Judgment and problem solving — SSC CGL Reasoning Notes

Concepts and rules

These questions give a short statement and 2 items marked I and II. You decide whether each conclusion follows, each assumption is implicit, or each argument is strong. Treat the statement as true even if it seems unusual.

Conclusion: follows only if it is definitely true from the statement, using only the statement and plain common knowledge. Probably true, possibly true or a good idea is not enough.

Words like only, all, always, never, definitely and must in a conclusion make it extreme; it follows only if the statement itself is that strong.

Assumption: something the speaker takes for granted without saying it. It is implicit if the statement would make no sense, or the advice or action would be pointless, without it.

Negation test for assumptions: reverse the assumption. If the statement then becomes absurd, the assumption is implicit; if the statement still stands, it is not.

An advertisement, notice, appeal or advice assumes that it will have some effect on the people it addresses and that they are able to act on it.

Argument: strong if it is directly related to the question, deals with an important aspect and gives a sound reason or established fact. Weak if it is irrelevant, trivial, emotional, a mere opinion, exaggerated, or based on a false generalisation.

A Yes argument and a No argument can both be strong; strength does not mean the side is correct, only that the reason deserves weight.

Method and shortcuts

Step 1: identify the type: conclusion (must be true), assumption (taken for granted) or argument (reason for or against).

Step 2: underline the key words of the statement: all, some, only, may, should, because, to encourage, and so on.

Step 3 for conclusions: ask whether the conclusion could be false while the statement is true. If yes, it does not follow.

Step 3 for assumptions: apply the negation test. Step 3 for arguments: check relevance, importance and reasoning in that order.

Shortcut: a purpose stated in the statement (to encourage, in order to) gives a conclusion or assumption that follows almost directly; a prediction about the future (will be banned, will clear) rarely follows.

Standard options: (a) Only I (b) Only II (c) Both I and II (d) Neither I nor II. Judge I and II separately, then pick the option.

Example 1: conclusion from a rule

Question: Statement: All candidates who scored above 140 in Tier I have been called for Tier II. Ritu scored 152 in Tier I. Conclusions: I. Ritu has been called for Tier II. II. Ritu will clear Tier II.

Solution: 152 is above 140, and the rule covers all such candidates, so I must be true. Nothing in the statement tells us how Ritu will do in Tier II, so II is only a guess about the future.

Answer: Only I follows.

Example 2: assumptions behind a notice

Question: Statement: The municipal corporation has asked residents of Ward 12 to boil drinking water for the next 7 days. Assumptions: I. The water supplied to Ward 12 may be unsafe to drink. II. Residents of Ward 12 are able to boil water.

Solution: Negate I: if the water were surely safe, the advice would be pointless, so I is implicit. Negate II: if residents could not boil water, the advice could not be followed, so II is implicit too.

Answer: Both I and II are implicit.

Example 3: strong and weak arguments

Question: Should mobile phones be banned inside classrooms? Arguments: I. Yes, phones distract students during lessons and can be used to cheat in tests. II. No, every student in India owns a costly smartphone.

Solution: I is directly related and gives a real reason about learning and fairness, so it is strong. II is a false generalisation, and owning a phone is not a reason to use it in class, so it is weak.

Answer: Only I is strong.

Example 4: stated purpose versus prediction

Question: Statement: The government has cut the GST on electric two-wheelers from 12% to 5% to encourage people to buy them. Conclusions: I. Petrol two-wheelers will be banned soon. II. The government wants more people to buy electric two-wheelers. (a) Only I follows (b) Only II follows (c) Both I and II follow (d) Neither I nor II follows

Solution: II restates the purpose given in the statement (to encourage people to buy them), so it follows. I is a prediction of a ban that the statement never mentions; encouraging one option does not mean banning the other.

Answer: (b) Only II follows.

