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GCE A/L Common General Test study materials
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GCE A/L Common General Test practice questions

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Question 1Verbal Reasoning and Language Ability

Choose the word that best completes the sentence: The committee's report was so ______ that even its critics admitted they could find no factual error in it.

  1. redundant
  2. ambiguous
  3. hasty
  4. meticulous Correct answer.

Explanation

The clause 'even its critics admitted they could find no factual error' signals careful, thorough accuracy. 'Meticulous' means showing great attention to detail, which fits that meaning. The other words describe speed, vagueness or repetition, none of which would silence critics looking for errors.

Question 2Verbal Reasoning and Language Ability

Which word is closest in meaning to 'frugal' as used in the sentence 'She led a frugal life, repairing her clothes rather than replacing them'?

  1. generous
  2. thrifty Correct answer.
  3. wealthy
  4. careless

Explanation

'Frugal' describes someone who avoids unnecessary expense and uses resources sparingly. The example of repairing clothes rather than replacing them illustrates economy, which 'thrifty' captures. The remaining options describe financial status, giving behaviour or negligence, none of which matches the sense shown.

Question 3Verbal Reasoning and Language Ability

In the sentence 'The judge, having heard both arguments, reserved her decision', what is the grammatical function of the phrase 'having heard both arguments'?

  1. It is a participial phrase modifying the subject 'the judge'. Correct answer.
  2. It is a noun phrase acting as the object of 'reserved'.
  3. It is a prepositional phrase modifying 'decision'.
  4. It is an independent clause joined without a conjunction.

Explanation

The phrase begins with a participle ('having heard') and describes an action performed by the judge, so it modifies the subject. It is set off by commas and contains no finite verb, so it cannot be an independent clause. It does not name a thing, so it is not a noun phrase, and it lacks a preposition, so it is not prepositional.

Question 4Verbal Reasoning and Language Ability

Identify the sentence in which the relative clause is used correctly for the meaning given.

  1. The novel that won the prize was written in prison. Correct answer.
  2. The novel, that won the prize, was written in prison.
  3. The novel, that won the prize was written in prison.
  4. The novel which won the prize, was written in prison.

Explanation

A restrictive relative clause identifies which novel is meant and takes no commas; 'that' is the standard relative pronoun in this defining use. Non-defining clauses need 'which' and paired commas, and a single comma or none at all breaks the sentence structure. Only the first option keeps punctuation and pronoun consistent with a defining clause.

Question 5Verbal Reasoning and Language Ability

Five students P, Q, R, S and T sit in a row. Q sits at one end. R sits immediately to the right of P. S sits between Q and T. Who must sit in the middle seat?

  1. Q
  2. T Correct answer.
  3. R
  4. P

Explanation

If Q occupies the left end, S must be next to it and T next to S, filling seats one to three with Q, S, T. The remaining seats four and five go to P and R, with R immediately right of P, so the middle seat (third) is held by T. The same result follows if Q sits at the right end, mirrored.

Question 6Verbal Reasoning and Language Ability

Read the argument: 'Every candidate who attended the workshop passed the test. Nuwan passed the test. Therefore Nuwan attended the workshop.' Which statement best describes the reasoning?

  1. It is valid, because Nuwan is a candidate who passed the test.
  2. It is invalid, because the first premise is a generalisation about candidates.
  3. It is valid, because the first premise guarantees that all passers attended.
  4. It is invalid, because passing the test does not prove attendance at the workshop. Correct answer.

Explanation

The premise states that attending implies passing, not that passing implies attending. Concluding attendance from a pass reverses the direction of the conditional, which is the fallacy of affirming the consequent. Other routes to a pass, such as private study, remain possible.

Question 7Verbal Reasoning and Language Ability

Choose the pair of words that completes the analogy in the same relationship: 'author : manuscript :: ______ : ______'

  1. museum : painting
  2. reader : library
  3. editor : error
  4. sculptor : statue Correct answer.

Explanation

An author creates a manuscript, so the relationship is creator to the work created. A sculptor likewise creates a statue, preserving that relationship. The other pairs relate a place to a thing, a user to a place, or a corrector to a fault, none of which matches creation.

Question 8Verbal Reasoning and Language Ability

Which sentence uses the semicolon correctly?

