Logic Syllogisms Venn Deduction Competitive Exams
50 questions · IQ Logic and Reasoning
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Question 1 of 50
Statements: Some shirts are ties. No tie is a coat. All coats are jugs. Conclusions: I. Some shirts are not coats II. Some jugs are not ties Which of the following is correct?
ExplanationThe shirts that are ties are not coats, so Some shirts are not coats (I). Coats are jugs and no tie is a coat, so some jugs (the coats) are not ties (II).
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Question 2 of 50
Statements: No pen is a book. No book is a cup. Conclusions: I. Some pens are cups II. No pen is a cup Which of the following is correct?
ExplanationTwo 'No' statements give no definite link between pens and cups. Some pens are cups and No pen is a cup are a contradictory pair, so one of them must be true: Either I or II follows.
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Question 3 of 50
The sum of three consecutive integers is 48. What is the largest of them?
ExplanationThe middle number = 48 ÷ 3 = 16, so the integers are 15, 16 and 17.
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Question 4 of 50
Statements: All trees are houses. Some trees are roads. Conclusions: I. Some houses are roads II. All roads are houses Which of the following is correct?
ExplanationThe trees that are roads are also houses, so Some houses are roads (I) follows. All roads are houses (II) does not, since only some roads are trees.
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Question 5 of 50
Statements: Some chairs are tables. All tables are boxes. Conclusions: I. Some chairs are boxes II. All chairs are boxes Which of the following is correct?
ExplanationThe chairs that are tables are also boxes, so Some chairs are boxes (I) follows. Only some chairs are known to be tables, so All chairs are boxes (II) does not follow.
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Question 6 of 50
Today is Wednesday. What day of the week will it be after 100 days?
Explanation100 = 14 × 7 + 2, so the day is 2 days after Wednesday, which is Friday.
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Question 7 of 50
Which diagram best represents the relationship among Doctors, Surgeons and Women?
ExplanationEvery surgeon is a doctor, so Surgeons lie inside Doctors. Some doctors and some surgeons are women, but women are not all doctors, so the Women circle overlaps both.
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Question 8 of 50
Four persons A, B, C and D sit in a row facing north. A sits immediately to the left of B, C sits to the right of B, and D sits at the extreme left. Who sits second from the right?
ExplanationThe order from left to right is D, A, B, C, so B is second from the right.
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Question 9 of 50
Statements: Some pens are books. All books are cups. No cup is a jug. Conclusions: I. Some pens are not jugs II. No book is a jug Which of the following is correct?
ExplanationBooks are cups and no cup is a jug, so No book is a jug (II). The pens that are books are therefore not jugs: Some pens are not jugs (I).
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Question 10 of 50
P is heavier than Q. R is heavier than P. S is lighter than Q. Which is the heaviest?
ExplanationThe order is R > P > Q > S, so R is heaviest.
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Question 11 of 50
Statements: No stone is a metal. No metal is a plank. All planks are cups. Conclusions: I. Some cups are not metals II. No stone is a cup Which of the following is correct?
ExplanationPlanks are cups and no metal is a plank, so some cups (the planks) are not metals (I). Stones and cups need not be unrelated, so No stone is a cup (II) does not follow.
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Question 12 of 50
In a survey of 200 people, 120 like tea, 90 like coffee and 30 like neither. How many like both?
ExplanationAt least one = 200 − 30 = 170. Both = 120 + 90 − 170 = 40.
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Question 13 of 50
In a class of 40, Ali's rank from the top is 12. What is his rank from the bottom?
ExplanationRank from bottom = 40 − 12 + 1 = 29.
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Question 14 of 50
Which diagram best represents Apples, Fruits and Red things?
ExplanationAll apples are fruits. Some apples and some fruits are red, but many red things are neither, so Red things overlaps both.
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Question 15 of 50
Which diagram best represents Pakistanis, Doctors and Teachers?
ExplanationSome Pakistanis are doctors, some are teachers, and some doctors are teachers, but there are doctors and teachers who are not Pakistani, so the circles overlap.
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Question 16 of 50
Statements: All pens are rings. All coins are rings. Some rings are coats. Conclusions: I. Some coats are not pens II. Some coats are coins Which of the following is correct?
