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Grammatical Structure

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Question 581Question →

Which of the following options correctly renders the sentence below in reported speech?

'Why did you not inform the bursar that the examination materials had arrived this morning?' the registrar asked the administrative officer.

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Answer: The registrar asked the administrative officer why he had not informed the bursar that the examination materials had arrived that morning.

Answer

The registrar asked the administrative officer why he had not informed the bursar that the examination materials had arrived that morning.
The sentence accurately converts direct speech to indirect speech by changing the simple past 'did not inform' to past perfect 'had not informed', modifying the demonstrative phrase 'this morning' to 'that morning', and applying normal statement word order ('why he had not informed').

Step-by-Step Solution

1
Identify the reporting verb and original clause structure.
The reporting verb 'asked' is in the past tense, and the direct clause is a WH-question containing simple past negative ('did not inform') and a time reference ('this morning').
Past reporting verbs require tense backshift and adjustment of demonstratives and word order.
2
Backshift the main verb tense and adjust time expressions.
Simple past 'did not inform' backshifts to past perfect 'had not informed'. The past perfect 'had arrived' remains unchanged. 'This morning' becomes 'that morning'.
Reporting events from a past point of perspective requires shifting past simple to past perfect and proximal time expressions to distal ones.
3
Apply declarative word order for indirect questions.
The inverted question order 'why did you not inform' becomes normal subject-verb statement order 'why he had not informed'.
Indirect questions do not use auxiliary inversion or question marks.

Key Concept

Tense backshift, word order transformation, and time adverbial adjustments in reported questions
Estimated Time:1m 30s
Question 582Question →

Supply the pronoun that correctly fills the blank in the sentence below, maintaining standard grammatical agreement.

Fill in the blanks below

Professor Nnamdi is one of those meticulous scholars who never compromise ethical standards for personal fame.
Show answer & explanation

Answer

their
In the sentence construction 'one of those [plural noun] who [plural verb]', the relative pronoun 'who' takes the plural noun 'scholars' as its antecedent. Consequently, the modifying relative clause requires the plural possessive pronoun 'their' to agree in number with 'scholars'.

Step-by-Step Solution

1
Identify the relative pronoun and its true antecedent.
In the construction 'one of those scholars who...', the relative pronoun 'who' refers to the plural object of the preposition, 'scholars', not to the singular subject 'one'.
The clause 'who never compromise...' modifies the entire group of 'scholars' who share this attribute.
2
Determine the plural possessive pronoun required for agreement.
Because 'scholars' is a plural noun, the pronoun replacing or referring back to it must also be plural.
Pronouns must agree in number with their antecedent. A plural antecedent ('scholars') requires the plural possessive pronoun 'their'.

Key Concept

Relative Pronoun Antecedent Agreement in 'One of those... who' Constructions
Estimated Time:1m 0s
Question 583Question →

Following the leak of classified financial documents, the board of directors insisted that the chief executive officer ________ an emergency press statement to clarify the situation. Which of the following verb forms correctly completes the sentence?

Show answer & explanation

Answer: tender

Answer

The base verb form 'tender' is grammatically correct because the sentence employs the mandative subjunctive mood.
In formal English grammar, when verbs expressing commands, requests, resolutions, or insistence (such as 'insist', 'demand', 'recommend', 'propose') are followed by a 'that'-clause, the verb in that clause must take the subjunctive mood. The mandative subjunctive takes the base form of the verb (bare infinitive) without any suffix modifications for tense or subject agreement. Therefore, the base verb form 'tender' is correct.

Step-by-Step Solution

1
Identify the main governing verb and clause structure.
The main clause contains the verb of demand/insistence 'insisted that'.
Verbs expressing demands, recommendations, or resolutions trigger the mandative subjunctive in subordinate 'that'-clauses.
2
Apply the grammatical rule for mandative subjunctive constructions.
The verb in the subordinate clause must remain in its uninflected base form (bare infinitive).
Subjunctive clauses following verbs like 'insist', 'demand', 'recommend', or 'resolve' do not take tense inflections (-ed) or third-person agreement markers (-s).
3
Select the uninflected base verb form among the given options.
'tender' is chosen as the bare infinitive form.
It strictly complies with formal standard English subjunctive requirements for JAMB UTME.

Key Concept

Mandative Subjunctive Mood
Estimated Time:1m 30s
Question 584Question →

Which of the options correctly completes the sentence below?