Example 5: extreme assumptions

Question: Statement: Ramesh tells his friend, Take the 7:40 local; the 8:10 local is always overcrowded. Assumptions: I. The friend will reach office on time only if he takes the 7:40 local. II. The 7:40 local is never crowded. (a) Only I is implicit (b) Only II is implicit (c) Both I and II are implicit (d) Neither I nor II is implicit

Solution: The advice is about avoiding the crowd, not about reaching on time, so I is not assumed; negate I and the advice still makes sense. For II, Ramesh needs only that the 7:40 local is less crowded than the 8:10, not that it is never crowded; never is extreme.

Answer: (d) Neither I nor II is implicit.

Example 6: both sides strong

Question: Should the minimum age for a car driving licence be raised from 18 to 21 years? Arguments: I. Yes, road transport data show that drivers aged 18 to 20 are involved in a higher share of accidents per licence than older drivers. II. No, people aged 18 to 20 are legal adults, and many of them need to drive for work or to support their families. (a) Only I is strong (b) Only II is strong (c) Both I and II are strong (d) Neither I nor II is strong

Solution: I rests on data about safety, the main purpose of a licence rule, so it is strong. II points to a real and important cost of the change (legal adulthood and livelihoods), not an emotional appeal, so it is also strong.

Answer: (c) Both I and II are strong.

Common mistakes

Accepting a conclusion because it is likely or sensible. It must be certain from the statement.

Using outside knowledge to reject or accept. Judge only from the statement, even if it differs from what you know.

Missing extreme words. Only, always and never in a conclusion or assumption usually make it fail.

Calling an argument strong because you agree with it. Strength depends on relevance and reasoning, not on your opinion.

Assuming that only one of I and II can be right. Both can follow, and both can fail.

Practice questions

Q1. Statement: No train from Patna to Delhi leaves before 6 a.m. on Sundays. Train X leaves Patna for Delhi at 5:30 a.m. on every day it runs. Conclusions: I. Train X does not run on Sundays. II. Train X runs only on weekdays. (a) Only I follows (b) Only II follows (c) Both I and II follow (d) Neither I nor II follows

Q2. Statement: Notice in a library: Mobile phones must be kept on silent mode inside the reading hall. Assumptions: I. Ringing phones can disturb readers. II. People bring mobile phones into the reading hall. (a) Only I is implicit (b) Only II is implicit (c) Both I and II are implicit (d) Neither I nor II is implicit

Q3. Should private cars be banned in city centres on weekends? Arguments: I. Yes, some other countries have done it. II. No, people love their cars. (a) Only I is strong (b) Only II is strong (c) Both I and II are strong (d) Neither I nor II is strong

Answers

Q1. (a) If Train X ran on a Sunday it would leave at 5:30 a.m., before 6 a.m., which the statement forbids; so I is certain. II fails: Train X may run on Saturdays too, so only on weekdays is not certain.

Q2. (c) Without I the rule has no purpose; without II there would be no phones to silence. Both are implicit.

Q3. (d) I only copies others without giving a reason why it suits our cities; II is an emotional appeal. Both are weak.

Quick revision

Conclusion: must be true from the statement alone; likely is not enough.

Assumption: negate it; if the statement collapses, it is implicit.

Argument: relevant + important + reasoned = strong; emotional, trivial or exaggerated = weak.

Extreme words (only, always, never) usually make an item fail.

Judge I and II separately; both or neither are common answers.

Concepts and rules

Course of action: a step that a responsible person or authority should take in view of a stated problem or situation. You judge each suggested course separately.

A course follows if it is practical (can actually be done), addresses the problem stated (removes it, reduces it or prevents it from recurring), and does not create a bigger problem.

A course does not follow if it is extreme (ban, shut down, punish everyone), impractical, unrelated to the problem, or only blames people without solving anything.

An immediate step (relief, inspection, temporary closure for safety) and a long-term step (repair, new policy) can both follow for the same problem.

Cause and effect: 2 statements describe events; decide whether one caused the other, whether both are independent causes, or whether both are effects of a common cause.

