is first reinstated by debiting the debtor's personal account and crediting the account. Next, the receipt of funds is recorded by debiting the cash or bank account and crediting the account.

Show answer & explanation

Answer

The first blank is 'Bad Debts Recovered' and the second blank is 'Debtor's' (or 'Trade Debtors').

When a debt previously written off is recovered, standard double-entry accounting mandates a two-stage entry: first, reinstate the debt by debiting the Debtor's Personal Account and crediting the Bad Debts Recovered Account; second, record payment by debiting Cash/Bank Account and crediting the Debtor's Personal Account.

Step-by-Step Solution

1

Identify the entry needed to reinstate the debtor's personal account balance.

Debit the Debtor's Personal Account and credit the Bad Debts Recovered Account.

Reinstating the debtor's account ensures complete ledger history for credit rating and audit purposes before settling the account.

2

Record the receipt of cash/cheque from the debtor.

Debit Cash/Bank Account and credit the Debtor's Personal Account.

Receiving cash increases cash assets and clears the reinstated personal balance of the debtor.

Key Concept

Accounting entry for bad debts recovered requires reinstating the debtor's account first before crediting the receipt of cash to the debtor's account.

Estimated Time:1m 30s

Question 4062Question →

Kolawole Nigeria Ltd has an authorized share capital of $500,000$ ordinary shares of ₦1 each, of which $300,000$ shares are fully issued and paid-up. If the directors declare a dividend of $10\%$ on ordinary shares, what is the total amount of dividend payable?

₦50,000

₦30,000

₦20,000

₦80,000

Show answer & explanation

Answer: ₦30,000

Answer

The total amount of dividend payable is ₦30,000.

Dividends are always calculated on the paid-up share capital of the company. With

300,000

fully paid-up shares at ₦1 each, total paid-up capital is ₦300,000. A

10\%

dividend yields

0.10 \times \text{₦}300,000 = \text{₦}30,000

.

Step-by-Step Solution

1

Determine the paid-up share capital value.

Paid-up Share Capital =

300,000 \text{ shares} \times \text{₦}1 = \text{₦}300,000

.

Dividends can only be declared and paid on shares that have actually been issued and paid for, not on authorized or unissued capital.

2

Calculate the declared dividend amount.

Dividend Payable =

10\% \times \text{₦}300,000 = \text{₦}30,000

.

Applying the declared percentage dividend rate (

10\%

) to the paid-up share capital.

Key Concept

Calculation of Ordinary Share Dividend on Paid-up Capital

Estimated Time:45s

Question 4063Question →

Match each commercial communication service on the left with its corresponding description or operational feature on the right.

Click a left item, then click its matching right item

Show answer & explanation

Answer

Express Mail Service (EMS) matches with expedited transport and delivery of urgent documents and parcels with tracking functionality; Franking Machine matches with printing official postage impressions directly onto outgoing envelopes in high-volume business mailrooms; Electronic Mail (E-mail) matches with instant digital transmission of written correspondence and document attachments over computer networks; Business Reply Service matches with permitting prospective customers to respond to promotional mailings without paying postage, as costs are paid by the recipient firm.

Each commercial communication service is correctly matched to its distinct function: Express Mail Service provides expedited parcel delivery with tracking; a Franking Machine automates postage stamping on business envelopes; Electronic Mail transmits digital messages instantly; and Business Reply Service enables customers to mail back responses at the receiving company's expense.

Step-by-Step Solution

1

Identify the primary purpose of Express Mail Service (EMS).

Recognize that EMS handles urgent physical parcels and letters with fast delivery and tracking.

EMS is a premium postal option specifically designed for speed and reliability in delivery.

2

Identify the operational function of a Franking Machine.

Match it with pre-stamping postage impressions on high-volume enterprise mail.

Businesses use franking machines in-house to save time purchasing individual adhesive postage stamps.

3

Determine the features of Electronic Mail (E-mail).