'Every one of the senior delegates who attended the international summit ______ that the proposed treaty, if ratified, will significantly impact regional trade.'

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Answer: believes

Answer

The option containing 'believes' is correct.
The main clause subject is the singular indefinite pronoun 'Every one'. Neither intervening prepositional phrases ('of the senior delegates') nor relative clauses ('who attended the international summit') affect the singular number of the head subject. Consequently, the singular verb 'believes' is required.

Step-by-Step Solution

1
Identify the main grammatical subject of the sentence
The subject of the main clause is 'Every one', which is a singular indefinite pronoun phrase.
The noun phrase 'the senior delegates' is embedded within a prepositional phrase ('of the senior delegates') and does not function as the main head noun.
2
Apply the appropriate concord rule for indefinite pronouns
Indefinite pronouns such as 'each', 'every one', and 'either' take singular verbs.
Grammatical concord dictates that 'Every one' requires a third-person singular verb inflection in the present tense.
3
Select the correct verb form
'Believes' is the third-person singular present tense form.
It matches the singular subject 'Every one' correctly.

Key Concept

Indefinite Pronoun Concord with Intervening Modifiers
Question 585Question →

Complete the sentence below by filling in the blank with the grammatically correct form of the verb to show the proper sequence of past events.

Fill in the blanks below

Before the school inspector arrived yesterday, the principal the morning assembly.
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Answer

had concluded (or had finished / had ended / had dismissed)
The sentence establishes a sequence of two past actions anchored by the time marker 'yesterday'. Because the principal's action was completed prior to the inspector's arrival, the past perfect aspect (auxiliary 'had' followed by the past participle form of the main verb) must be used.

Step-by-Step Solution

1
Analyze the temporal relationship between the two events in the past.
The dismissal of the morning assembly took place prior to the arrival of the school inspector.
When expressing two actions that took place in the past where one was completed before the other, the earlier action requires the past perfect tense ('had' + past participle).

Key Concept

Past Perfect Tense Sequence
Question 586Question →

Read the sentence below carefully. Which pronoun accurately maintains grammatical agreement with its antecedent to fill the blank?

Fill in the blanks below

The panel of independent auditors, alongside the forensic investigators, completed report on the financial discrepancy before the regulatory deadline.
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Answer

The correct pronoun to complete the sentence is 'its'.
The head noun of the subject is the singular collective noun 'panel', which acts as a unified entity in submitting a single report. Prepositional phrases introduced by 'alongside' are syntactically parenthetical and do not pluralize the subject. Therefore, the singular possessive pronoun 'its' correctly maintains agreement with 'panel'.

Step-by-Step Solution

1
Identify the primary antecedent in the sentence structure.
The grammatical subject and antecedent is the singular collective noun 'panel'.
Intervening phrases introduced by quasi-conjunctions or prepositions such as 'alongside the forensic investigators' do not alter the number of the head noun.
2
Select the pronoun that matches the grammatical number and gender of the antecedent.
Since 'panel' functions as a single unified body, it requires the singular neuter possessive pronoun 'its'.
Attracting the pronoun to the nearer plural noun 'investigators' creates a proximity error.

Key Concept

Pronoun-Antecedent Agreement with Collective Nouns and Intervening Phrases
Question 587Question →

Complete the following sentence by identifying the correct concessive conjunction that completes the clause structure.

Fill in the blanks below

the permanent secretary presented detailed financial records, the probe panel uncovered major discrepancies in the procurement accounts.
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Answer

The sentence requires a concessive conjunction such as 'Much as' or 'Inasmuch as' to contrast the action of presenting detailed financial records with the unexpected discovery of major discrepancies.
The concessive conjunction 'Much as' correctly introduces a subordinate clause of concession, indicating that despite the thorough presentation of financial records, the probe panel still found discrepancies. It fits the formal register and syntax of complex sentence structures.

Step-by-Step Solution

1
Analyze the clause structure and semantic relationship between the main clause and the subordinate clause.
The subordinate clause describes an attempt/action ('presented detailed financial records') while the main clause highlights an opposing outcome ('uncovered major discrepancies').
This establishes a concessive relationship where the main clause occurs despite the event in the subordinate clause.
2
Select the appropriate concessive conjunction that functions fronted before a finite clause.
'Much as' (or 'Inasmuch as') correctly introduces a concessive clause of degree/extent meaning 'although to a great extent'.
It maintains both grammatical precision and appropriate academic register for complex sentence structure.