  1. The results were inconclusive; which the team repeated.
  2. The results were inconclusive; because the team repeated the experiment.
  3. The results were inconclusive; and the team repeated the experiment.
  4. The results were inconclusive; the team repeated the experiment. Correct answer.

Explanation

A semicolon may join two independent clauses that are closely related and not already linked by a conjunction. The first option places a complete clause on each side. The others attach a conjunction, a subordinate clause or a relative clause, all of which need different punctuation.

Question 9Verbal Reasoning and Language Ability

The word 'bank' can mean a financial institution or the side of a river. This is best described as an example of:

  1. hyponymy
  2. polysemy Correct answer.
  3. synonymy
  4. antonymy

Explanation

Polysemy describes one word form carrying several related or historically connected senses, as with 'bank'. Synonymy concerns different words with similar meaning, antonymy concerns opposites, and hyponymy concerns a specific term falling under a broader one. Only polysemy names the phenomenon of multiple senses in a single form.

Question 10Verbal Reasoning and Language Ability

Choose the option that best replaces the underlined part to make the sentence grammatically correct: 'Neither the manager nor the clerks *was informed* about the new procedure.'

  1. was being informed
  2. has informed
  3. is informed
  4. were informed Correct answer.

Explanation

With 'neither ... nor', the verb agrees with the nearer subject, which here is the plural 'clerks'. The plural past form 'were informed' is therefore required. Singular forms conflict with 'clerks', and the active form 'has informed' changes the meaning and the number.

Question 11Verbal Reasoning and Language Ability

A notice reads: 'Students may borrow three books, provided that no book is kept for more than two weeks.' A student borrows three books and returns all of them after ten days. Which statement is true?

  1. The student has broken the rule because books must be returned in seven days.
  2. The student has complied with the notice. Correct answer.
  3. The student has complied only if one book was returned early.
  4. The student has broken the rule because three books were taken.

Explanation

The notice sets two conditions: a maximum of three books and a maximum loan period of two weeks. Ten days is within fourteen days and three books is the permitted maximum, so both conditions are met. No condition requires an early return of any single book.

Question 12Verbal Reasoning and Language Ability

Which option correctly completes the sentence with the appropriate conditional form? 'If the laboratory ______ the samples earlier, the results would have been published by now.'

  1. would process
  2. has processed
  3. processed
  4. had processed Correct answer.

Explanation

The main clause uses 'would have been published', which marks a third conditional about an unreal past. The if-clause of a third conditional takes the past perfect, 'had processed'. Simple past, present perfect and 'would' forms belong to other conditional patterns and clash with the main clause.

Question 13Verbal Reasoning and Language Ability

In the passage, 'The proposal was welcomed by the junior staff, but the senior managers remained lukewarm.' The word 'lukewarm' most nearly means:

  1. unenthusiastic Correct answer.
  2. confused
  3. indifferent to detail
  4. hostile

Explanation

'Lukewarm' literally means only slightly warm and figuratively means lacking enthusiasm. The contrast with 'welcomed' shows the managers were less than eager. 'Hostile' is too strong, since the text does not report opposition, and the other options describe different attitudes altogether.

Question 14Verbal Reasoning and Language Ability

Six people A, B, C, D, E and F are divided into three pairs. A refuses to pair with B, and C must pair with D. How many different pairings satisfy these conditions?

  1. 4
  2. 2
  3. 6
  4. 3 Correct answer.

Explanation

Fixing the pair C-D leaves A, B, E and F. A cannot pair with B, so A must pair with E or with F. If A pairs with E, then B pairs with F; if A pairs with F, then B pairs with E. That gives exactly two valid pairings, and no third arrangement avoids the forbidden pair.

Question 15Verbal Reasoning and Language Ability

Which sentence contains a dangling modifier?

  1. While walking through the archive, the researcher found the documents.
  2. Walking through the archive, the researcher found the documents.
  3. Walking through the archive, the documents were found by the researcher. Correct answer.
  4. The researcher, walking through the archive, found the documents.

Explanation

An introductory participial phrase must describe the subject of the main clause. In the first option the subject is 'the documents', which cannot walk, so the modifier dangles. The other options place the researcher as the subject or attach the phrase correctly.

Question 16Verbal Reasoning and Language Ability

Choose the word that best completes the sentence: The witness's account was ______, contradicted as it was by three independent records.

  1. verbose
  2. plausible
  3. tentative
  4. untenable Correct answer.

