Syllogisms, statements and conclusions, assumptions and arguments: previous-year questions
88 real UPSC Prelims questions (2011–2026) with the official answer and a clear explanation. 17 of them came in the last five papers.
How often UPSC asks this
Questions per year, counted from the official papers.
Attempt the questions
Newest papers first. Tap an option; the answer and the reason appear instantly.
Consider two Statements and four Conclusions given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statements, disregarding the commonly known facts.
Statement-1 : Some greens are blues.
Statement-2 : Some blues are blacks.
Conclusion-1 : Some greens are blacks.
Conclusion-2 : No green is black.
Conclusion-3 : All greens are blacks.
Conclusion-4 : All blacks are greens.
Which one of the following is correct ?
Answer (d) & explanation
None of the four conclusions follows (d). Step 1: "some greens are blues" and "some blues are blacks" give no sure link between greens and blacks. The blues that are black may not be the green ones. Step 2: so "some greens are blacks" (1), "no green is black" (2), "all greens are blacks" (3) and "all blacks are greens" (4) are each possible, but none is certain. Step 3: options (a), (b) and (c) pair conclusions that do not follow. Conclusions 1 and 2 do form an "either-or" pair, but no option offers "either 1 or 2".
Tip: two "some" statements never give a definite conclusion. Draw the circles in two ways; if the answer changes, nothing follows.
1 and 2 form an 'either–or' pair, but no option offers 'either 1 or 2'.
UPSC repeats traps like this year after year. The PYQ Book gathers every trap in one place, so you see them coming. Try the free sample
Answer as per the official UPSC answer key.
Two Statements S1 and S2 are given below followed by a Question :
S1 : There are not more than two figures on any page of a 51-page book.
S2 : There is at least one figure on every page.
Question : Are there more than 100 figures in that book?
Which one of the following is correct in respect of the above Statements and the Question?
Answer (c) & explanation
S1 and S2 together are not sufficient (c). Step 1: S1 says at most 2 figures per page. S2 says at least 1 figure per page. Step 2: with 51 pages, the total lies between 51 × 1 = 51 and 51 × 2 = 102. Step 3: 102 is above 100, but 51 is not. So the answer could be "yes" or "no". Even together, the statements do not settle it. Options (a), (b) and (d) fail.
Tip: in data sufficiency, find the full possible range. If the range crosses the question's line (here 100), the data are not enough. S1 alone gives 0 to 102; S2 alone gives 51 or more; neither settles it.
Answer as per the official UPSC answer key.
Two Statements are given followed by two Conclusions :
Statements : All numbers are divisible by 2. All numbers are divisible by 3.
Conclusion-I : All numbers are divisible by 6.
Conclusion-II : All numbers are divisible by 4.
Which of the above Conclusions logically follows/follow from the two given Statements?
Answer (a) & explanation
Only Conclusion I follows (a). Step 1: all numbers are divisible by 2 and by 3. Since 2 and 3 share no common factor, a number divisible by both is divisible by 2 × 3 = 6. So Conclusion I follows. Step 2: Conclusion II says all are divisible by 4. But being divisible by 2 does not mean divisible by 4. For example, 6 is divisible by 2 and 3, but not by 4. Step 3: so II does not follow. Options (b), (c) and (d) fail.
Tip: if a number is divisible by two co-prime numbers (no shared factor), it is divisible by their product. This does not work for 2 and 4, which share a factor.
Answer as per the official UPSC answer key.
Two Statements are given followed by two Conclusions :
Statements : All cats are dogs. All cats are black.
Conclusion-I : All dogs are black.
Conclusion-II : Some dogs are not black.
Which of the above Conclusions logically follows/follow from the two given Statements, disregarding commonly known facts?
Answer (c) & explanation
Neither conclusion follows (c). Step 1: "All cats are dogs" puts the cats inside the dogs group. "All cats are black" says the cats are black. Step 2: so we know the cat part of the dogs is black. The other dogs may or may not be black. Step 3: so "all dogs are black" (I) is not certain, and "some dogs are not black" (II) is not certain either. Neither follows. Options (a), (b) and (d) fail.
Tip: draw circles: a small "cats" circle inside "dogs", also inside "black". The rest of "dogs" is unknown. When I and II are opposites, check if they form an either-or pair; here they do not, because "all dogs are black" is only possible, not certain.
I and II are opposites, so one of them must be true. But neither follows by itself, and no option says 'either I or II'.
Answer as per the official UPSC answer key.
Read the following statements S1 and S2 and answer the item that follows :
S1 : Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.