Key Concept

Concessive Subordinate Clauses and Conjunctions
Estimated Time:1m 30s
Question 588Question →

The principal expressed that he would rather the disciplinary panel ________ the matter thoroughly before publishing the official report. Which of the following verb forms correctly completes the sentence?

Show answer & explanation

Answer: investigated

Answer

The verb form that correctly completes the sentence is 'investigated'.
The correct choice is 'investigated'. In standard English grammar, when the expression 'would rather' is followed by a clause with a different subject (in this case, 'the disciplinary panel'), the verb must take the simple past form to denote a present or future preference.

Step-by-Step Solution

1
Analyze the sentence structure following 'would rather'
The main subject ('he') is different from the subject in the subordinate clause ('the disciplinary panel').
When subjects differ in 'would rather' constructions, special subjunctive/unreal past tense rules apply.
2
Determine the time frame of the action
The action refers to a present or future expectation before publishing the report.
Time reference determines whether simple past or past perfect form is required.
3
Select the correct verb tense form
The simple past form 'investigated' must be selected.
For present/future reference with a change of subject after 'would rather', standard English requires the simple past tense form.

Key Concept

Unreal Past Tense with 'Would Rather'
Estimated Time:45s
Question 589Question →

Select the pair of verb forms that correctly completes the sentence below according to the rules of subject-verb agreement:

'Not only the lead researcher but also his assistants _______ committed to publishing the report, although neither of the sponsor organizations _______ willing to fund the follow-up study.'

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Answer: are / is

Answer

The pair 'are / is' correctly completes the sentence.
The option containing 'are / is' accurately satisfies both concord rules present in the sentence. First, when subject nouns are joined by 'not only ... but also', proximity concord dictates that the verb agrees with the subject nearest to it ('his assistants' -> plural verb 'are'). Second, the indefinite pronoun 'neither' functions as a singular subject, requiring the singular verb form 'is' regardless of the plural noun 'sponsor organizations' within the modifying prepositional phrase.

Step-by-Step Solution

1
Analyze the first clause containing the correlated conjunction 'Not only ... but also ...'
Under the principle of proximity concord, when subjects are connected by 'not only ... but also', the verb agrees in number with the noun subject closest to it. Here, 'his assistants' (plural) is closest to the verb, requiring the plural verb 'are'.
Correlated conjunctions require the verb to match the nearest subject element.
2
Analyze the second clause containing the structure 'neither of the sponsor organizations'
The head of the noun phrase is the indefinite pronoun 'neither', which is grammatically singular. The plural noun 'sponsor organizations' is inside a prepositional phrase modifier and does not govern the verb, so the singular verb 'is' is required.
Indefinite pronouns such as 'neither' take singular verbs regardless of intervening plural complement phrases.

Key Concept

Proximity concord with correlated subjects and singular agreement with indefinite pronouns
Question 590Question →

Consider the following direct speech statement made during an official university senate hearing: "If the administration had implemented the revised welfare policy last year, the staff union would not be striking today," the registrar remarked. Which of the following options correctly converts this statement into indirect speech?

Show answer & explanation

Answer: The registrar remarked that if the administration had implemented the revised welfare policy the previous year, the staff union would not be striking that day.

Answer

The registrar remarked that if the administration had implemented the revised welfare policy the previous year, the staff union would not be striking that day.
The correct indirect speech conversion accurately preserves the past perfect conditional verb form ('had implemented'), retains the appropriate modal expression ('would not be striking'), and shifts both time adverbs ('last year' becoming 'the previous year' and 'today' becoming 'that day').

Step-by-Step Solution

1
Analyze the tense and conditional structure in the direct speech clause.
The clause 'had implemented' is in the past perfect tense (third conditional condition), which remains unchanged in reported speech. 'would not be striking' represents a mixed conditional continuous result.
Past perfect tenses do not backshift further when reported after a past-tense reporting verb.
2
Identify and convert temporal adverbials.
'last year' shifts to 'the previous year' (or 'the year before'), and 'today' shifts to 'that day'.
Adverbials of time must shift to reflect the indirect, past point of reference.
3
Combine the reported clauses with the reporting verb.
The complete correct indirect statement maintains the exact conditional logic and updates all temporal indicators accurately.
Ensures full grammatical precision and meaning retention.