Associate it with instantaneous transmission of computer-based messages and file attachments.

E-mail relies on digital network infrastructure for instantaneous paperless communication.

4

Understand the mechanism of Business Reply Service.

Connect it to customer response envelopes where postage is paid by the receiving business upon delivery.

This service encourages customer response by removing postage costs from the consumer.

Key Concept

Classification and operational roles of postal, telecommunication, and digital communication services in commerce.

Estimated Time:1m 0s

Question 4064Question →

Tayo Traders had a trade debtors balance of $\text{₦}450,000$ before year-end adjustments for the financial year ended 31st December 2024. At the end of the year, additional unrecorded bad debts of $\text{₦}15,000$ were identified to be written off. During the same year, cash of $\text{₦}10,000$ was received from a customer whose debt of $\text{₦}10,000$ had been written off in 2022. What is the net trade debtors balance to be shown in the Statement of Financial Position as at 31st December 2024?

Show answer & explanation

Answer: 435000

Answer

The net trade debtors balance to be shown in the Statement of Financial Position at 31st December 2024 is

\text{₦}435,000

.

To calculate the net trade debtors figure for the Statement of Financial Position, only additional bad debts written off at year-end (

\text{₦}15,000

) are deducted from the unadjusted trade debtors balance of

\text{₦}450,000

, resulting in

\text{₦}435,000

. Bad debts recovered (

\text{₦}10,000

) are recognized as revenue in the Income Statement and received in cash, having no effect on closing trade debtors.

Step-by-Step Solution

1

Determine the unadjusted trade debtors balance

Unadjusted Trade Debtors =

\text{₦}450,000

This represents the recorded receivables prior to writing off year-end unrecorded bad debts.

2

Subtract additional bad debts written off at year-end

Adjusted Trade Debtors =

\text{₦}450,000 - \text{₦}15,000 = \text{₦}435,000

Bad debts written off represent irrecoverable amounts and must be deducted directly from trade debtors.

3

Evaluate the treatment of bad debts recovered

Effect on Trade Debtors =

\text{₦}0

Bad debts recovered during the year are recorded by debiting Cash/Bank and crediting Bad Debts Recovered (an income account). Because the original personal account of the debtor was already cleared when written off in a previous period, recovery does not alter the closing trade debtors balance.

Key Concept

Treatment of Bad Debts Written Off and Bad Debts Recovered on the Statement of Financial Position

Estimated Time:1m 30s

Question 4065Question →

A trading enterprise recently implemented a modern computerized accounting system. Management assumed that because the newly installed accounting application software and server hardware feature automated processing algorithms, the system would automatically eliminate internal accounting errors and fraud without requiring written operational guidelines, internal approval workflows, or staff oversight. Which fundamental principle concerning the components of a computerized accounting system did management fail to appreciate?

Automated system software merges hardware and database layers, thereby rendering human oversight and user management redundant.

Hardware and software components cannot replace procedural internal controls and personnel oversight in maintaining system data integrity.

Accounting application software acts as system software that converts periodic batch processing into continuous real-time processing without user input.

Computerized accounting components automatically unify routine transaction recording with high-level financial interpretation without human intervention.

Show answer & explanation

Answer: Hardware and software components cannot replace procedural internal controls and personnel oversight in maintaining system data integrity.

Answer

Hardware and software components cannot replace procedural internal controls and personnel oversight in maintaining system data integrity.

A Computerized Accounting System (CAS) relies on five essential components: Hardware, Software, Data, Procedures, and Peopleware. Management's mistake was assuming that acquiring advanced hardware and application software removes the necessity of internal control procedures and administrative oversight. Technology automates processing speed and accuracy but cannot enforce organizational accountability or prevent fraudulent data input without rigorous procedural controls and human monitoring.

Step-by-Step Solution

1

Identify the five core components of a Computerized Accounting System (CAS).

