Chapter- Syllogism
1. Know the basic structure of syllogisms
A syllogism has three parts-
(a) Major premise (b) Minor premise (c) Conclusion
The major term in the major premise, which forms the predicate of the conclusion, and the minor term in the minor premise, which forms the subject of the conclusion. The categorical term in common in the premises is called the "middle term".
For example:
Major premise: All birds are animals.
Minor premise: All peacocks are birds.
Conclusion: All peacocks are animals.
In this example, "animal" is the major term and predicate of the conclusion, " peacock " is the minor term and subject of the conclusion, and "bird" is the middle term.
2. Think of each term as representing a category
I. Universal Affirmative: All (100%)
II. Universal Negative: No (100%)
III. Particular Affirmative: Some (50%)
IV. Particular Negative: Some not (50%)
3. Understand each part is expressed as "Some/all/no
A is/are [not] B," with four possible variation.
- The universal affirmative (symbolized as A) is expressed as
"all A is/are B," abbreviated as AAB.
Example:
Statement: All birds are animals
All peacocks are birds
Conclusion: All peacocks are animals
- The universal negative (symbolized as E) is expressed as
"no A is/are B," abbreviated as AEB.
- The particular affirmative (symbolized as I) is expressed as
"some A is/are B," abbreviated as AIB.
- The particular negative (symbolized as O) is expressed as
"some A is/are not B," abbreviated as AOB.
4. Determine the figure of the syllogism.
Depending on whether the middle term serves as subject or predicate in the premises, a syllogism may be classified as
one of four possible figures:
First figure: The middle term serves as subject in the major premise and predicate in the minor premise. Thus, first figure takes the form:
Major premise: M-P..........e.g., "All birds are animals"
Minor premise: S-M..........e.g., "All parrots are birds"
Conclusion: S-P..........e.g., "All parrots are animals".
Second figure: The middle term serves as predicate in the major premise and predicate in the minor premise. Thus, second figure takes the form:
Major premise: P-M..........e.g., "No foxes are birds"
Minor premise: S-M..........e.g., "All parrots are birds"
Conclusion: S-P..........e.g., "No parrots are foxes".
Third figure: The middle term serves as subject in the major premise and subject in the minor premise. Thus, third figure takes the form:
Major premise: M-P..........e.g., "All birds are animals"
Minor premise: M-S..........e.g., "All birds are mortals"
Conclusion: S-P..........e.g., "Some mortals are animals"
Fourth figure: The middle term serves as predicate in the major premise and subject in the minor premise. Thus, fourth figure takes the form:
Major premise: P-M..........e.g., "No birds are cows"
Minor premise: M-S..........e.g., "All cows are animals"
Conclusion: S-P..........e.g., "Some animals are not birds".
We are explaining the concept of Syllogism with some examples by using some simple rules.
First and foremost have a quick glance at the Main rules to solve Syllogism Problems…
1. Statements: All smarts are dumb.
All bad are smarts.
ALL
All bad are dumb.
SOME
Some bad are smarts.
Some bad are dumb.
SOME (REVERSE)
Some smarts are bad.
Some dumb are bad.
All + No
2. Statements: All cities are houses.
No lands is a cities.
Total Definite Conclusions:
NO
All cities are not lands.
Or
No cities is a lands.
SOME
Some cities are houses.
SOME (REVERSE)
Some houses are cities.
SOME NOT
Some cities are not lands.
Some houses are not lands.
SOME NOT (REVERSE)
Some lands are not cities.
All + Some
3. Statements:
All kitchens are closets.
Some closets are shelves.
Total Definite Conclusions:
Some
Some kitchens are closets.
Some (Reverse)
Some closets are kitchens.
Some shelves are closets.
Some + All
4. Statements: Some ambulances are savers.
All ambulances are cars.
Total Definite Conclusions:
SOME
Some ambulances are savers.
Some ambulances are cars.
Some cars are savers.
SOME (REVERSE)
Some savers are ambulances.
Some cars are ambulances.
Some savers are cars.
Some + No
5. Statements: Some A are B.
No B is a C.
Total definite conclusions:
ALL NOT / NO (REVERSE)
No C is a B.
SOME NOT
Some B are not C.
Some A are not C.
SOME NOT (REVERSE)
Some C are not B.
SOME (REVERSE)
Some B are A.
Some + Some
6. Statements: Some A are B.
Some B are C.
Total definite conclusions:
SOME (REVERSE)
Some B are A
Some C are B
No + All
7. Statements:
No segment is a translator.
All translators are website.
Total Definite Conclusions:
NO/ALL NOT (REVERSE)
No translator is a segment.