Key Concept

Reporting Mixed Conditionals and Shifting Temporal Adverbials in Indirect Speech
Estimated Time:1m 30s
Question 591Question →

Fill in the blanks in the sentence below with the grammatically correct verb forms that satisfy the rules of subject-verb concord.

Fill in the blanks below

Neither the chief editor nor the senior reporters aware that a series of investigative articles published without the management's prior approval.
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Answer

The first blank requires 'were' and the second blank requires 'was'.
The correct verb forms are 'were' for the first blank and 'was' for the second blank. The first blank is governed by the proximity rule for correlated subjects ('neither... nor'), which mandates agreement with the plural noun 'senior reporters'. The second blank requires the singular verb 'was' because the functional subject of the clause is the singular head noun 'series'.

Step-by-Step Solution

1
Determine the subject and applying concord rules for the first blank.
The subject consists of two elements connected by 'neither... nor': 'the chief editor' (singular) and 'the senior reporters' (plural).
When subjects are joined by correlative conjunctions such as 'neither... nor', the principle of proximity applies, meaning the verb must agree with the subject closest to it ('senior reporters'). Therefore, the plural past verb 'were' is correct.
2
Determine the subject and applying concord rules for the second blank.
The subject of the subordinate clause is the noun phrase 'a series of investigative articles'.
The head noun of the phrase is 'series', which is singular. Collective noun phrases formed by 'a series of' take a singular verb despite the intervening plural noun ('articles'). Therefore, the singular past verb 'was' is required.

Key Concept

Subject-Verb Agreement (Proximity Concord and Noun Phrase Head Concord)
Question 592Question →

Read the direct speech statement below and complete the reported speech sentence by supplying the correct expressions for each blank. What are the appropriate words to complete the indirect speech transformation?

Fill in the blanks below

Direct Speech: "Did the accreditation panel inspect the newly commissioned laboratory yesterday?" the provost inquired.

Reported Speech: The provost inquired whether the accreditation panel the newly commissioned laboratory .
Show answer & explanation

Answer

blank_1: had inspected; blank_2: the day before (or the previous day)
In reported speech with a past reporting verb like 'inquired', direct questions in the simple past tense ('did inspect') backshift to the past perfect tense ('had inspected'). Simultaneously, the temporal adverbial 'yesterday' converts to 'the day before' or 'the previous day'.

Step-by-Step Solution

1
Identify the verb tense in the direct speech question.
The direct question uses the simple past tense ('did inspect').
When converting a sentence from direct speech to indirect speech with a past tense reporting verb ('inquired'), simple past tense verbs must backshift to the past perfect tense ('had inspected').
2
Determine the corresponding shift for the time adverbial.
'yesterday' shifts to 'the day before' or 'the previous day'.
Time words referring to a specific past day relative to the time of speaking must be adjusted to match the past perspective of the reporting verb.

Key Concept

Backshifting Simple Past tense to Past Perfect tense and modifying temporal adverbials in reported questions.
Estimated Time:1m 30s
Question 593Question →

Which of the following options logically and grammatically completes the sentence below?

"To minimize water loss during the severe drought, ___________."

Show answer & explanation

Answer: farmers must prune the lower leaves of the crops regularly.

Answer

The option stating 'farmers must prune the lower leaves of the crops regularly.' is correct because the subject 'farmers' logically performs the action stated in the introductory modifying phrase 'To minimize water loss'.
The introductory infinitival phrase 'To minimize water loss during the severe drought' functions as an adverbial modifier expressing purpose. To avoid a dangling modifier error, the main clause must begin with the entity that performs this action. The phrase starting with 'farmers' correctly identifies who is minimizing the water loss, followed by the appropriate adverb 'regularly' modifying the verb 'prune'.

Step-by-Step Solution

1
Identify the introductory modifying phrase in the sentence stem.
The phrase is an infinitival modifying phrase: 'To minimize water loss during the severe drought'.
An introductory modifying phrase must immediately precede the noun phrase that logically performs the implied action.
2
Determine the logical subject of the action 'to minimize water loss'.
Human agents ('farmers') are the logical subject who take action to minimize water loss.
Crops or leaves cannot intentionally take measures to minimize water loss.
3
Evaluate each option for correct modifier placement and appropriate adverbial form.
The option beginning with 'farmers' and ending with the adverb 'regularly' correctly aligns the subject and uses the proper adverbial form.
Options placing 'leaves' or 'pruning' immediately after the introductory phrase commit dangling modifier errors, and using the adjective 'continuous' to modify a verb is ungrammatical.