A complete CAS consists of Hardware, Software, Data/Database, Procedures (internal controls and operational rules), and Peopleware (users and administrators).

Evaluating system integrity requires viewing all five components as interdependent elements.

2

Analyze management's erroneous assumption in the scenario.

Management relied solely on technology (hardware and application software) while neglecting procedural controls and human oversight (peopleware).

Software executes instructions accurately, but without authorization procedures and user access controls, fraudulent or erroneous data can still enter the system.

3

Determine the correct accounting principle governing system controls.

Computerization does not eliminate internal control risks; hardware and software must be paired with well-defined procedures and diligent peopleware oversight.

Internal accounting control is a procedural and organizational discipline, not merely a software feature.

Key Concept

Interdependence of CAS Components and Internal Control Procedures

Estimated Time:2m 0s

Question 4066Question →

When a partnership firm operates the fixed capital account system, in which account is a partner's share of net profit credited at the end of the accounting period?

Partner's Current Account

Partner's Capital Account

Profit and Loss Account

Drawings Account

Show answer & explanation

Answer: Partner's Current Account

Answer

Partner's Current Account

Under the fixed capital account system, the partner's capital account maintains a constant balance containing only initial capital, permanent additions, or permanent capital withdrawals. All recurring operational allocations such as profit shares, partner salaries, interest on capital, and drawings are credited or debited to the partner's current account.

Step-by-Step Solution

1

Identify the accounting method specified in the prompt

The firm uses the fixed capital account method.

Partnership accounting distinguishes between fixed and fluctuating capital methods.

2

Apply the rule of the fixed capital account method

The Capital Account balance is kept fixed, while all annual appropriations (profit share, salaries, drawings, interest) are posted to the Current Account.

This maintains the initial capital structure distinct from accumulated profits and appropriations.

3

Determine the crediting account for share of profit

The share of profit increases the partner's equity, so it is credited to the Partner's Current Account.

Crediting the current account reflects the allocation of profits available to the partner without altering original capital.

Key Concept

Fixed Capital Accounts Method

Estimated Time:45s

Question 4067Question →

Complete the sentence below by filling in the blank with a word that is opposite in meaning to the highlighted word.

Fill in the blanks below

Despite the mediator's persistent efforts to reach a compromise, the union leader remained completely intransigent, whereas the management proved unexpectedly .

Show answer & explanation

Answer

accommodating (or flexible / yielding / compliant / cooperative)

The sentence uses the contrastive conjunction 'whereas' to contrast the union leader's refusal to compromise with the management's behavior. 'Intransigent' means unwilling or refusing to change one's views or agree about something. Therefore, an antonym such as 'accommodating', 'flexible', or 'yielding' correctly completes the sentence.

Step-by-Step Solution

1

Analyze the meaning of the highlighted target word in its sentence context.

The word 'intransigent' refers to someone who is stubborn, uncompromising, or refusing to change their views.

Understanding the precise contextual definition of the target word is necessary before determining its opposite.

2

Identify the contrasting relationship established in the sentence structure.

The conjunction 'whereas' sets up a direct opposition between the stance of the union leader and that of the management.

Since the union leader was uncompromising ('intransigent'), management's contrasting behavior requires a word meaning willing to compromise or adapt.

3

Select the appropriate antonym that completes the blank grammatically and semantically.

Words such as 'accommodating', 'flexible', 'yielding', or 'compliant' serve as accurate contextual antonyms for 'intransigent'.

These terms precisely denote a willingness to cooperate and yield in negotiations.

Key Concept

Identifying Contextual Antonyms

Estimated Time:1m 0s

Question 4068Question →

Evaluate the trigonometric expression $\tan 60^\circ \times \sin 60^\circ$ . What is the exact simplified value of the expression?

\frac{3}{2}

\frac{\sqrt{3}}{2}

3

\frac{\sqrt{3}}{4}

Show answer & explanation

Answer: $\frac{3}{2}$

Answer

The exact simplified value of the expression is

\frac{3}{2}

.