SOME NOT
Some segments are not translator.
Some websites are not segment.
SOME NOT (REVERSE)
Some translators are not segment.
SOME
Some websites are translators.
SOME (REVERSE)
Some translators are website.
No + Some
8. Statements:
No segment is a translator.
Some translators are website.
Total Definite Conclusions:
NO/ALL NOT (REVERSE)
No translator is a segment.
SOME NOT
Some segments are not translator.
Some websites are not segment.
SOME NOT (REVERSE)
Some translators are not segment.
SOME (REVERSE)
Some websites are translator.
No + No
9. Statements: No dog is a brown.
No bull is a brown.
Total Definite Conclusions:
NO / ALL NOT (REVERSE
No brown is a dogs.
No brown is a bulls.
SOME NOT
Some dogs are not brown.
Some brown are not bulls.
SOME NOT (REVERSE)
Some brown are not dogs.
Some bulls are not brown.
Lets discuss Either-Or condition in syllogism:
Complementary pair of conclusions:
Students are required to be more attentive in selecting complementary pair of conclusion, where neither of the conclusions is definitely true but a combination of both makes a complementary pair.
I. Complementary pair means Subject and Predicate are same in given statements.
II. One should be in positive and one should be in negative.
Example:
Statement: Some reference books are encyclopedias
Some encyclopedias are schedules
Conclusions:
I. Some reference books are schedules
II. Some schedules are not reference books
Explanation: Here,
I. Complimentary pair…….
II. + ve and – ve …….
Hence EITHER conclusion I OR conclusion II is true.
Special cases
Combinations Conclusion
A + E Either I or II follows
E + I Either I or II follows
I + O Either I or II follows
E + O Either I or II follows
IMPORTANT NOTE:
EITHER and OR case takes place between these three complimentary pairs only when they share same element between them and there have no relation between them.
Between ALL ……and SOME NOT………..
Between SOME……. and SOME NOT……….
Between SOME……… and NO……………
EITHER AND OR case should not take place when there is combination of ALL………. and NO………….
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Question of the day
Q.1-6. In each of the questions below is given two/three statements followed by two conclusions numbered I and II. You have to take the given statements to be true even if they seem to be at variance with commonly known facts. Read all the conclusions and then decide which of the given conclusions logically follows.
Give answer-
(1) If only conclusion I follows.
(2) If only conclusion II follows.
(3) If either conclusion I or II follows.
(4) If neither conclusion I nor II follows.
(5) If both conclusions I and II follow.
Q.1. Statements: Some papers are test
No paper is a answer
Conclusions:
I. No answer is a test.
II. Some papers are definitely not test.
Ans: (4)
Explanation:
Q.2-3.Statements: No cool is a point.
All force are energy
All energy are point
Q.2. Conclusions:
I. Some force are definitely not point.
II. No cool is a force.
Ans: (2)
Explanation:
Q.3. Conclusions:
I. No energy is a cool.
II. Some force being cool is a possibility.
Ans: (1)
Explanation:
Q.4-5.Statements: Some good are nice.
No song is a good
All book are song
Q.4. Conclusions:
I. No good is a book
II. All book being nice is a possibility.
Ans :( 5)
Explanation:
Q.5. Conclusions:
I. No nice is a book
II. All song are book
Ans: (4)
Explanation:
Q.6. Statements: Some rings are fingers.
All fingers are foot
No foot is a hand.
Conclusions:
I. No ring is a foot.
II. Some hands are ring.
Ans:(4)
Explanation:
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Directions (1-5): Following questions are based on the five four-digit numbers given below
4851 2894 3645 8731 1239
Q.1. If the positions of first and fourth digits in each number are interchanged, which of the following will be the second digit of third highest number?
(1) 1 (2) 4 (3) 8
(4) 9 (5) 6
Ans: (3)
Explanation:
4851 2894 3645 8731 1239
After interchanging:
1854 4892 5643 1738 9231
Third highest number: 4892
Second digit: 8
Q.2. If the first digit in all the numbers starting with an even digit is replaced by a number preceding it and then which of the following will be the sum of the first digits of the highest and the lowest numbers of the new formed series?
(1) 4 (2) 8 (3) 7
(4) 6 (5) 3
Ans: (2)
Explanation:
4851 2894 3645 8731 1239
After replacing:
3851 1894 3645 7731 1239
Highest number: 7731
First digit: 7
Lowest number: 1239
First digit: 1
Sum = 7 + 1 = 8
Q.3. If the positions of the third and the fourth digits in each number are interchanged, which of the following will be the second highest number thus formed?
