Unit 2: Syllogism and Number Ranking - Practice Quiz

1 What is a syllogism?

2 Statements: All cats are animals. All animals are living beings. Which conclusion follows?

3 Statements: No pen is a pencil. Some pencils are blue. Which conclusion follows?

4 Which Venn diagram relationship represents the statement "All squares are rectangles"?

5 Which arrangement represents the statement "No doctor is an engineer"?

6 Which Venn diagram relationship best represents "Some students are athletes"?

7 How should the groups Sparrows, Birds, and Animals be represented?

8 Which diagrammatic relationship best represents Apples, Bananas, and Fruits?

9 Statements: All poets are writers. Some writers are teachers. What can be said about the conclusion "Some poets are teachers"?

10 Statements: No cup is a plate. Some plates are made of steel. What can be said about the conclusion "Some steel items are cups"?

11 Statements: All roses are flowers. No flower is a stone. Which conclusion is impossible?

12 Arrange in descending order. Which number is third?

13 Arrange in ascending order. Which number is third?

14 Which number is the second highest among ?

15 Which is the greatest number?

16 Which is the smallest number?

17 Which number lies exactly midway between and ?

18 Riya is seventh from the top in a class of students. What is her rank from the bottom?

19 Aman is ninth from the front and twelfth from the back in a line. How many people are in the line?

20 In a race, Arun finishes ahead of Bala, and Bala finishes ahead of Charan. Who ranks lowest among them?

21 Statements:

- All roses are flowers.
- Some flowers are red.
- No red object is fragrant.

Conclusions:

I. Some roses are red.
II. Some flowers are not fragrant.

Which conclusion follows?

22 Statements:

- Some teachers are writers.
- All writers are readers.
- No reader is illiterate.

Conclusions:

I. Some teachers are readers.
II. No teacher is illiterate.
III. Some teachers are not illiterate.

Which conclusions follow?

23 Statements:

- All laptops are machines.
- No machine is handmade.
- Some gifts are handmade.

Conclusions:

I. No laptop is handmade.
II. Some gifts are not machines.

Which conclusion follows?

24 All mothers are women. Some doctors are mothers, while some doctors are not women. Which Venn-diagram arrangement represents these facts?

25 Some scientists are writers, some writers are painters, and no scientist is a painter. Which diagrammatic description is correct?

26 Which nested-circle arrangement correctly represents integers, even integers, and multiples of ?

27 Which set relationship best represents Delhi, India, and Asia?

28 Which diagrammatic relationship best represents mammals, dogs, and cats?

29 Statements:

- Some lamps are tables.
- All tables are wooden.
- No wooden object is metallic.

Which conclusion is possible?

30 Statements:

- All engineers are graduates.
- Some graduates are artists.
- No artist is a pilot.

Which statement can be true?

31 Statements:

- No chef is a singer.
- Some dancers are singers.
- Some chefs are artists.

Which statement is possible?

32 In a class of students, Priya ranks th from the top. What is her rank from the bottom?

33 Karan is th from the left and th from the right in a row. How many people are in the row?

34 In a class of students, Anil is th and Beena is th from the top. If they exchange positions, what will Anil's rank be from the bottom?

35 The digits of are arranged in ascending order. By how many positions does the digit move from its original position?

36 In the number , the first and second digits are interchanged, the third and fourth are interchanged, and so on. Which digit is third from the right in the resulting number?

37 From the number , remove every digit divisible by . Which digit is then fourth from the left?

38 Five students have different scores. Asha scored higher than Bharat but lower than Charu. Deepak scored lower than Bharat, and Esha scored higher than Charu. Who ranked third?

39 In a race, Riya finished before Sameer but after Tarun. Uma finished after Sameer but before Varun. Who finished third?

40 Meera is ranks above Kavya, who is th from the top. Rohan is ranks below Meera. What is Rohan's rank from the top?

41 Statements:

1. All poets are dreamers.
2. No dreamer is an accountant.
3. Some historians are accountants.
4. All historians are critics.

Conclusions:

I. No poet is an accountant.
II. Some critics are not dreamers.
III. All critics are historians.

Which conclusions follow?

42 Statements:

1. All jurists are readers.
2. Some readers are musicians.
3. No musician is an athlete.
4. All athletes are jurists.

Conclusions:

I. Some readers are not athletes.
II. Some jurists are not musicians.
III. No athlete is a musician.

Which conclusions follow?

43 A Venn diagram represents these statements: Every is a ; no is an ; some are ; and every is a . Which feature must appear in the diagram?

44 Under the usual Euclidean definitions, which diagrammatic relationship correctly represents squares, rectangles, rhombuses, and parallelograms?

45 Statements:

1. All archivists are scholars.
2. No scholar is reckless.
3. All explorers are reckless.
4. All explorers are patient.
5. No patient is a librarian.

Which situation is logically possible?

46 Statements:

1. No is a .
2. All are .
3. Some are .
4. All are .

Which statement can be true but is not necessarily true?

47 In a class, Aarav is 18th from the top and Bhavna is 25th from the bottom. Exactly seven students are ranked between them. If the class contains more than 40 students, how many students are there?

48 In a row, P is 17th from the left and Q is 23rd from the right. After P and Q exchange positions, P becomes 29th from the left. What is the sum of P's new rank from the left and Q's new rank from the right?

49 The numbers 472, 815, 639, 284, and 751 are reversed digit-wise and the resulting numbers are arranged in descending order. What is the absolute difference between the original units digit of the second-ranked number and the original hundreds digit of the fourth-ranked number?

50 Eight runners—W, U, R, P, Q, S, T, and V—finish without ties. R finishes ahead of P but behind U; Q finishes behind P but ahead of S; V finishes behind T; W finishes ahead of U; and T finishes behind S. What is P's rank?

51 In a row of 53 people, A is 16th from the left. B is 11 places to the right of A, and C is 7 places to the left of B. D's position is exactly midway between the positions of A and C. What is D's rank from the right?

52 For each number in 4837, 6159, 7426, 3584, and 9271, interchange the first and third digits and then interchange the second and fourth digits. If the transformed numbers are arranged in ascending order, which original number produces the fourth-ranked result?

53 Statements:

1. All navigators are observers.
2. No observer is careless.
3. Some engineers are careless.
4. All engineers are inventors.
5. Some inventors are navigators.

Conclusions:

I. Some inventors are not careless.
II. No engineer is a navigator.
III. Some inventors are not navigators.

Which conclusions follow?

54 A Venn diagram satisfies these conditions: some are , some are , some are , and no object belongs to all three sets. What is the minimum number of distinct objects needed to satisfy all the statements?

55 Which description best represents the relationship among mammals, aquatic animals, whales, and fish?

56 Statements:

1. All are .
2. Some are .
3. No is a .
4. All are .
5. Some are .

Which situation is logically possible?

57 A class initially has 60 students, and K is 19th from the top. Five students ranked ahead of K and three students ranked behind K leave the class. What is K's new rank from the bottom?

58 For a three-digit number with hundreds digit , tens digit , and units digit , define its score as . The numbers 472, 816, 635, 294, and 751 are ranked by score in descending order. Which number ranks third?

59 Seven runners A, B, C, D, E, F, and G finish without ties. E finishes immediately before A; A finishes before B; F finishes after B but before C; D finishes before C; and G finishes after D. Which finishing order is possible?

60 Nine books A through I have distinct heights. A is taller than B and C; D is shorter than B but taller than E; F is taller than I, which is taller than A; G is shorter than C; and H is taller than D but shorter than B. What is the lowest possible rank of C when ranked from tallest to shortest?