ExplanationRings are linked to both pens and coins, but 'Some rings are coats' leaves open which rings. Neither Some coats are not pens nor Some coats are coins is certain.
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Question 17 of 50
Of 60 students, 35 study Maths, 30 study Science and 10 study neither. How many study both?
ExplanationAt least one = 50. Both = 35 + 30 − 50 = 15.
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Question 18 of 50
P is older than Q. R is younger than Q. S is older than P. T is younger than R. Who is the second oldest?
ExplanationThe order is S > P > Q > R > T, so P is second oldest.
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Question 19 of 50
Statements: No fan is a clock. All clocks are bags. Conclusions: I. No fan is a bag II. Some bags are not fans Which of the following is correct?
ExplanationEvery clock is a bag and no clock is a fan, so some bags (the clocks) are not fans (II). Fans could still be bags, so No fan is a bag (I) does not follow.
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Question 20 of 50
Statements: All lamps are keys. Some keys are doors. Conclusions: I. Some lamps are doors II. Some doors are keys Which of the following is correct?
ExplanationSome keys are doors converts to Some doors are keys (II). The doors that are keys need not be the keys that are lamps, so Some lamps are doors (I) is not certain.
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Question 21 of 50
Statements: No ring is a coin. Some coins are bags. Conclusions: I. Some rings are not bags II. Some bags are not rings Which of the following is correct?
ExplanationThe coins that are bags cannot be rings, so Some bags are not rings (II) follows. Some rings are not bags (I) is not certain.
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Question 22 of 50
Statements: All houses are roads. Some roads are trees. No tree is a sea. Conclusions: I. Some roads are not seas II. Some houses are not seas Which of the following is correct?
ExplanationThe roads that are trees are not seas, so Some roads are not seas (I). The houses that are roads are not guaranteed to be those trees, so II is not certain.
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Question 23 of 50
Ali is taller than Bilal. Chand is shorter than Bilal. Who is the tallest?
ExplanationAli > Bilal > Chand, so Ali is the tallest.
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Question 24 of 50
A is taller than B, B is taller than C and C is taller than D. Who is the shortest?
ExplanationThe order from tallest is A > B > C > D, so D is shortest.
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Question 25 of 50
Which diagram best represents Cats, Dogs and Animals?
ExplanationNo cat is a dog, so those circles are separate, while both are kinds of animal and lie inside the Animals circle.
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Question 26 of 50
Statements: All tools are desks. All desks are mugs. All mugs are plates. Conclusions: I. All tools are plates II. Some plates are tools Which of the following is correct?
ExplanationAll tools are desks, all desks are mugs and all mugs are plates, so All tools are plates (I). By conversion, Some plates are tools (II).
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Question 27 of 50
A is taller than B. C is shorter than B. D is taller than A. Who is the shortest?
ExplanationThe order is D > A > B > C, so C is shortest.
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Question 28 of 50
Statements: All pens are books. All books are cups. Conclusions: I. All pens are cups II. Some cups are pens Which of the following is correct?
ExplanationFrom All pens are books and All books are cups, All pens are cups follows (I). All pens are cups also gives Some cups are pens (II) by conversion, taking each group as non-empty as in the standard exam convention.
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Question 29 of 50
In a class of 40, 25 play cricket, 20 play hockey and 10 play both. How many play only cricket?
ExplanationOnly cricket = 25 − 10 = 15.
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Question 30 of 50
Statements: If a number is divisible by 6, it is divisible by 3. The number 18 is divisible by 3. Which conclusion is logically valid from the statements alone?
ExplanationThe rule goes from 'divisible by 6' to 'divisible by 3', not the other way round. Being divisible by 3 does not guarantee divisibility by 6 from these statements alone.
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Question 31 of 50
Of 120 students, 70 study Mathematics and 60 study Physics. Every student studies at least one subject. How many study both?
ExplanationBoth = 70 + 60 − 120 = 10.
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Question 32 of 50
All students are hardworking. Zara is a student. Which conclusion must be true?
ExplanationZara belongs to the group of students, and every student is hardworking.
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Question 33 of 50
Sana finished before Mina, and Mina finished before Rida. Hina finished after Rida. Who finished last?
ExplanationThe finishing order is Sana, Mina, Rida, Hina, so Hina is last.