(1) 4851 (2) 3645 (3) 1239
(4) 2894 (5) 8731
Ans: (1)
Explanation:
4851 2894 3645 8731 1239
After interchanging:
4815 2849 3654 8713 1293
Second highest number: 4815
Q.4. If all digits are arranged in ascending order in each number then which of the following will be third digit of the highest number thus formed?
(1) 8 (2) 6 (3) 3
(4) 5 (5) 9
Ans: (4)
Explanation:
4851 2894 3645 8731 1239
After arranging in ascending order:
1458 2489 3456 1378 1239
Highest number: 3456
Third digit: 5
Q.5. If all the digits of all five numbers are added then it will divisible by which number?
(1) 8 (2) 6 (3) 2
(4) 9 (5) 3
Ans: (5)
Explanation:
4851 2894 3645 8731 1239
After adding:
4 + 8 + 5 + 1 + 2 + 8 + 9 + 4 + 3 + 6 + 4 + 5 + 8 + 7 + 3 + 1 + 1 + 2 + 3 + 9
= 93
Divisible by = 3
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QUESTION OF THE DAY
Q.1-5. The questions are based on following set of number.
539 869 742 683 348
Q.1. If all the numbers are arranged in descending order what will be the difference between the second digit of third number and third digit of second number?
(1) 6 (2) 5 (3) 4
(4) 2 (5) None of these
Q.2. If in each number the first and the third digits are interchanged then which number will be the third highest?
(1) 869 (2) 348 (3) 683
(4) 742 (5) None of these
Q.3. If one is subtracted from the first and third digit of each of the numbers what will be the difference between the first digit of the highest number and the first digit of the lowest number?
(1) 6 (2) 3 (3) 4
(4) 5 (5) None of these
Q.4. If in each number first digit is replaced by the third digit, second digit is replaced by the first digit and third digit is replaced by the second digit then which number will be the second highest?
(1) 539 (2) 869 (3) 348
(4) 683 (5) None of these
Q.5. If third digit of second lowest number is multiplied by the first digit of third highest number then what will be the resultant?
(1) 52 (2) 53 (3) 54
(4) 64 (5) None of these
EXPLANATION
Q.1.(1) 869 742 683 539 348
8 - 2 = 6
Q.2.(2) 935 968 247 389 843
Q.3.(4) 438 768 641 582 247
7 - 2 = 5
Q.4.(1) 953 986 274 368 834
Q.5.(3) 539 683 = 9 × 6 = 54
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Question of the day
Q.1-5. Study the following diagram carefully and answer the questions given below:
Q.1. How many players are there who play both cricket and chess?
(1) Five (2) Four (3) Six
(4) Cannot be determined (5) None of these
Ans: (1) Five
Q.2. How many players play either hockey or football but not cricket?
(1) Five (2) One (3) Two (4) Either 2 or 3
(5) None of these
Ans: (5) Three
Q.3. How many players play neither football nor cricket?
(1) Five (2) Four (3) Three (4) Two
(5) None of these
Ans: (3) Three
Q.4. How many players play hockey?
(1) Five (2) Four (3) Six
(4) Cannot be determined (5) None of these
Ans: (2) Four
Q.5. How many players play all four games?
(1) Four (2) One (3) Five (4) Two
(5) None of these
Ans: (2)
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Puzzle of the day
Q.1-5.Read the following information carefully and answer the questions given below:
Seven neighbours Meera, Tara, Charu, Laila, Sonali, Divya and Rani all are living in a building on ground floor, first, second, third, fourth, fifth and sixth floor. All are going outside from the building in a week i.e., Sunday, Monday, Tuesday, Wednesday, Thursday, Friday and Saturday (not necessarily in the same order). Only one person goes outside from the building in a day.
Sonali lives on second floor and goes outside on Tuesday. Tara and Charu are not the neighbours of Sonali and go outside on Friday and Thursday respectively. Meera lives on sixth floor and goes outside on Saturday. Two persons live between the floor of Charu and Divya. Rani is the neighbour of Divya and lives on ground floor and goes outside on Sunday. Charu lives just below Tara's floor. Laila does not go outside on Monday.
Q.1. Charu lives on which floor?
(1) Second floor (2) Fifth floor (3) Sixth floor (4) Fourth floor (5) None of these
Q.2. Divya goes outside on which day?
(1) Monday (2) Sunday (3) Tuesday (4) Wednesday (5) None of these
Q.3. Who of the following is the neighbour of Laila?
(1) Tara (2) Meera (3) Sonali (4) Divya (5) None of these
Q.4. Laila go outside on which day?
(1) Thursday (2) Wednesday (3) Monday (4) Tuesday (5) None of these
Q.5. Which of the following statements is true?