Substituting the exact surd values of the special angles yields

\tan 60^\circ = \sqrt{3}

and

\sin 60^\circ = \frac{\sqrt{3}}{2}

. Multiplying these gives

\sqrt{3} \times \frac{\sqrt{3}}{2} = \frac{3}{2}

, which is the correct exact value.

Step-by-Step Solution

1

Identify the values of the special trigonometric angles.

\tan 60^\circ = \sqrt{3}

and

\sin 60^\circ = \frac{\sqrt{3}}{2}

.

Special angle values must be known in exact surd form.

2

Multiply the two trigonometric ratios together.

\tan 60^\circ \times \sin 60^\circ = \sqrt{3} \times \frac{\sqrt{3}}{2} = \frac{(\sqrt{3} \times \sqrt{3})}{2}

.

Substitute the special angle values into the product expression.

3

Simplify the radical expression in the numerator.

\frac{3}{2}

.

The product of

\sqrt{3} \times \sqrt{3}

equals

3

.

Key Concept

Evaluation of Special Angle Trigonometric Values

Estimated Time:45s

Question 4069Question →

Read the excerpt below carefully:

"Listen! The drums beat no longer for war,
Nor for the solemn burial of a fallen chief,
But for the harvest of yam and the laughter of maiden daughters.
Throw open the gates and let the palm wine flow!"

What is the dominant tone of the speaker in the excerpt above?

Jubilant and celebratory

Mournful and solemn

Hostile and aggressive

Anxious and fearful

Show answer & explanation

Answer: Jubilant and celebratory

Answer

Jubilant and celebratory

The correct answer is 'Jubilant and celebratory' because the speaker uses vibrant, festive imagery—such as the yam harvest, laughter, opening gates, and sharing palm wine—to convey a enthusiastic attitude of community celebration and joy.

Step-by-Step Solution

1

Identify the key words and imagery in the excerpt

Phrases like 'harvest of yam', 'laughter of maiden daughters', and 'let the palm wine flow' point toward a festive event.

Tone is determined by the author or speaker's attitude conveyed through word choice and imagery.

2

Analyze negations in the text

The speaker explicitly rejects negative or sombre reasons for drumming ('no longer for war', 'nor for the solemn burial').

Recognizing what the speaker rejects prevents misinterpreting the excerpt as gloomy or aggressive.

3

Synthesize the overall speaker attitude

The speaker's call to open gates and celebrate reveals a festive, joyful, and triumphant tone.

Connecting the joyful imagery leads directly to the correct classification of a jubilant tone.

Key Concept

Textual Tone, Mood, and Atmosphere

Estimated Time:45s

Question 4070Question →

Read the excerpt below carefully:

"The ancient iroko yields no green today,
Its hollow trunk groans against the rising gale;
The elders gather their woven shawls in silence,
Watching the grey mist swallow the drying fields."

Which of the following best describes the dominant atmosphere established in the passage?

ominous and melancholic

festive and celebratory

angry and vengeful

indignant and sarcastic

Show answer & explanation

Answer: ominous and melancholic

Answer

ominous and melancholic

The atmosphere of a literary passage is established through sensory imagery, setting details, and word connotations. Phrases like 'yields no green', 'hollow trunk groans', 'in silence', and 'grey mist swallow the drying fields' evoke a pervading sense of impending misfortune (ominous) and quiet sorrow (melancholic). Therefore, describing the atmosphere as ominous and melancholic accurately captures the scene.

Step-by-Step Solution

1

Analyze the descriptive imagery in the excerpt

Identified imagery such as 'yields no green', 'hollow trunk groans', 'rising gale', 'silence', and 'grey mist swallow the drying fields'.

Atmosphere and mood are created through sensory details, setting, and word choices.