Key Concept

Adjectives, Adverbs, and Modifiers: Participial and Infinitival Modifier Alignment
Question 594Question →

Fill in the blank to complete the indirect speech transformation accurately.

Fill in the blanks below

Direct statement: "I shall present the updated audit report tomorrow," the accountant promised.

Reported statement: The accountant promised that he the updated audit report the following day.
Show answer & explanation

Answer

The blank must be filled with 'would present'.
When converting direct speech into indirect speech with a past reporting verb ('promised'), the first-person modal verb 'shall' expressing a future commitment shifts to 'would' to match the third-person pronoun ('he').

Step-by-Step Solution

1
Identify the original tense and modal auxiliary in the direct statement.
The direct statement uses 'shall present' to express future action with a first-person pronoun ('I').
Determining the modal verb and reporting verb tense is essential for correct tense backshifting.
2
Apply backshift rules for modal verbs when the reporting verb is in the past tense ('promised').
'Shall' expressing future intention backshifts to 'would' when changing the subject from 'I' to 'he'.
When changing from direct to reported speech with a past reporting verb, future modals ('shall' / 'will') shift to their past conditional counterparts ('would').

Key Concept

Modal Verb Backshifting in Reported Speech
Estimated Time:1m 0s
Question 595Question →

The judicial panel agreed to admit the electronic transaction records, _______ their authenticity had been verified by independent cyber-forensic experts. Which subordinating conjunction correctly completes the clause structure to express the rationale for the panel's decision?

Show answer & explanation

Answer: inasmuch as

Answer

The correct subordinating conjunction is 'inasmuch as', which properly joins the subordinate clause of cause/reason to the main clause.
The phrase 'inasmuch as' functions as a formal subordinating conjunction introduced to express a reason or cause. Because the segment following the blank contains a full finite subject-verb clause ('their authenticity had been verified...'), a subordinating conjunction is grammatically required to establish the causal relationship.

Step-by-Step Solution

1
Analyze the clause structure following the blank space.
The structure 'their authenticity had been verified by independent cyber-forensic experts' is a complete finite clause with a subject ('their authenticity') and a verb phrase ('had been verified').
Identifying whether the structure is a clause or a noun phrase dictates whether a conjunction or a preposition is required.
2
Determine the logical relationship between the main clause and the subordinate clause.
The verification of authenticity provides the cause/justification for admitting the records.
The connector must express reason/cause rather than concession or contrast.
3
Evaluate the grammatical category and meaning of the options.
'Inasmuch as' is a formal subordinating conjunction of cause that fits both the grammatical requirement (introducing a finite clause) and semantic requirement (expressing reason).
Prepositional expressions like 'in spite of' cannot introduce full finite clauses without structural errors.

Key Concept

Subordinating Conjunctions of Cause and Clause Structure
Question 596Question →

Supply the correct verb form to complete the temporal sequence in the sentence below.

Fill in the blanks below

By the time the regulatory agency inspects the facility next Friday, the engineering team the structural repairs.
Show answer & explanation

Answer

will have completed
The phrase 'will have completed' correctly uses the future perfect tense to show that the action of finishing the repairs will occur before the future inspection takes place.

Step-by-Step Solution

1
Analyze the temporal expression and clause structure.
The clause beginning with 'By the time...' uses the present simple verb 'inspects' to mark a future point in time.
Time clauses introduced by 'by the time' establish a future deadline before which another action must be finished.
2
Apply the appropriate verb tense and aspect.
The main clause requires the future perfect tense ('will have completed').
The future perfect tense (will + have + past participle) expresses an action that will be completed prior to a specified future reference point.

Key Concept

Future Perfect Tense with Temporal Adverbial Clauses
Question 597Question →

Supply the correct form of the verb 'examine' to complete the sentence below.

Fill in the blanks below

The lead investigator expressed deep regret, wishing that the forensic team the crime scene more meticulously before the heavy torrential rain washed away the vital evidence.
Show answer & explanation

Answer

had examined
The past perfect form 'had examined' correctly expresses unreal past time (a regret about a prior past event that did not happen). Because the investigation needed to happen before the rain destroyed the evidence in the past, the past perfect aspect must be used.