(1) Rani – Monday (2) Divya – Sunday (3) Sonali –Wednesday (4) Laila – Thursday (5) None of these
Explanation:
Q.1.(4)
Q.2.(1)
Q.3.(3)
Q.4.(2)
Q.5.(5)
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------More questions based on INEQUALITIES
Q.1. Which of the following symbols should replace the question mark (?) in the given expression in order to make the expressions P > A and T < L definitely true?
P > L (?) A > N = T
(1) < (2) > (3) < (4) >
(5) Either < or <
Explanation: P > L (?) A > N = T
(1) P > L < A > N = T
We cannot find the relation between P and A or T and L because they have opposite symbols between them.
Hence option (1) is not correct.
(2) P > L > A > N = T
Symbols are in one direction between P and A and they have 100% sign between them so P > A is true.
For T< L
Let us concentrate on given expression
P > L > A > N = T
There are >, >, = signs between L and T.
According to the short trick,
P > L > A > N OR P > L > A > T
L and T elements have one direction symbols of 100 % and 50% signs between them, so 100% sign will be true.
Therefore L > T is true.
Hence option (2) is correct.
(3) P > L < A > N = T
Since, there are opposite symbols between P and A or T and L, therefore there is no relation between them.
Hence option (3) is not correct.
(4) P > L > A > N = T
Firstly we have found that all symbols are in one direction.
We get 100% sign between P and A so P > A is true but we don’t
have 100% sign between L and T so L > T is false.
Hence option (4) is not correct.
(5) As we discuss in (1) and (3) similarly option (5) is not correct.
Q.2. Which of the following conclusion will be true, if the expression T > S < A=O < R is definitely true?
(1) T < O (2) S < R (3) T > A (4) S =O
(5) T < R
Explanation: T > S < A=O < R
For conclusion (1): Since, there are 100 % but opposite symbols (means >, <) between T and O, therefore there is no relation between them and T < O is false.
Hence conclusion (1) is not correct.
For conclusion (2): Since, there are 100 % and one direction symbol (means <, <) between S and R, therefore R > S is true.
Hence conclusion (2) is correct.
For conclusion (3): Since, there are 100% but opposite symbols (means >, <) between T and A, therefore there is no relation between them and T > A is false.
Hence conclusion (3) is not correct.
For conclusion (4): Since, there are two symbols < and = between S and O. Therefore O > S is true while S = O is false.
Hence conclusion (4) is not correct.
For conclusion (5): Since, there are 100% but opposite symbols (>, <) between T and R, therefore there is no relation between them and T < R is false.
Hence conclusion (5) is not correct.
Q.3. What should come in place of question mark (?) in the given expression in order to make ‘Z > F’ and ‘G ≥ U’ definitely true?
U ≤ R (?) G ≤ T > Z (?) S ≥ N = O > F
(1) <, >
(2) < or =, ≤
(3) =, <
(4) ≤, >
(5) ≥, ≤
Explanation:
(1) U ≤ R < G ≤ T > Z > S ≥ N = O > F
For Z > F
There are one direction symbols between Z and F. Also they have 100% sign between them. Therefore Z > F is true.
For G ≥ U
G and U have both 100% and 50 % sign between them, in one direction thus only 100 % sign is true.
Therefore G > U is false.
Hence option (1) is not correct.
(2) U ≤ R = G ≤ T > Z < S ≥ N = O > F
G > U is true but Z > F is false because Z and F have opposite symbols between them.
Hence option (2) is not correct.
(3) U < R = G < T > Z < S > N = O > F
G > U is true but Z > F is false because Z and F have opposite symbols between them.
Hence option (3) is not correct.
(4) U < R < G <T > Z > S ≥ N = O > F
G and U have only 50% sign between them therefore G > U is true and Z and F have both 100 % and 50% signs so Z > F is also true.
Hence option (4) is correct.
(5) U < R > G < T > Z < S > N = O > F
Due to opposite signs option (5) is not correct.
Q.4. Which of the following should be placed in the blank spaces respectively (in the same order from left to right) in order to complete the given expression in such a manner that makes the expression ‘Z < K’ definitely false?
____ ≤ ___ < ___ > ____ = _____
(1) O, M, K, Z, U
(2) O, Z, K, M, U
(3) Z, O, K, M, U
(4) M, Z, K, U, O
(5) K, M, Z, O, U
Explanation:
(1) O ≤ M < K > Z = U
K > Z is true.
Hence option (1) is not correct.
(2) O ≤ Z < K > M = U
Z < K is true.
Hence option (2) is not correct.
(3) Z ≤ O < K > M = U
K > Z is true.
Hence option (3) is not correct.