S2 : Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.
Which one of the following statements is correct ?
Answer (b) & explanation
Sohan's weight is the least (b). Step 1: S1 says 2S < M and 2S < R. Step 2: so S < M/2, which is less than M. And S < R/2, which is less than R. So Sohan is lighter than both Mohan and Rohan. Step 3: therefore Sohan is the lightest. Options (a) and (c) name the wrong person. Option (d) fails because S1 alone fixes the lightest.
Tip: "twice A is less than B" means A is less than half of B, so A is certainly below B. This item and the previous one use the same data: one ordering (least) is fixed, the other (greatest) is not.
Answer as per the official UPSC answer key.
Consider the following Statements and Conclusions :
Statements :
- 1. Some rats are cats.
- 2. Some cats are dogs.
- 3. No dog is a cow.
Conclusions :
- I. No cow is a cat.
- II. No dog is a rat.
- III. Some cats are rats.
Which of the above conclusions is/are drawn from the statements ?
Answer (c) & explanation
Only conclusion III follows (c). Step 1: "Some rats are cats" can be turned round: some cats are rats. So III is true. Step 2: conclusion I says no cow is a cat. The cats that are dogs cannot be cows, but other cats may still be cows. Nothing rules this out, so I fails. Step 3: conclusion II says no dog is a rat. Nothing links dogs and rats either way, so II fails. Options (a), (b) and (d) fail.
Tip: "some A are B" always means "some B are A". But "some" statements cannot give "no" conclusions. Drawing quick circles (Venn diagrams) shows what must be true and what only may be true.
Answer as per the official UPSC answer key.
In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two-wheeler. Which of the following conclusions cannot be drawn from the above data ?
- 1. 60% of the students do not have two-wheelers.
- 2. No cricketer has a two-wheeler.
- 3. Cricket players do not play football.
Select the correct answer using the code given below :
Answer (d) & explanation
None of the three conclusions can be drawn, so the answer is 1, 2 and 3 (d). Step 1: we know the 40% who do not play cricket play football, and every football player has a two-wheeler. Step 2: about cricketers we know nothing more. A cricketer may also play football, and may or may not own a two-wheeler. Step 3: so 1 (60% have no two-wheelers), 2 (no cricketer has one) and 3 (cricketers do not play football) are all unproven. Options (a), (b) and (c) fail.
Tip: "A student who does not play cricket plays football" does not mean cricketers never play football. A one-way rule cannot be reversed.
the question asks what cannot be drawn. Read 'cannot' twice.
UPSC repeats traps like this year after year. The PYQ Book gathers every trap in one place, so you see them coming. Try the free sample
Answer as per the official UPSC answer key.
Read the following statements S1 and S2 and answer the item that follows :
S1 : Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.
S2 : Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.
Which one of the following statements is correct ?
Answer (d) & explanation
Whose weight is greatest cannot be determined (d). Step 1: S1 says 2S < M and 2S < R. So Sohan is lighter than half of each of the others. Sohan is the lightest. Step 2: S2 says 2R > M and 2R > S. This tells us R is more than half of M. But M could be above or below R. Step 3: for example, M = 10, R = 8 fits, and so does M = 8, R = 10. So we cannot tell who is heaviest. Options (a), (b) and (c) fail.
Tip: "twice R is greater than M" does not mean R is greater than M. Test two sets of numbers to see whether an order is fixed.
Answer as per the official UPSC answer key.
If Pen < Pencil, Pencil < Book and Book > Cap, then which one of the following is always true?
Answer (b) & explanation
Pen < Book is always true (b). Step 1: chain the facts: Pen < Pencil and Pencil < Book. So Pen < Pencil < Book, and Pen < Book always. Step 2: Cap is only linked to Book: Book > Cap. That tells us Cap is below Book, but not where it stands against Pen or Pencil. Step 3: so option (a), Pen > Cap, option (c), Pencil = Cap, and option (d), Pencil > Cap, are only possible, not certain.
Tip: join signs that point the same way into a chain. When two items are both smaller than the same thing (here Pencil and Cap are both below Book), you cannot compare them with each other.
Answer as per the official UPSC answer key.
Consider the given information and answer the item that follows.
No supporters of 'party X', who knew Z and supported his campaign strategy, agreed for the alliance with 'party Y'; but some of them had friends in 'party Y'.
With reference to the above information, which one among the following statements must be true?