Step-by-Step Solution

1
Analyze the temporal context and structural requirement of the sub-clause following the verb 'wishing'.
The main context is set in the past ('expressed', 'washed away'), indicating that the regret concerns a past action that did not occur.
Expressing regret about an unfulfilled action in the past requires the unreal past construction using the past perfect tense.
2
Form the correct past perfect tense of the verb 'examine'.
Combine the auxiliary verb 'had' with the past participle form 'examined' to get 'had examined'.
The past perfect tense ('had' + past participle) is grammatically mandated after 'wish' when referring to past time.

Key Concept

Unreal Past with 'Wish' (Past Perfect for Past Regret)
Question 598Question →

Which connective correctly completes the sentence below while maintaining standard subordinating clause structure?

'The commission approved the capital expenditure request, ______ the audit panel submitted a certified risk assessment report.'

Show answer & explanation

Answer: inasmuch as

Answer

The connective 'inasmuch as' correctly completes the sentence because it is a subordinating conjunction of reason that introduces a full finite clause.
The choice 'inasmuch as' serves as a formal subordinating conjunction meaning 'since' or 'because'. It correctly connects the main clause ('The commission approved...') to the subordinate finite clause ('the audit panel submitted...').

Step-by-Step Solution

1
Analyze the structure of the dependent clause following the blank space.
The element following the blank is a complete finite clause containing a subject ('the audit panel') and a conjugated verb phrase ('submitted').
Determining whether a finite clause or noun phrase follows dictates whether a conjunction or preposition is required.
2
Evaluate the syntactic function of each option choice.
'Inasmuch as' is a formal subordinating conjunction of cause/reason suitable for introducing finite clauses. 'In spite' and 'with regard' are truncated prepositional phrases missing mandatory prepositions ('of' and 'to'). 'Owing to that' is a non-standard construction in formal academic English.
Only a grammatically complete subordinating conjunction can join a subordinate finite clause to a main clause.
3
Confirm semantic alignment and grammatical correctness.
'Inasmuch as' logically establishes that the submission of the audit report was the reason/basis for approving the expenditure request.
The causal relationship between the approval and the report submission requires a conjunction meaning 'since' or 'because'.

Key Concept

Subordinating Conjunctions and Clause Structure
Estimated Time:1m 30s
Question 599Question →

The committee was established with a view _____ streamlining the administrative procedures of the institution. Which preposition correctly completes the sentence?

Show answer & explanation

Answer: to

Answer

The correct preposition is 'to', completing the fixed phrase 'with a view to'.
The phrase 'with a view to' is a standard fixed compound preposition in English that expresses purpose and takes a gerund object (in this case, 'streamlining').

Step-by-Step Solution

1
Identify the multi-word prepositional structure in the sentence.
The target structure is 'with a view _____'.
The sentence expresses the underlying aim or intention of establishing the committee.
2
Recall the fixed idiomatic collocation for expressing intention with this noun phrase.
The correct fixed compound preposition is 'with a view to', which is followed by a gerund ('streamlining').
Standard English grammar dictates that 'with a view' takes 'to' as its dependent preposition, not 'of', 'at', or 'for'.

Key Concept

Fixed Multi-word Prepositional Phrases
Estimated Time:50s
Question 600Question →

Which preposition correctly completes the fixed prepositional phrase in the sentence below?

Fill in the blanks below

The newly proposed civil service policy is completely at variance the existing constitutional provisions regarding workers' rights.
Show answer & explanation

Answer

The correct preposition to complete the blank is 'with'.
The fixed prepositional phrase 'at variance with' is an established idiom meaning to be in disagreement or inconsistency with something. Therefore, 'with' is the precise and correct word required.

Step-by-Step Solution

1
Identify the multi-word prepositional idiom being used in the sentence structure.
The sentence uses the idiomatic construction 'at variance', which signifies conflict, contradiction, or disagreement.
Recognizing fixed idiomatic collocations is necessary to select the correct complementing preposition.
2
Select the standard dependent preposition required by 'at variance'.
The standard English idiom is strictly 'at variance with'.
'With' is the only grammatically acceptable preposition that collocates with 'at variance' when specifying the item being contradicted.

Key Concept

Prepositions and Prepositional Phrases: Fixed Idiomatic Collocations
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