(4) M ≤ Z < K > U = O
Z < K is true.
Hence option (4) is not correct.
(5) K ≤ M < Z > O = U
Here Z > K is true and K > Z is false.
Hence option (5) is correct.
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More questions based on INEQUALITIES
Let’s know some short tricks:
· If all symbols are in one direction and elements have 100 % sign in between them then 100 % relation can be find out.
Example: If A > B > C
Then A > B (True)
B > C (True)
A > C (True)
Again A < B < C
Then A < B (True)
B < C (True)
A < C (True)
· If all symbols are in one direction and elements have 50 % sign in between them then 50 % relation can be find out.
Example: If A > B > C
Then A > B (True)
B > C (True)
A > C (True)
· If all symbols are in one direction and elements have both 100% and 50 % signs in between them then only 100 % relation can be find out.
Example: If A > B > C or A > B > C
Then A > B (True)
A > C (True)
But B > C (False) and B = C (False)
Only ‘Either-Or’ condition will be true in between B and C.
· Equal is a magic symbol. It only works when elements have ‘= ‘sign between them.
Example:
Equal relation is true only when
Statement: A = B = C or A = B = C = D …etc...
Then A = B (True)
B = C (True)
A = C (True)
· Equal sign will be neglect, in other cases when
Statement:
A = B > C = D or A = B > C = D or A > B = C > D or …etc….
· If element have opposite symbols between them:-
Example: 1
If statement:
A > B < C or A < B > C or A > B < C or A > B < C
Conclusions:
I. A > C
II. A < C
Either I or II is true.
Note: If all three relations (<, > and =) are shown in between two same elements then there should be
‘Either-Or’ condition.
Example: 2
If statement:
A > B < C or A > B < C
(1) Conclusions:
I. A > B
II. A = B
Either I or II is true.
(2) Conclusions:
I. A > B
II. A = B
Only I is true.
Example: 3
If statement:
A > B < C or A > B < C
Conclusions:
I. B < C
II. B = C
Either I or II is true.
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More questions based on INEQUALITIES
Q.1-6.In the following questions, the symbols %, d, *, + and /
are used with the following meaning as illustrated below:
'B % C' means ‘B is neither greater than nor equal to C'.
'B d C’ means ‘B is neither smaller than nor equal to C.
'B * C’ means ‘B is not greater than C'.
'B + C’ means ‘B is not smaller than C'.
'B / C' means ‘B is neither smaller than nor greater than C.
In the following questions statements showing, relationship between different elements has been given, which are followed by conclusions I & II.
Give answer:
(1) If only conclusion I is true.
(2) If only conclusion II is true.
(3) If either conclusion I or II is true.
(4) If neither conclusion I nor II is true.
(5) If both conclusions I and II are true
Q.1-2. Statements: P + Q d T, M / R / Y % Q, A * C d T d X
Q.1. Conclusions: I. P d Y II. P d R
Q.2. Conclusions: I. T % R II. T % M
Q.3-4. Statements: M + L * J + Y, L d U d V d S, N * G * V d A
Q.3. Conclusions: I. M % S II. M d S
Q.4. Conclusions: I. Y + V II. V d Y
Q.5-6. Statements: F + K d H * Z, Q d R * S * H, D + O d R d W
Q.5. Conclusions: I. F d S II. F d R
Q.6. Conclusions: I. S d D II. S % O
Explanations: For these questions firstly we have to know that the meaning of the symbols %, d, *, + and /.
Q.1-2. Statements: P + Q d T, M / R / Y % Q, A * C d T d X
P > Q > T, M = R = Y < Q, A < C > T > X
After combining-
Q.1. (5) Conclusions:
I. P > Y True
II. P > R True
Both I and II are true
Q.2. (4) Conclusions:
I. T < R False
II.T < M False
Neither I nor II is true
Q.3-4. Statements: M + L * J + Y, L d U d V d S, N * G * V d A
M > L < J > Y, L > U > V > S, N < G < V > A
After combining-
(There is no need to show the relation between V and A)
Q.3. (2) Conclusions:
I. M < S False
II. M > S True
Only II is true
Q.4. (3) Conclusions:
I. Y > V
II. V > Y
Either I or II is true
Q.5-6. Statements: F + K d H * Z, Q d R * S * H, D + O d R d W
F > K > H < Z, Q > R < S < H, D > O > R > W
After combining-
Q.5. (5) Conclusions:
I. F > S True
II. F > R True
Both I and II are true
Q.6. (4) Conclusions:
I. S > D False
II. S < O False
Neither I nor II is true
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Q.1-5. In each of the following questions, assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true.
Give answer -
(1) If only conclusion I is true.