The cause happens first and directly explains the effect. Look for a plausible, direct mechanism, such as heavy rain damaging crops leading to higher prices.

If 2 events happen together but neither explains the other, ask what single event could explain both, such as dense fog delaying both flights and trains.

Method and shortcuts

Step 1 (course of action): write the problem in 1 line, then for each course ask 3 questions: Is it practical? Does it address this problem? Is it proportionate?

Step 2: reject words like ban all, close down, permanently, everyone, at once for every case, unless the danger stated is that serious.

Step 3 (cause and effect): put the 2 events on a timeline. If one must come first and explains the other, it is the cause.

Step 4: test the reverse direction too; if the reverse makes no sense, your direction is right. Rising onion prices cannot cause crop damage.

Shortcut: a course that only finds fault (punish, blame, criticise) without fixing anything almost never follows; a course that inspects, repairs, informs or provides relief usually does.

Example 1: the vacant post

Question: Statement: Many students of a village government school fail in mathematics because the post of maths teacher has been vacant for a year. Courses of action: I. The education department should fill the maths teacher's post at the earliest. II. The school should be closed down.

Solution: I removes the stated cause of the problem and is practical. II is extreme and makes things worse, since students would lose the whole school.

Answer: Only I follows.

Example 2: repo rate and loans

Question: I. The Reserve Bank of India raised the repo rate by 0.5 percentage point. II. Banks increased the interest rates on home loans. Which is the cause and which the effect?

Solution: The repo rate is the rate at which banks borrow from the RBI. When it rises, banks' cost of funds rises and they pass it on to borrowers. The reverse direction makes no sense: banks' loan rates do not set the repo rate.

Answer: Statement I is the cause and statement II is its effect.

Example 3: immediate and preventive steps

Question: Statement: Dengue cases have risen sharply in several wards of the city after the monsoon. Courses of action: I. The municipal body should carry out fogging and clear stagnant water in the affected wards. II. City hospitals should be told to keep extra beds and testing kits ready.

Solution: I attacks the source (mosquito breeding) and II handles the patients already affected. Both are practical and address the problem from different sides.

Answer: Both I and II follow.

Example 4: direction of cause

Question: I. Onion prices rose sharply in city markets. II. Unseasonal heavy rain damaged the onion crop in the main growing districts. (a) Statement I is the cause and statement II is its effect (b) Statement II is the cause and statement I is its effect (c) Both statements are independent causes (d) Both statements are effects of some common cause

Solution: Crop damage happens first and cuts supply; lower supply with the same demand pushes prices up. Prices in city markets cannot damage a crop, so the direction is II to I.

Answer: (b)

Example 5: a hidden common cause

Question: I. Many flights at Delhi airport were delayed on a December morning. II. Several trains arriving in Delhi were running hours late on the same morning. (a) Statement I is the cause and statement II is its effect (b) Statement II is the cause and statement I is its effect (c) Both statements are independent causes (d) Both statements are effects of some common cause

Solution: Late flights do not delay trains and late trains do not delay flights, so neither is the cause of the other. Both are delays, that is effects, and a single event explains both: dense winter fog over north India reduces visibility for pilots and loco pilots alike.

Answer: (d)

Example 6: choosing among 3 courses

Question: Statement: An inspection report says that a bridge on a busy highway has developed cracks. Courses of action: I. The authorities should immediately stop heavy vehicles on the bridge and divert them until structural engineers examine it. II. Repair work should start as soon as the engineers' assessment is ready. III. Heavy vehicles should be banned from the whole highway permanently. (a) Only I (b) Only I and II (c) Only II and III (d) All I, II and III

Solution: I is the immediate safety step, limited to the bridge and to the time needed for inspection. II is the long-term fix of the actual problem. III is extreme: the problem is one bridge, not the whole highway, and a permanent ban would cripple freight.

Answer: (b)

Common mistakes

Choosing the toughest-sounding course. Strong action is right only when it fits the size of the problem.