Explanation

The clause 'contradicted as it was by three independent records' shows the account cannot be maintained. 'Untenable' means not defensible against objection, which matches that logic. 'Plausible' contradicts the evidence, while the other options describe style or hesitation rather than defensibility.

Question 17Verbal Reasoning and Language Ability

'No sooner had the bell rung ______ the students left the hall.' Which word completes the sentence correctly?

  1. when
  2. that
  3. then
  4. than Correct answer.

Explanation

The fixed correlative pattern is 'no sooner ... than', used with the past perfect in the first clause and the past simple in the second. 'Then' is an adverb of time, 'when' belongs to patterns such as 'hardly ... when', and 'that' has no place in this construction.

Question 18Verbal Reasoning and Language Ability

A sign states: 'Entry is restricted to members and their guests.' Four people arrive: a member alone, a non-member with a member, a non-member alone, and a member with a non-member. How many of these four arrivals may enter?

  1. Three Correct answer.
  2. Two
  3. Four
  4. One

Explanation

Members may enter, and non-members may enter as guests of a member. The member alone qualifies, the non-member accompanying a member qualifies as a guest, and the member with a non-member qualifies as a member plus guest. Only the non-member alone fails, so three of the four arrivals may enter.

Question 19Verbal Reasoning and Language Ability

Which word is the odd one out in terms of meaning?

  1. momentary
  2. fleeting
  3. transient
  4. permanent Correct answer.

Explanation

'Transient', 'fleeting' and 'momentary' all describe something lasting only a short time. 'Permanent' describes something lasting indefinitely, so it is the opposite rather than a synonym. The odd-one-out question therefore points to the fourth option.

Question 20Verbal Reasoning and Language Ability

Read the argument: 'All effective teachers explain clearly. Some clear explainers use visual aids. Therefore some effective teachers use visual aids.' Which is the strongest criticism of this argument?

  1. The middle term 'clear explainers' is not distributed, so the conclusion does not follow. Correct answer.
  2. The first premise is false because some teachers explain poorly.
  3. The argument is valid but relies on an unstated definition of teaching.
  4. The conclusion is true but the premises are irrelevant to it.

Explanation

The premises say that effective teachers are clear explainers and that some clear explainers use visual aids. The group of clear explainers who use visual aids may lie entirely outside the group of effective teachers, so no overlap is guaranteed. In syllogistic terms the middle term is undistributed, which is the formal flaw.

Question 21Verbal Reasoning and Language Ability

Choose the correct passive transformation of 'The technician will calibrate the instrument tomorrow.'

  1. The instrument will calibrate by the technician tomorrow.
  2. The instrument is being calibrated by the technician tomorrow.
  3. The instrument would be calibrated by the technician tomorrow.
  4. The instrument will be calibrated by the technician tomorrow. Correct answer.

Explanation

The passive of a future with 'will' is formed with 'will be' plus the past participle, giving 'will be calibrated'. The agent follows in a 'by' phrase, and the time adverb is retained. The other options change the auxiliary, drop the participle or shift the modal.

Question 22Verbal Reasoning and Language Ability

In a code, each letter is replaced by the letter three places after it in the alphabet, so A becomes D. What does the coded word 'PHQ' decode to?

  1. QIR
  2. NEP
  3. MEN Correct answer.
  4. MEO

Explanation

Decoding reverses the shift, so each coded letter moves three places back. P becomes M, H becomes E and Q becomes N, giving MEN. Encoding forward instead, or shifting the wrong number of places, produces the other options.

Question 23Verbal Reasoning and Language Ability

Which sentence uses 'whose' correctly?

  1. The scientist whose research was funded by the grant resigned. Correct answer.
  2. The scientist who's research was funded by the grant resigned.
  3. The scientist whose research was funded by the grant he resigned.
  4. The scientist whose research was funded by the grant, resigned.

Explanation

'Whose' is the possessive relative pronoun and directly modifies 'research'. The first option uses it correctly in a defining relative clause without extra commas. The contraction 'who's' means 'who is', and the other options introduce punctuation or pronoun errors.

Question 24Verbal Reasoning and Language Ability

A survey found that students who ate breakfast scored higher on a test than students who skipped it. Which conclusion is best supported by this finding alone?