(2) If only conclusion II is true.
(3) If either conclusion I or II is true.
(4) If neither conclusion I nor II is true.
(5) If both conclusions I and II are true.
Explanation:
This equation will be written in two ways because T = S.
The common sign between U and R is ‘>’
So, conclusion I is definitely true.
For conclusion II,
Let us see the given statement.
We can see there are two relations between R and P so we cannot be sure about one relation.
Therefore, R > P is false.
Hence the answer is option (1).
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Inequalities
Dear students today we are going to discuss inequality chapter. Simply inequality is based on only three symbols i.e.
> (greater than), < (smaller than) and = (equals to).
Other symbols i.e. > and < are formed with the help of those three symbols given above.
Now-a-days these questions are coming in every exam and nearly five in number. Some of you can solve it easily but there are so many students who don’t know how to solve it.
But there is a simple method to solve these questions in exams in seconds without using pen. Today we will consider simple example and in our next post we will discuss it’s another part.
Example:
(I) Statement: 
Conclusions:
Now we will consider each conclusion one by one-
First conclusion is: N > I
Now you just see these two alphabets in the question, as the arrows between N and I are in one direction which is pointing in the direction of N and easily we can say that N > D and as well as N > I, so first conclusion is true. Remember if the arrow was pointing in the direction of I i.e. even if one arrow is towards I, than the conclusion becomes false.
Now let us take second conclusion: N > W
Here, N > W = L
Its mean W = L
So, N > L or W is definitely true.
But, N > L or W is false and N = W or L is also false.
And a specific rule will be form
When,
Third conclusion is: L > G
In the given statement: I < D < N > W = L < G, G is either greater than or equal to L (means the sign between G and L is not decidable). Therefore the third conclusion is false.
Fourth conclusion is: G > D
In the given statement, the symbols which are used between G and D are in opposite directions of each other. So the conclusion fourth is false.
Fifth conclusion is: G > W
In the given statement W is equal to L and L is less than or equal to G that’s way W is also less than or equal to G. Hence, the conclusion fifth is true.
Formulas for Order and Ranking
· Finding ranks either from left or from right:
Total – (given rank – 1) = required rank
· Finding total numbers:
When ranks of one person is given from both sides of the row.
Ranks of common person from both sides (R1 + R2) – 1
· Finding total number of the person: (Misc. Case)
When ranks of two persons and number of the persons who are sitting between these two persons are given.
(a) (R1+R2) + number of middle persons
(b) (R1+R2) - (number of middle persons +2)
NOTE: Apply condition (b) only for overlapping case.
· Finding the number of persons who are sitting between any two persons: (Simple case)
Total - (Rank from left + Rank from right)
· Finding the number of persons who are sitting between any two persons: (Overlapping Case)
(Rank from left + Rank from right) - (Total + 2)
· Finding Rank of middle person: (Quick Trick)
Step 1- Convert both ranks from same side (side from which rank of exactly mid asked)
Step 2- Finds the average of both ranks (answer)
· Shortcut for calculating total number of maximum and minimum persons in a row:
NOTE: Mid no. means number of the middle persons.
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More questions based on the chapter :- Order and RankingQ.1-2. Study the following information carefully and answer the questions given below.
In a class of boys and girls, Jadeja's rank is 20th and Sunanda's rank is 11th.
Jadeja's rank among the boys is 11th and Sunanda's rank among the girls is 6th.
In the class, Sunanda's rank is 64th from the other end.
From the other end, Jadeja's rank among the boy's is 34th.
Q.1. How many total boys and girls in the class?
(1) 65 (2) 77 (3) 71 (4) 74 (5) None of these
Q.2. How many girls are there between Jadeja and last rank holder (assuming it is a boy) in the class?
(1) 25 (2) 21 (3) 23 (4) 22 (5) None of these
Explanations of Q-1 and Q-2:
Among Nikhil, Moon, Kapil, Jagdish and Gulshan each securing different marks in a subject, Moon secured more marks than only Kapil. Gulshan and Jagdish secured less marks than only Nikhil.
Q.3. Who among them secured third least marks?
(1) Nikhil (2) Jagdish (3) Moon (4) Cannot be determined (5) None of these
Q.4. If Nikhil secured 80 marks and Jagdish secured 65 marks then what is the possibility of Gulshan’s marks?
(1) 78 (2) 63 (3) 60 (4) Cannot be determined (5) None of these
Explanation:
(1) Yo (2) Zojo (3) Xe (4) Data inadequate (5) None of these
Explanation:
Ans: (4)
Q.6. Zombo, correctly remembers that his father's birthday is before 29th July but after 24th July whereas his younger brother correctly remembers that their father's birthday is after 23rd July but before 28th July and his elder brother correctly remembers that their father's birthday is on an odd date. On which date of July is definitely their father's birthday?