Answer (b) & explanation
Option (b) must be true: at least one supporter of party Y knows some supporter of party X as a friend (b). Step 1: the information says some X supporters, who knew Z and backed his strategy, "had friends in party Y". Step 2: a friendship goes both ways. So at least one Y supporter has an X supporter as a friend. That is option (b). Step 3: options (c) and (d) say no X supporter backed Z's strategy or knew Z. Both contradict the information. Option (a) is about what Y supporters thought of the alliance, which is never given.
Tip: "must be true" needs proof from the facts. Turn the given sentence around; friendship is mutual, so the reverse also holds.
Answer as per the official UPSC answer key.
(Same information as the question above.)
With reference to the above information, consider the following statements :
- 1. Some supporters of 'party X' knew Z.
- 2. Some supporters of 'party X', who opposed Z's campaign strategy, knew Z.
- 3. No supporters of 'party X' supported Z's campaign strategy.
Which of the statements given above is/are not correct?
Answer (c) & explanation
Only statement 3 is not correct (c). Step 1: the information talks about X supporters who knew Z and supported his strategy. So some X supporters knew Z, and statement 1 is correct. Step 2: statement 3 says no X supporter backed Z's strategy. That plainly contradicts the information, so 3 is not correct. Step 3: statement 2 is about other X supporters, who opposed Z's strategy but knew him. The information neither confirms nor denies this. So it cannot be called wrong. Options (a), (b) and (d) fail.
Tip: "not correct" means proven false. A statement the facts do not mention is "unknown", not "incorrect". Keep these three groups apart: true, false and unknown.
Answer as per the official UPSC answer key.
Consider the following :
Statement : Good voice is a natural gift but one has to keep practising to improve and excel well in the field of music.
Conclusions :
- I. Natural gifts need nurturing and care.
- II. Even though one's voice is not good, one can keep practising.
Which one of the following is correct in respect of the above statement and conclusions?
Answer (a) & explanation
Only conclusion I follows (a). Step 1: the statement says a good voice is a natural gift, but one must keep practising to excel. So even a natural gift needs work and care. That is conclusion I. Step 2: conclusion II is about people without a good voice practising. The statement says nothing about such people. So II does not follow. Step 3: so option (b), only II, and option (c), either I or II, fail. Option (d), neither, fails because I follows.
Tip: a conclusion must stay within what the statement talks about. If the statement is only about people with good voices, you cannot conclude anything about people without them.
Answer as per the official UPSC answer key.
Consider the given statement and the two conclusions that follow :
Statement : Morning walk is good for health.
Conclusions :
- 1. All healthy people go for morning walk.
- 2. Morning walk is essential for maintaining good health.
What is/are the valid conclusion/conclusions?
Answer (d) & explanation
Neither conclusion is valid (d). Step 1: the statement says morning walk is good for health. Step 2: conclusion 2 says morning walk is essential for good health. "Good for" is not "essential for"; people can stay healthy through other exercise. So 2 does not follow. Step 3: conclusion 1 says all healthy people take morning walks. Healthy people may stay fit in other ways, like yoga or sport. So 1 does not follow either. Options (a), (b) and (c) fail.
Tip: "A is good for B" never means "B needs A" or "everyone with B does A". Do not reverse a statement or make it stronger than it is.
words like 'all' and 'essential' are stronger than the statement. Reject them.
Answer as per the official UPSC answer key.
Examine the following statements :
- 1. All colours are pleasant.
- 2. Some colours are pleasant.
- 3. No colour is pleasant.
- 4. Some colours are not pleasant.
Given that statement 4 is true, what can be definitely concluded?
Answer (d) & explanation
Statement 1 is definitely false (d). Step 1: statement 4 says "some colours are not pleasant". Step 2: this is the exact opposite of statement 1, "all colours are pleasant". If some colours are not pleasant, then not all are. So 1 is false. Step 3: statement 2, "some colours are pleasant", could be true or false. Statement 3, "no colour is pleasant", could also be true or false. So options (a), (b) and (c) are not certain.
Tip: learn the opposite pairs: "all are" against "some are not", and "none are" against "some are". If one of a pair is true, the other is false. Other pairs tell you nothing for sure.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. Either A and B are of the same age or A is older than B
- 2. Either C and D are of the same age or D is older than C
- 3. B is older than C
Which of the following conclusions can be drawn from the above statements ?
Answer (d) & explanation
A is older than C (d). Step 1: write each statement as a sign. Statement 1: A is the same age as or older than B, so A ≥ B. Statement 2: D ≥ C. Statement 3: B > C. Step 2: join them: A ≥ B and B > C, so A > C for certain. Step 3: test the others. Option (a), A older than B, is only possible, since A and B may be equal. Option (c), D older than C, is also only possible, since they may be equal. Option (b), B and D the same age, is never linked by any statement.