  1. There is an association between eating breakfast and higher scores. Correct answer.
  2. Eating breakfast causes higher test scores.
  3. Skipping breakfast is the only cause of low scores.
  4. Students who skip breakfast are less intelligent.

Explanation

An observational comparison can establish an association but not a causal direction. Other factors, such as sleep or study habits, may influence both breakfast and scores. Only the modest claim of association is warranted by the finding as described.

Question 25Verbal Reasoning and Language Ability

Which option correctly completes the sentence? 'The committee decided ______ the proposal until the budget was confirmed.'

  1. for deferring
  2. defer
  3. to defer Correct answer.
  4. deferring

Explanation

The verb 'decide' takes a to-infinitive complement when it refers to a future action, so 'decided to defer' is correct. Gerund and bare-infinitive forms do not follow 'decide' in this sense, and 'for deferring' is not an idiomatic complement here.

Question 26Verbal Reasoning and Language Ability

A library rule reads: 'A borrower may renew a book twice, but only if no other reader has reserved it.' Kamala has renewed a book once, and another reader has now reserved it. What does the rule allow?

  1. She may renew it if she returns it first and borrows it again.
  2. She may not renew it again while the reservation stands. Correct answer.
  3. She may renew it twice more because reservations do not count.
  4. She may renew it once more because one renewal remains.

Explanation

The permission to renew is conditional: it applies only when no other reader has reserved the book. Once a reservation exists, the condition fails, so no further renewal is allowed even though one renewal of the two has been used.

Question 27Verbal Reasoning and Language Ability

Choose the pair of words that completes the analogy in the same relationship: 'thermometer : temperature :: barometer : ______'

  1. altitude
  2. humidity
  3. pressure Correct answer.
  4. rainfall

Explanation

A thermometer is an instrument for measuring temperature, so the second pair must name what a barometer measures. A barometer measures atmospheric pressure, which preserves the instrument-to-quantity relationship.

Question 28Verbal Reasoning and Language Ability

In the sentence 'The supervisor, together with the two technicians, ______ responsible for checking the gauges each morning,' which verb form correctly fills the blank?

  1. are
  2. were
  3. is Correct answer.
  4. have been

Explanation

The subject is the singular noun 'supervisor'; the phrase 'together with the two technicians' is a parenthetical addition and does not change the number of the subject. A singular present-tense verb is therefore required, and 'is' is the only singular present form offered.

Question 29Verbal Reasoning and Language Ability

A notice states: 'Visitors must report to the front desk before entering the laboratory.' Ravi enters the laboratory first and reports to the desk afterwards. How should his action be judged against the notice?

  1. He did not comply, because visitors may never enter the laboratory.
  2. He complied, because he did report to the desk.
  3. He did not comply, because reporting must happen before entry. Correct answer.
  4. He complied, because the order of the two actions is unimportant.

Explanation

The word 'before' fixes a sequence: reporting must precede entering. Ravi reversed the sequence, so he failed the condition even though both actions occurred.

Question 30Verbal Reasoning and Language Ability

Read the argument: 'Every student who joined the debating society improved their public speaking. Dilani improved her public speaking. Therefore Dilani joined the debating society.' Which statement best describes the flaw?

  1. It assumes that improvement is impossible without practice.
  2. It generalises from a single example to a whole population.
  3. It attacks the person rather than the argument.
  4. It treats a sufficient condition as though it were necessary. Correct answer.

Explanation

Joining the society is presented as sufficient for improvement, but the argument reasons backwards as if it were the only route to improvement. Improvement may have many causes, so the conclusion does not follow.

Question 31Verbal Reasoning and Language Ability

Choose the word that best completes the sentence: 'The auditor's report was so ______ that even the board, accustomed to vague summaries, could follow every figure.'

  1. verbose
  2. redundant
  3. tentative
  4. lucid Correct answer.

Explanation

The clause 'even the board ... could follow every figure' signals that the report was unusually clear. 'Lucid' means clear and easy to follow, which fits the contrast with vague summaries.

Question 32Verbal Reasoning and Language Ability

In the sentence 'Having submitted the application late, the officer told the candidate that the form could not be processed,' what is the structural problem?

  1. The passive construction 'could not be processed' lacks an agent.
  2. The verb 'told' requires a gerund rather than an infinitive clause.
  3. The adverb 'late' should modify 'processed' rather than 'submitted'.
  4. The participle 'having submitted' attaches to the officer rather than the candidate. Correct answer.