Rejecting a good course because it does not solve the problem fully. Reducing the problem is enough.

Thinking only 1 course can follow. Immediate relief and long-term prevention often both follow.

Reversing cause and effect because the effect is mentioned first. The order of the statements does not tell you the order of the events.

Marking 2 linked events as cause and effect when both are results of a third event. Ask whether one could happen without the other.

Practice questions

Q1. Statement: Passengers wait for hours in long queues at a railway reservation counter. Courses of action: I. Reservation should be stopped for some days. II. The railways should open more counters during peak hours and promote online booking. (a) Only I (b) Neither I nor II (c) Only II (d) Both I and II

Q2. I. Heavy rain flooded the roads leading to the school on Sunday night. II. The school declared a holiday on Monday. (a) Statement I is the cause and statement II is its effect (b) Statement II is the cause and statement I is its effect (c) Both statements are independent causes (d) Both statements are effects of some common cause

Q3. Statement: Several guests fell ill with food poisoning after a wedding feast in a town. Courses of action: I. The food safety department should collect and test samples of the food served. II. Doctors should treat the affected guests and report the cases to the health authorities. III. All wedding feasts in the town should be banned for a month. (a) Only I and II (b) Only I (c) Only II and III (d) All I, II and III

Answers

Q1. (c) II reduces waiting directly and is practical; I is extreme and leaves passengers with no tickets at all.

Q2. (a) The flooding came first on Sunday night and explains the holiday on Monday.

Q3. (a) I finds the source, II treats the victims; III punishes everyone for one caterer's lapse and is extreme.

Quick revision

Course of action: practical + addresses this problem + proportionate.

Reject ban-all, shut-down and blame-only courses unless the danger is that serious.

Immediate relief and long-term repair can both follow.

Cause comes first and explains the effect; test the reverse direction.

2 effects with no link between them often share a hidden common cause.

Concepts and rules

A trend question gives values over time (sales, population, production, users) and asks for the next value, the year in which a level is crossed, or the period with the biggest change.

Linear trend: the difference between consecutive values is constant. Next value = last value + common difference.

Quadratic trend: the differences themselves change by a constant amount (second difference constant). Extend the differences first, then add.

Growth-rate trend: each value is the previous value times the same factor; a growth of r% means multiply by (1 + r/100). For 10% growth the factor is 1.1.

Alternating trend: the steps follow a repeating cycle, such as +4, −2, +4, −2. Find the cycle and apply the next step in it.

Percentage change from A to B = (B − A)/A × 100. The biggest absolute increase and the biggest percentage increase can fall in different years.

To find when a growing value first crosses a level, step year by year and stop at the first year above the level; do not round in between.

Method and shortcuts

Step 1: write the differences between consecutive values. If they are equal, the trend is linear.

Step 2: if the differences are not equal, write their differences. If those are equal, the trend is quadratic.

Step 3: if differences grow in proportion to the values, divide each value by the previous one; a constant ratio means a growth-rate trend.

Step 4: if the differences alternate in sign or size, look for a cycle of 2 or 3 steps.

Shortcut for growth: 10% of a number is the number with the decimal point moved 1 place left; add it on to get the next value (53,240 + 5,324 = 58,564).

Why check every step: a trend fitted only to the last 2 values ignores the rule that produced the whole series, so it fails for alternating and quadratic data.

Example 1: linear sales

Question: A shop's sales (₹ lakh) from 2019 to 2023 were 12, 15, 18, 21, 24. If the trend continues, what will the sales be in 2024?

Solution: Differences are 3, 3, 3, 3, so the trend is linear. 24 + 3 = 27.

Answer: ₹27 lakh

Example 2: constant growth rate

Question: A town's population in 4 successive years was 40,000, 44,000, 48,400 and 53,240. Find the next year's population if the trend continues.