(1) Twenty-five or Twenty-seven (2) Twenty-seven (3) Twenty-five (4) Twenty-six (5) None of these
(1) Twenty-five or Twenty-seven (2) Twenty-seven (3) Twenty-five (4) Twenty-six (5) None of these
Explanation:
Ans: (1)
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More questions related to the chapter order and ranking
Q.1. In the row of 40 students, Mahesh is 28th from left end and Suresh is 25th from right end. If Danish is sitting exactly in between them, what will be Danish’s position from left?
(1) 14 (2) 22 (3) 28 (4) 18 (5) None of these
Explanation:
Ans: (2)
Q.2. Jai is 25th from left and Vijay is 24th from right. When they interchange their positions respectively then Vijay becomes 31st from right end. What will be Jai's position from left after interchanging?
(1) 25 (2) 26 (3) 27 (4) 28 (5) None of these
Explanation:
Jai's position from the left after interchanging = 25 + 6 + 1 = 32
Ans: (5)
Q.3. In a row of girls, Rita and Monika occupy the ninth place from the right end and tenth place from the left end, respectively. If they interchange their places, then Rita and Monika occupy seventeenth place from the right and eighteenth place from the left respectively. How many girls are there in the row?
(1) 25 (2) 26 (3) 27 (4) Data inadequate (5) None of these
(1) 25 (2) 26 (3) 27 (4) Data inadequate (5) None of these
Explanation:
Ans: (2)
Q.4. Ram is 27th place from left end in the row of 44 boys. Rohit is 15th from the right end in the same row .How many boys are there between them in the row?
(1) Eleven (2) Ten (3) Six (4) Two (5) None of these
(1) Eleven (2) Ten (3) Six (4) Two (5) None of these
Explanation:
Ans: (4)
Q.5. Students line up in a queue in which Aman stands fifteenth from the left and Simran is seventh from the right. If they interchange their places, Simran would be fifteenth from the right. How many students are there in the queue?
(1) 21 (2) 22 (3) 28 (4) 29 (5) None of these
Explanation:
Simran’s new position is 15th from the right as well as the left end of the row.
Therefore number of students in the queue = (14 + 1 + 14) = 29.
(1) 21 (2) 22 (3) 28 (4) 29 (5) None of these
Explanation:
Simran’s new position is 15th from the right as well as the left end of the row.
Therefore number of students in the queue = (14 + 1 + 14) = 29.
Ans: (4)
Q.6. In a queue of children, Ajay is fifth from the left and Sunil is sixth from the right. When they interchange their places among themselves, Ajay becomes thirteenth from the left. Then, what will be Sunil's position from the right?
(1) 8th (2) 14th (3) 15th (4) 16th (5) None of these
Explanation:
Since Ajay and Sunil interchange places, so Ajay’s new position (13th from left) is the same as Sunil’s earlier position (6th from right).
So, number of children in the queue = (12 + 1 + 5) = 18.
Now, Sunil’s new position is the same as Ajay's earlier position fifth from left.
Therefore Sunil’s position from the right = (18 - 4) = 14th.
Ans: (2)
Q.7. Kunal ranked sixteenth from the top and twenty ninth from the bottom among those who passed an examination. Six boys did not participate in the competition and five failed in it. How many boys were there in the class?
(1) 35 (2) 45 (3) 50 (4) 55 (5) None of these
Explanation:
Number of boys who passed = (15 + 1 + 28) = 44
Total number of boys in the class = 44 + 6 +5 = 55.
Ans: (4)
Q.8. In a queue, Vijay is fourteenth from the front and Jack is seventeenth from the end, while Mary is exactly at the middle of Vijay and Jack. If Vijay be ahead of Jack and there be 48 persons in the queue, how many persons are there between Vijay and Mary?
(1) 5 (2) 6 (3) 7 (4) 8 (5) None of these
Explanation:
Number of persons between Vijay and Jack = 48 – (14 + 17) = 17.
Now, Mary lies in middle of these 17 persons i.e., at the ninth position.
So, number of persons between Vijay and Mary = 8.
Ans: (4)
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ORDER AND RANKING
In this chapter generally the rank of a person from both sides left or right or from top and from bottom are mentioned and total numbers of persons are asked. In other words a set, group or series of numerals is given and the candidates is asked to trace out numerals following certain given conditions. Sometimes the questions are based on their interchanged positions.