2

Determine the emotional impact and environmental tone created by these details

The visual and auditory details evoke feelings of loss, decay, quiet sadness, and impending trouble.

Describing nature in decline combined with silent apprehension builds foreboding and sadness.

3

Match the identified emotional quality with the correct descriptor

The mood aligns precisely with an atmosphere that is ominous (foreboding danger/gale) and melancholic (sad and gloomy).

Selecting the pair of adjectives that accurately synthesizes both the dread and sadness of the scene.

Key Concept

Textual Tone, Mood, and Atmosphere

Question 4071Question →

Consider the following excerpt from an essay on urban sociology:

"In her critique of modern city planning, the researcher observed that local community identity is far from static; rather, it remains remarkably plastic, constantly reshaped by influxes of new cultural traditions and shifting economic realities."

In the excerpt above, what is the contextual meaning of the word plastic?

adaptable and capable of being shaped

synthetic and manufactured from polymers

superficial and lacking in genuine authenticity

fragile and vulnerable to complete destruction

Show answer & explanation

Answer: adaptable and capable of being shaped

Answer

The word 'plastic' in this context means adaptable and capable of being shaped.

The sentence establishes a direct contrast between 'static' (unchanging) and 'plastic', followed immediately by the explanation that identity is 'constantly reshaped'. Therefore, the correct interpretation is that the community identity is malleable, flexible, and adaptable.

Step-by-Step Solution

1

Analyze the structural contrast in the sentence

The semi-colon links 'far from static' with 'remains remarkably plastic', indicating that 'plastic' serves as a direct antonym to 'static'.

Contextual meaning is often revealed through antonymic relationships within the sentence structure.

2

Examine the surrounding descriptive context

The phrase 'constantly reshaped by influxes of new cultural traditions' clarifies how the identity behaves.

The clause following the target word explicitly elaborates on its specific function in the sentence.

3

Substitute candidate definitions into the excerpt

Replacing 'plastic' with 'adaptable and capable of being shaped' preserves both syntactic structure and semantic coherence.

Proper contextual substitution verifies that the chosen meaning aligns with the author's intended argument.

Key Concept

Contextual Word Meaning (Polysemy and Antonymic Contrast)

Estimated Time:1m 30s

Question 4072Question →

The variable $y$ varies inversely as $x$ . If $y = 6$ when $x = 4$ , what is the value of $y$ when $x = 8$ ?

3

12

16

48

Show answer & explanation

Answer: 3

Answer

The value of

y

when

x = 8

is 3.

Since

y

varies inversely as

x

, the formula connecting them is

y = \frac{k}{x}

. Substituting

y = 6

when

x = 4

gives

6 = \frac{k}{4}

, which yields

k = 24

. Using this constant, when

x = 8

,

y = \frac{24}{8} = 3

.

Step-by-Step Solution

1

Write the relationship for inverse variation.

y = \frac{k}{x}

Inverse variation means

y

is inversely proportional to

x

, where

k

is the constant of variation.

2

Substitute given values

y = 6

and

x = 4

to solve for

k

.

6 = \frac{k}{4} \implies k = 6 \times 4 = 24

To complete the equation of variation, the constant

k

must be determined.

3

Substitute

k = 24

and

x = 8

into the variation equation to find

y

.

y = \frac{24}{8} = 3

Evaluating the relationship at

x = 8

gives the requested value.

Key Concept

Inverse Variation

Question 4073Question →

Read the passage excerpt below carefully.

"Although the committee was open to new suggestions, the chairperson refused to entertain any proposal that exceeded the approved budget."

In the context of the sentence above, what is the meaning of the word entertain?

amuse or provide enjoyment for

consider or give thought to

approve or officially pass

reject or dismiss summarily

Show answer & explanation

Answer: consider or give thought to

Answer

The word 'entertain' in this context means to consider or give thought to.

In formal English discourse, when someone refuses to 'entertain' an idea or proposal, it means they will not consider or give thought to it. Substituting 'consider or give thought to' maintains the exact logical sense of the sentence.