Solution: Differences 4,000, 4,400, 4,840 are not equal, but each value is 1.1 times the previous one (10% growth). 53,240 × 1.1 = 53,240 + 5,324 = 58,564.

Answer: 58,564

Example 3: biggest percentage rise

Question: A factory's output (tonnes) from 2020 to 2024 was 200, 230, 276, 300, 345. In which year was the percentage increase over the year before the highest?

Solution: 2021: 30/200 = 15%. 2022: 46/230 = 20%. 2023: 24/276 ≈ 8.7%. 2024: 45/300 = 15%. The highest is 20% in 2022.

Answer: 2022

Example 4: second differences

Question: Registered users of an app (thousand) in successive months were 5, 8, 13, 20, 29. What is the next value if the trend continues? (a) 38 (b) 40 (c) 41 (d) 39

Solution: Differences 3, 5, 7, 9 rise by 2 each time, so the next difference is 11. 29 + 11 = 40. Adding the last difference again (29 + 9 = 38) is the trap in option (a).

Answer: (b) 40

Example 5: alternating steps

Question: A company's profit (₹ crore) for 6 successive years was 20, 24, 22, 26, 24, 28. What will it be in year 7 if the pattern continues? (a) 32 (b) 30 (c) 26 (d) 29

Solution: Steps are +4, −2, +4, −2, +4, a cycle of 2. The step after +4 is −2, so year 7 = 28 − 2 = 26. Continuing +4 gives 32, option (a), the trap.

Answer: (c) 26

Example 6: when one trend overtakes another

Question: In 2021, Town A registered 1,600 two-wheelers and Town B 2,400. Registrations in A grow by 25% a year; in B they grow by 200 a year. In which year will A first register more than B? (a) 2023 (b) 2025 (c) 2026 (d) 2024

Solution: A (× 1.25 each year): 2022: 2,000; 2023: 2,500; 2024: 3,125. B (+ 200 each year): 2022: 2,600; 2023: 2,800; 2024: 3,000. In 2023, 2,500 < 2,800; in 2024, 3,125 > 3,000.

A growth-rate trend always overtakes a linear one in the end, because its yearly increase keeps growing (400, 500, 625) while the linear increase stays at 200.

Answer: (d) 2024

Common mistakes

Repeating the last difference when the differences themselves are growing. Check the second differences.

Treating a growth-rate series as linear. If the differences grow in step with the values, use the ratio.

Confusing the biggest absolute increase with the biggest percentage increase. Divide by the earlier value each time.

Continuing the last step of an alternating series. Find the full cycle and take the next step in it.

Dividing a percentage change by the later value. The base is always the earlier value.

Practice questions

Q1. Daily visitors to a museum over 5 days were 7, 11, 16, 22, 29 (hundred). What is the next value if the trend continues? (a) 36 (b) 38 (c) 37 (d) 35

Q2. A firm's exports (₹ crore) in 4 successive years were 500, 550, 605, 665.5. What will they be in the next year if the trend continues? (a) 720.5 (b) 732.05 (c) 715.5 (d) 726

Q3. Production (tonnes) from 2019 to 2023 was 400, 460, 506, 552, 621. In which year was the percentage increase over the year before the highest? (a) 2020 (b) 2021 (c) 2022 (d) 2023

Answers

Q1. (c) Differences 4, 5, 6, 7 rise by 1, so the next is 8; 29 + 8 = 37.

Q2. (b) Each value is 1.1 times the previous (10% growth): 665.5 + 66.55 = 732.05.

Q3. (a) 2020: 60/400 = 15%; 2021: 46/460 = 10%; 2022: 46/506 ≈ 9.1%; 2023: 69/552 = 12.5%. The biggest absolute rise (69 in 2023) is the trap.

Quick revision

Equal differences: linear, add the difference.

Differences change by a constant: extend the differences first.

Constant ratio: multiply by (1 + r/100) each step.

Alternating steps: find the cycle, apply its next step.

Percentage change uses the earlier value as the base.