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Question 34 of 50
In a group of 80, 45 like tea, 40 like coffee and 15 like both. How many like only tea?
ExplanationOnly tea = 45 − 15 = 30.
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Question 35 of 50
Statements: Some pens are rings. Some rings are boxes. Conclusions: I. Some pens are boxes II. Some boxes are pens Which of the following is correct?
ExplanationTwo 'Some' statements give no certain link between the end terms. The pens that are rings may differ from the rings that are boxes, so neither conclusion follows.
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Question 36 of 50
Which diagram best represents Mothers, Daughters and Women?
ExplanationMothers and daughters are both women, so both lie inside Women. A woman can be both a mother and a daughter, so those two circles overlap.
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Question 37 of 50
In a town, 40% read newspaper A, 30% read newspaper B and 10% read both. What percentage read neither?
ExplanationAt least one = 40 + 30 − 10 = 60%. Neither = 100 − 60 = 40%.
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Question 38 of 50
If P > Q and Q > R, which statement must be true?
ExplanationThe relation is transitive: P > Q > R, so P > R.
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Question 39 of 50
Which diagram best represents Punjab, Pakistan and Asia?
ExplanationPunjab is a province of Pakistan and Pakistan is a country of Asia, so each lies wholly inside the next.
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Question 40 of 50
If it rains, the match is cancelled. The match was not cancelled. Which conclusion is valid?
ExplanationRain would certainly have cancelled the match. Since it was not cancelled, it did not rain.
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Question 41 of 50
In a group of 100 people, 60 drink tea, 50 drink coffee and 20 drink both. How many drink neither?
ExplanationAt least one drink = 60 + 50 − 20 = 90, so neither = 100 − 90 = 10.
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Question 42 of 50
Statements: All lamps are keys. Some keys are doors. All doors are fans. Conclusions: I. Some lamps are fans II. Some keys are fans Which of the following is correct?
ExplanationSome keys are doors and all doors are fans, so Some keys are fans (II). The keys that are doors need not be lamps, so Some lamps are fans (I) is not certain.
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Question 43 of 50
Statements: All stones are metals. No metal is a plank. Conclusions: I. No stone is a plank II. No plank is a stone Which of the following is correct?
ExplanationAll stones are metals and no metal is a plank, so no stone is a plank (I). 'No' statements are reversible, so no plank is a stone (II).
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Question 44 of 50
Statements: All rivers are lakes. Some seas are not lakes. Conclusions: I. No sea is a river II. Some seas are not rivers Which of the following is correct?
ExplanationThe seas that are not lakes cannot be rivers (all rivers are lakes), so Some seas are not rivers (II) follows. No sea is a river (I) does not follow.
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Question 45 of 50
Statements: Some bags are cups. No cup is a jug. Conclusions: I. Some bags are not jugs II. No bag is a jug Which of the following is correct?
ExplanationThe bags that are cups cannot be jugs, so Some bags are not jugs (I) follows. Other bags may be jugs, so No bag is a jug (II) does not follow.
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Question 46 of 50
In a row of five, C is to the left of A, A is to the left of B, B is to the left of D and D is to the left of E. Who is in the middle?
ExplanationThe order is C, A, B, D, E, so B is in the middle.
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Question 47 of 50
Statements: No chair is a table. All tables are boxes. Some boxes are bags. Conclusions: I. Some bags are tables II. Some bags are boxes Which of the following is correct?
ExplanationSome boxes are bags converts to Some bags are boxes (II). The bags that are boxes need not be tables, so Some bags are tables (I) is not certain.
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Question 48 of 50
Among 50 members, 30 speak Urdu, 25 speak English and 10 speak neither. How many speak exactly one language?
ExplanationAt least one = 40. Both = 30 + 25 − 40 = 15. Exactly one = 40 − 15 = 25.
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Question 49 of 50
Statements: All shirts are coats. All ties are coats. Conclusions: I. All shirts are ties II. Some shirts are ties Which of the following is correct?
ExplanationBoth shirts and ties are inside coats, but there is no certain overlap between them. Neither All shirts are ties nor Some shirts are ties follows.
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Question 50 of 50
In a college of 300 students, 180 study English, 150 study Urdu and 50 study neither. How many study both?
ExplanationAt least one = 250. Both = 180 + 150 − 250 = 80.
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