Step-by-Step Solution

1

Analyze the sentence context surrounding the highlighted word

The sentence indicates that proposals exceeding the budget will not be given consideration or brought up for discussion.

Contextual meaning depends on how the target word functions within the specific sentence structure.

2

Substitute plausible definitions into the sentence structure

Replacing 'entertain' with 'consider or give thought to' preserves the logical and grammatical meaning of the sentence.

Syntactic and semantic substitution confirms whether a definition fits the intended contextual nuance.

Key Concept

Contextual Word Meaning

Question 4074Question →

Read the passage excerpt carefully:

"In his critique of modern urban planning, the sociologist noted that municipal authorities often discount the spontaneous social networks formed in informal settlements, viewing them merely as chaotic rather than vital structures of community resilience."

Which of the following best captures the meaning of the word discount as used in the excerpt?

dismiss as insignificant

reduce the financial cost of

actively dismantle and replace

miscalculate the total number of

Show answer & explanation

Answer: dismiss as insignificant

Answer

The word 'discount' as used in the passage means to dismiss as insignificant.

In the excerpt, 'discount' is used as a verb meaning to minimize or disregard the importance of something. The contrast between viewing social networks 'merely as chaotic' rather than 'vital structures' confirms that municipal authorities underestimate or dismiss their true value.

Step-by-Step Solution

1

Analyze the sentence context surrounding the highlighted word

The text explains that municipal authorities view spontaneous social networks 'merely as chaotic rather than vital structures.'

Contextual clues reveal the attitude of the authorities toward these networks.

2

Determine the contextual sense of 'discount'

Because authorities see the networks as chaotic and unimportant, they disregard or fail to value them.

The verb 'discount' functions here figuratively to express undervaluation or dismissal.

3

Test option substitution

Replacing 'discount' with 'dismiss as insignificant' maintains identical sentence logic and tone.

A valid contextual synonym must fit both syntactically and semantically.

Key Concept

Contextual Word Meaning (Figurative vs. Primary Dictionary Meaning)

Question 4075Question →

If $x$ is an acute angle such that $\sin x - \cos x = \frac{1}{\sqrt{5}}$ , what is the exact value of $\tan x + \cot x$ ?

\frac{5}{2}

\frac{5}{4}

\frac{2}{5}

\frac{4}{5}

Show answer & explanation

Answer: $\frac{5}{2}$

Answer

The exact value of

\tan x + \cot x

is

\frac{5}{2}

.

Squaring both sides of

\sin x - \cos x = \frac{1}{\sqrt{5}}

yields

1 - 2\sin x \cos x = \frac{1}{5}

, which simplifies to

\sin x \cos x = \frac{2}{5}

. Expressing

\tan x + \cot x

in terms of sine and cosine gives

\frac{\sin^2 x + \cos^2 x}{\sin x \cos x} = \frac{1}{\sin x \cos x}

. Substituting

\frac{2}{5}

gives

\frac{1}{2/5} = \frac{5}{2}

.

Step-by-Step Solution

1

Square both sides of the given equation

\sin x - \cos x = \frac{1}{\sqrt{5}}

(\sin x - \cos x)^2 = \left(\frac{1}{\sqrt{5}}\right)^2 \implies \sin^2 x - 2\sin x \cos x + \cos^2 x = \frac{1}{5}

Squaring enables the use of the Pythagorean trigonometric identity.

2

Apply the fundamental identity

\sin^2 x + \cos^2 x = 1

to isolate

\sin x \cos x

1 - 2\sin x \cos x = \frac{1}{5} \implies 2\sin x \cos x = 1 - \frac{1}{5} = \frac{4}{5} \implies \sin x \cos x = \frac{2}{5}

This determines the value of the product of sine and cosine.