Explanation

An introductory participle phrase is understood to describe the subject of the main clause, which here is 'the officer'. That produces the absurd reading that the officer submitted the application, so the modifier is dangling.

Question 33Verbal Reasoning and Language Ability

A message reads: 'The meeting has been postponed to Thursday, not cancelled, so please bring the draft report you prepared for Monday.' Which inference is best supported?

  1. The meeting will occur on Thursday and the report is still required. Correct answer.
  2. The meeting will no longer take place at all.
  3. The draft report is no longer needed.
  4. The report must be rewritten before Thursday.

Explanation

The message explicitly denies cancellation and names Thursday as the new date, while the instruction to bring the draft shows it remains needed. Only the option that keeps both facts is supported.

Question 34Verbal Reasoning and Language Ability

A code replaces each letter with the letter two places before it in the alphabet, so that D becomes B. Using the same code, what does 'JGPF' decode to?

  1. HERE
  2. IDPE
  3. HEND Correct answer.
  4. HFNE

Explanation

Decoding means shifting each letter back by two positions: J to H, G to E, P to N, and F to D. Applying the shift consistently to every letter gives HEND.

Question 35Verbal Reasoning and Language Ability

Which sentence uses the relative pronoun 'whose' correctly?

  1. The engineer whose designed the bridge received an award.
  2. The engineer whose won the competition received an award.
  3. The engineer whose the design won the competition received an award.
  4. The engineer, whose design won the competition, received an award. Correct answer.

Explanation

'Whose' is a possessive relative pronoun and must be followed by the noun possessed, here 'design'. The clause 'whose design won the competition' is correctly formed and correctly set off by commas as non-defining information.

Question 36Verbal Reasoning and Language Ability

A survey reports that students who ate breakfast scored higher on a test than students who skipped it. Which conclusion is most justified by the survey alone?

  1. All high-scoring students eat breakfast.
  2. Eating breakfast causes higher test scores.
  3. Skipping breakfast is the main cause of low scores.
  4. Students who ate breakfast scored higher in this survey. Correct answer.

Explanation

A survey of this kind establishes an association between two observed groups, nothing more. The causal and universal claims go beyond the evidence, while the descriptive statement stays within it.

Question 37Verbal Reasoning and Language Ability

Choose the option that best completes the sentence: 'The committee decided ______ the proposal until the budget was confirmed.'

  1. deferring
  2. for deferring
  3. defer
  4. to defer Correct answer.

Explanation

The verb 'decide' takes a to-infinitive complement, so 'decided to defer' is the correct pattern. The infinitive also fits the meaning of postponing action until the budget is known.

Question 38Verbal Reasoning and Language Ability

Read the argument: 'No candidate who missed the practical test was awarded a licence. Some candidates who attended every lecture missed the practical test. Therefore some candidates who attended every lecture were not awarded a licence.' Which statement about the argument is accurate?

  1. It is valid only if every candidate attended every lecture.
  2. It is invalid because the first premise is a negative statement.
  3. It is invalid because it generalises from too few cases.
  4. It is valid, since the conclusion follows necessarily from the premises. Correct answer.

Explanation

The second premise places some lecture-attenders inside the group that missed the test, and the first premise excludes that entire group from licensing. The conclusion therefore follows necessarily, making the argument valid.

Question 39Verbal Reasoning and Language Ability

A passage notes: 'Although the new timetable reduced waiting times, it lengthened journeys for passengers who had previously changed trains only once.' Which statement best captures the passage's overall point?

  1. The timetable improved one measure of service while worsening another. Correct answer.
  2. Passengers prefer longer journeys to shorter waits.
  3. Waiting times are the only measure of a timetable's success.
  4. The timetable was a failure for all passengers.

Explanation

The concessive 'although' sets a benefit against a drawback: shorter waits but longer journeys for a particular group. The passage therefore presents a mixed outcome rather than a uniform verdict.

Question 40Verbal Reasoning and Language Ability

Five reports are filed in order: P is filed before Q; R is filed after Q; S is filed before P; T is filed last. Which filing order satisfies all the conditions?

  1. P, S, Q, R, T
  2. S, Q, P, T, R
  3. S, P, Q, R, T Correct answer.
  4. Q, S, P, R, T

Explanation

The conditions require S before P, P before Q, Q before R, and T in the final position. Only the order S, P, Q, R, T places every report correctly relative to the others.