Tip: turn age words into ≥ and > signs. A chain with a strict ">" anywhere gives a strict ">" at the end.
Answer as per the official UPSC answer key.
A ate grapes and pineapple; B ate grapes and oranges; C ate oranges, pineapple and apple; D ate grapes, apple and pineapple. After taking fruits, B and C fell sick. In the light of the above facts, it can be said that the cause of sickness was :
Answer (d) & explanation
The cause of sickness was oranges (d). Step 1: B and C fell sick. A and D stayed well. Look for a fruit that both sick people ate and neither healthy person ate. Step 2: B ate grapes and oranges. C ate oranges, pineapple and apple. The fruit common to B and C is oranges. Step 3: check the healthy pair. A ate grapes and pineapple, and D ate grapes, apple and pineapple. Neither ate oranges. Apple (a) and pineapple (b) were eaten by A or D, who stayed well. Grapes (c) were eaten by both A and D.
Tip: in "find the cause" puzzles, the cause appears in every bad case and in none of the good ones. Remove anything a healthy person also had.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. The rate of population growth is increasing in the country
- 2. The death rate is declining faster in the country compared to birth rate
- 3. The birth rate is declining faster in the country compared to death rate
- 4. Rural-urban migration is taking place regularly in the country
Which one of the following conclusions may be true in the light of the above facts ?
Answer (d) & explanation
Population growth rises because the death rate falls faster than the birth rate (d). Step 1: growth = birth rate − death rate. If the death rate falls faster than the birth rate, the gap between them widens. So growth rises. This matches statements 1 and 2. Step 2: option (a) blames migration. But people moving from villages to cities stay in the same country, so the national total does not change. Step 3: options (b) and (c) use the word only. The facts show both rates falling, so neither single cause explains it. Statement 3 contradicts statement 2, so it cannot be used.
Tip: population growth is simply births minus deaths, plus or minus migration across the border. Internal migration never changes the national count.
Answer as per the official UPSC answer key.
Consider the following statement :
"We shall go either for a picnic or for trekking".
Which of the following, if true, would falsify this claim ?
Answer (d) & explanation
Only "we go for neither" falsifies the claim (d). Step 1: "We shall go either for a picnic or for trekking" means at least one of the two will happen. Step 2: such a claim is broken only when neither happens. So option (d) falsifies it. Step 3: test the others. Option (a), picnic but no trekking, fits the claim. Option (c), trekking but no picnic, also fits. Option (b), about health authorities, has nothing to do with whether the claim is true.
Tip: "either A or B" is false only when both are missing. "If A then B" is false only when A happens and B does not. Learn these two rules; they settle many logic questions.
Answer as per the official UPSC answer key.
There were 50 faculty members comprising 30 males and the rest females. No male faculty member knew music, but many of the female faculty members did. The Head of the institution invited six faculty members to a tea party by draw of lots. At the party it was discovered that no member knew music. The conclusion is that :
Answer (d) & explanation
Nothing can be said about the gender mix of the party (d). Step 1: no male knew music. But only "many", not all, of the 20 women knew music. So some women may not know music. Step 2: the six chosen people knew no music. They could be all men, all women who do not know music, or a mix of both. Step 3: so option (a), only men, is not certain. Option (b), only non-musical women, is not certain. Option (c), both men and women, is also only possible. None of them must be true.
Tip: "many" and "some" never mean "all". When a group is chosen by lottery, any combination that fits the facts is possible, so be slow to draw a conclusion.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. A man had a wife, two sons and two daughters in his family.
- 2. The daughters were invited to a feast and the male members of the family went out to take part in a picnic.
- 3. The man's father did not return from his work.
Which of the following statements is true ?
Answer (b) & explanation
It is likely that the wife was at home (b). Step 1: account for each person. The two daughters went to a feast. The male members (the man and his two sons) went on a picnic. The man's father did not return from work. Step 2: the only person not accounted for is the man's wife. Step 3: but we are not told where she was. She might have stayed home or gone out. So it is only likely, not certain, that she was home. Option (a) is too certain. Option (c) is not supported. Option (d) is wrong: no one else could be home.
Tip: CSAT logic rewards careful wording. If the facts do not settle a point, prefer "likely" or "possibly" over a definite claim.
Answer as per the official UPSC answer key.