3

Rewrite

\tan x + \cot x

using quotient identities

\tan x + \cot x = \frac{\sin x}{\cos x} + \frac{\cos x}{\sin x} = \frac{\sin^2 x + \cos^2 x}{\sin x \cos x} = \frac{1}{\sin x \cos x}

Expressing tangent and cotangent with a common denominator simplifies the expression into a reciprocal.

4

Substitute

\sin x \cos x = \frac{2}{5}

into the simplified expression

\tan x + \cot x = \frac{1}{2/5} = \frac{5}{2}

Inverting the fraction gives the final numerical answer.

Key Concept

Pythagorean and Quotient Trigonometric Identities

Estimated Time:2m 0s

Question 4076Question →

Read the passage excerpt below carefully:

"In his treatise on cognitive architecture, the philosopher noted that empirical inquiries often fail not because the instruments are defective, but because investigators attempt to sound the depths of human consciousness using metrics calibrated only for superficial behavioral observations."

In the passage above, what is the contextual meaning of the word sound?

produce an audible resonance or acoustic signal

fathom or measure the depth of

affirm the logical validity of

examine using acoustic medical imaging

Show answer & explanation

Answer: fathom or measure the depth of

Answer

In the given excerpt, the word 'sound' contextually means to fathom or measure the depth of.

The option stating 'fathom or measure the depth of' is correct because 'sound' is used contextually as a verb derived from nautical measurement (plumbing depths). In philosophical and literary contexts, 'to sound the depths' is an established idiom meaning to investigate or penetrate deep, complex ideas.

Step-by-Step Solution

1

Analyze the grammatical function of the target word in context.

The word 'sound' follows the infinitive marker 'to' ('attempt to sound the depths...') and takes 'the depths' as its direct object, functioning as a transitive verb.

Identifying the part of speech eliminates meanings associated with adjectives or nouns.

2

Examine the surrounding contextual clues and imagery.

The phrase 'sound the depths... using metrics calibrated only for superficial... observations' uses nautical measurement metaphors where depth and calibration are contrasted with surface observations.

Contextual clues reveal that the author is contrasting deep measurement with superficial observation.

3

Select the synonym that correctly matches the metaphor and syntax when substituted.

Substituting 'fathom' or 'measure the depth of' yields: 'attempt to fathom the depths of human consciousness', which preserves both exact meaning and sentence structure.

A valid contextual definition must fit both semantically and syntactically.

Key Concept

Contextual Word Meaning in Reading Comprehension

Estimated Time:1m 30s

Question 4077Question →

A quantity $y$ is partly constant and partly varies directly as $x$ . When $x = 2$ , $y = 10$ , and when $x = 5$ , $y = 19$ . What is the value of $y$ when $x = 8$ ?

28

35

40

25

Show answer & explanation

Answer: 28

Answer

The value of

y

when

x = 8

is 28.

By representing partial variation as

y = c + kx

, substituting the given conditions gives two simultaneous linear equations:

10 = c + 2k

and

19 = c + 5k

. Subtracting the first equation from the second yields

3k = 9

, so

k = 3

. Substituting

k = 3

back into the first equation yields

c = 4

. The general equation is

y = 4 + 3x

. Evaluating at

x = 8

gives

y = 4 + 3(8) = 28

.

Step-by-Step Solution

1

Set up the partial variation equation

y = c + kx

, where

c

is the constant part and

k

is the constant of variation.

Partial variation consists of a fixed term plus a variable term.

2

Substitute given values to form simultaneous equations

Equation 1:

10 = c + 2k

Equation 2:

19 = c + 5k

Two pairs of

(x, y)

values are provided to solve for the two unknown constants

c

and

k

.

3

Solve for

k

and

c

Subtract Equation 1 from Equation 2:

9 = 3k \implies k = 3

.
Substitute

k = 3

into Equation 1:

10 = c + 2(3) \implies c = 4

.
Thus,

y = 4 + 3x

.