Question 41Numerical Reasoning and Quantitative Aptitude

A shopkeeper marks an item at Rs. 2,400 and offers a discount of 15%. What is the selling price?

  1. Rs. 2,160
  2. Rs. 2,340
  3. Rs. 2,280
  4. Rs. 2,040 Correct answer.

Explanation

The discount is 15% of 2,400, which equals 360. Subtracting gives 2,400 − 360 = 2,040. Equivalently, the selling price is 85% of 2,400 = 2,040.

Question 42Numerical Reasoning and Quantitative Aptitude

The ratio of two numbers is 3 : 5 and their sum is 96. What is the larger number?

  1. 36
  2. 48
  3. 60 Correct answer.
  4. 72

Explanation

The ratio has 3 + 5 = 8 equal parts, so one part is 96 ÷ 8 = 12. The larger number is 5 parts, giving 5 × 12 = 60.

Question 43Numerical Reasoning and Quantitative Aptitude

A train travels 180 km in 2 hours 30 minutes. What is its average speed in km/h?

  1. 72 Correct answer.
  2. 68
  3. 80
  4. 75

Explanation

2 hours 30 minutes is 2.5 hours. Average speed equals distance divided by time, so 180 ÷ 2.5 = 72 km/h.

Question 44Numerical Reasoning and Quantitative Aptitude

What is the average of the first ten positive even numbers 2, 4, 6, …, 20?

  1. 12
  2. 10
  3. 11 Correct answer.
  4. 14

Explanation

The sum of the first ten even numbers is 2 × (1 + 2 + … + 10) = 2 × 55 = 110. Dividing by 10 gives an average of 11.

Question 45Numerical Reasoning and Quantitative Aptitude

A sum of money doubles itself in 8 years under simple interest. In how many years will it become four times itself?

  1. 16 years
  2. 20 years
  3. 32 years
  4. 24 years Correct answer.

Explanation

Doubling means the interest earned in 8 years equals the principal, so the annual rate is 100 ÷ 8 = 12.5%. To become four times, the interest must equal three times the principal, needing 3 × 8 = 24 years.

Question 46Numerical Reasoning and Quantitative Aptitude

A can complete a job in 12 days and B in 18 days. Working together, in how many days will they finish it?

  1. 7.2 days Correct answer.
  2. 9.0 days
  3. 6.0 days
  4. 7.5 days

Explanation

A does 1/12 and B does 1/18 of the work per day. Together they do 3/36 + 2/36 = 5/36 per day, so the job takes 36/5 = 7.2 days.

Question 47Numerical Reasoning and Quantitative Aptitude

A rectangular field is 40 m long and 30 m wide. A path 2 m wide runs inside along its entire boundary. What is the area of the path?

  1. 276 m²
  2. 144 m²
  3. 300 m²
  4. 264 m² Correct answer.

Explanation

The inner rectangle measures 36 m by 26 m, with area 936 m². The whole field is 1,200 m², so the path area is 1,200 − 936 = 264 m².

Question 48Numerical Reasoning and Quantitative Aptitude

If 3x + 7 = 2x + 15, what is the value of x?

  1. 11
  2. 4
  3. 6
  4. 8 Correct answer.

Explanation

Subtracting 2x from both sides gives x + 7 = 15. Subtracting 7 then gives x = 8.

Question 49Numerical Reasoning and Quantitative Aptitude

A number is increased by 20% and the result is then decreased by 20%. The final value compared with the original is:

  1. 2% less
  2. 4% less Correct answer.
  3. unchanged
  4. 4% more

Explanation

Multiplying by 1.20 and then by 0.80 gives 0.96 of the original. The final value is therefore 4% less than the original, because the decrease applies to the larger intermediate value.

Question 50Numerical Reasoning and Quantitative Aptitude

The present ages of a father and son are in the ratio 7 : 2. Five years ago the ratio was 6 : 1. What is the son's present age?

  1. 6 years
  2. 10 years Correct answer.
  3. 12 years
  4. 8 years

Explanation

Let the ages be 7k and 2k. Then (7k − 5)/(2k − 5) = 6/1, so 7k − 5 = 12k − 30, giving 5k = 25 and k = 5. The son's age is 2k = 10 years.