Eliminating

c

yields the value of

k

, which is then used to find

c

.

4

Calculate

y

for

x = 8

y = 4 + 3(8) = 4 + 24 = 28

.

Substitute the required value of

x

into the established formula.

Key Concept

Partial Variation and Simultaneous Equations

Question 4078Question →

What is the result of the subtraction $41_5 - 23_5$ in base 5?

18_5

13_5

22_5

23_5

Show answer & explanation

Answer: $13_5$

Answer

13_5

The answer

13_5

is correct because borrowing 1 from the fives place contributes 5 to the units place, making the calculation

(1 + 5) - 3 = 3

for the units place and

3 - 2 = 1

for the fives place.

Step-by-Step Solution

1

Set up column subtraction for

41_5 - 23_5

in base 5.

In the units position, we evaluate

1 - 3

.

Since 1 is smaller than 3, a borrow operation from the fives column is required.

2

Borrow 1 from the fives column (reducing 4 to 3) and add the base value 5 to the units digit 1.

Units column value becomes

1 + 5 = 6

. Fives column value becomes 3.

When borrowing in base

n

, the borrowed amount is equal to

n

, which is 5 for base 5.

3

Subtract digits in each column.

Units column:

6 - 3 = 3

. Fives column:

3 - 2 = 1

. The result is

13_5

.

Completing the column subtraction yields the final digits in base 5.

Key Concept

Subtraction in Non-Decimal Number Bases

Estimated Time:45s

Question 4079Question →

Given that $P$ varies directly as the square of $r$ , and $P = 48$ when $r = 4$ , calculate the value of $P$ when $r = 6$ .

Show answer & explanation

Answer: 108

Answer

The value of

P

when

r = 6

is

108

.

Since

P

varies directly as

r^2

, the relationship is expressed as

P = k r^2

. Substituting the given values

P = 48

and

r = 4

yields

48 = 16k

, so

k = 3

. Substituting

k = 3

and

r = 6

into the equation gives

P = 3 \times 6^2 = 3 \times 36 = 108

.

Step-by-Step Solution

1

Set up the variation equation using constant of variation

k

P = k r^2

Direct variation with the square of a variable means

P

is directly proportional to

r^2

.

2

Substitute the initial values

P = 48

and

r = 4

to determine

k

48 = k \times 4^2 \implies 48 = 16k \implies k = 3

Finding the variation constant

k

allows us to establish a specific relationship between

P

and

r

.

3

Calculate

P

for

r = 6

using the specific equation

P = 3 r^2

P = 3 \times 6^2 = 3 \times 36 = 108

Evaluating the formula with the new input

r = 6

yields the required value of

P

.

Key Concept

Direct variation involving square powers

Question 4080Question →

Which word nearest in meaning to 'recalcitrant' correctly completes the sentence below?

Fill in the blanks below

Despite numerous attempts by the mediator to negotiate a settlement, the union leader remained in his refusal to concede any demands.

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Answer

intransigent (or obdurate / unyielding)

The word 'recalcitrant' means stubbornly resistant to authority, control, or persuasion. In the context of a labor dispute where a leader refuses to compromise despite mediation, 'intransigent' (or 'obdurate') accurately expresses this uncompromising stance.

Step-by-Step Solution

1

Analyze the meaning of the target word 'recalcitrant' within the sentence context.

The target word describes an individual who is stubbornly defiant of authority or resistant to compromise.

The surrounding phrase 'refusal to concede any demands' despite repeated mediation indicates an obstinate and inflexible posture.

2

Determine the word nearest in meaning that maintains both semantic precision and formal register.

'Intransigent' (or 'obdurate') serves as the exact contextual synonym.

Both 'recalcitrant' and 'intransigent' signify an unyielding refusal to change one's stance or come to an agreement.

Key Concept

Identifying high-register synonyms and words nearest in meaning in formal discourse

Estimated Time:1m 15s

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