There are mainly three/four types of questions -
1. Total persons and position of one person (either from left or right) are given.
2. Position of more than one person is given.
3. Over lapping conditions:
a. Overlapping case: When (left + right) positions > Total number of students
b. Not overlapping case: When Total number of students > (left +right) positions
4. Ascending/Descending Order according age, height, marks etc.
We have to find out:
1. Position from other side.
2. Total number of persons.
3. Number of persons in between
4. Minimum/maximum number of persons in the row.
5. Number of persons on either side of a particular person. Examples:
Here is a table.
Ema’s rank from top = 1 and from bottom = 5
Now total member in the row = 5
Means total rank = (rank from top + rank from bottom) – 1
= (1+ 5) – 1 = 5
Rank from top = total rank – (rank from bottom-1)
= 5 – (5-1) = 1
Rank from bottom = total rank – (rank from top – 1)
= 5 – (1-1) = 5
Practice on these questions:
Q.1. Meenam is fourteenth from the right end in a row of 40 girls. What is her position from the left end?
(1) 24th (2) 25th (3) 26th (4) 27th (5) None of these
EXPLANATION:
Clearly, number of girls towards the right of Meenam = 13
So, Meenam’s rank from left end = 40 – 13 = 27th
Ans. (4)
Q.2. Raju is seventh from left and Rohan is ninth from right.
If there are six students between them then how many students are there in a row?
(1) 8 (2) 10 (3) 22 (4) 21 (5) Cannot be determined
EXPLANATION:
Total number of students in a row = 7+9+6 = 22
Note: We cannot apply overlapping case in this question because if we are applying overlapping case then the minimum student is eight which conflict with the rank of Rohan from right.
Q.3. Rohan’s rank 25 from the top and Sohan’s rank 30 from the bottom. If there are three students in between Rohan and Sohan then find out the total number of student ?
(1) 50 (2) 62 (3) 58 (4) Can't be determined (5) None of these
EXPLANATION:
Ans (4) Either (1) or (3) Minimum student = 50 while maximum student 58.
Q.4. Ram is eighth from left end and is fourth to the left of Shyam who is eighth from right end. Then how many students are there in a row?
(1) 19 (2) 21 (3) 24 (4) 20 (5) None of these
EXPLANATION:
Ans: (1)
Q.5. In a row of boys facing towards North, A is sixteenth from the left end and C is sixteenth from the right end. B, who is fourth to the right of A, is fifth to the left of C then. How many boys are there in the row?
(1) 39 (2) 40 (3) 41 (4) 42 (5) None of these
EXPLANATION:
Clearly, according to the given conditions, there are 15 boys to the left of A, as well as to the right of C. Also, B lies between A and C such that there are 3 boys between A and B; and 4 boys between B and C.
So, number of boys in the row = (15 + 1+ 3 + 1+4 +1+15)
= 40
Ans: (2)
Q.6. Three persons A, B and C are standing in a queue. There are five persons between A and B and eight persons between B and C. If there are three persons ahead of C and 21 behind A, then what could be the minimum number of persons in the queue?
(1) 27 (2) 28 (3) 40 (4) 41 (5) None of these
EXPLANATION:
As per the given conditions, there are two possible arrangements as shown below:
Minimum person
Clearly, for the minimum number of person, we shall consider arrangement (ii).
In (ii), number of persons in the queue
= (3 + 1 + 2 + 1 + 21) = 28.
Ans. (2)
Q.7. In a row of 40 girls, when Komal was shifted to her left by 4 places her number from the left end of the row became 10. What was the place of Swati from the right end of the row if Swati was three places to the right of Komal’s original position?
(1) 22 (2) 23 (3) 25 (4) 26 (5) None of these
EXPLANATION:
On shifting 4 places to the left, Komal becomes 10th from the left end of the row. Thus, Komal’s original position was 14th from the left end.
Clearly, for the minimum number of person, we shall consider arrangement (ii).
In (ii), number of persons in the queue
= (3 + 1 + 2 + 1 + 21) = 28.
Ans. (2)
Q.7. In a row of 40 girls, when Komal was shifted to her left by 4 places her number from the left end of the row became 10. What was the place of Swati from the right end of the row if Swati was three places to the right of Komal’s original position?
(1) 22 (2) 23 (3) 25 (4) 26 (5) None of these
EXPLANATION:
On shifting 4 places to the left, Komal becomes 10th from the left end of the row. Thus, Komal’s original position was 14th from the left end.
Swati is 3 places to the right of Komal’s original position.
Clearly, Swati is 17th from the left end.
Number of girls to the right of Swati = (40 – 17) = 23.
Thus, Swati is 24th from the right end of the row.
Clearly, Swati is 17th from the left end.
Number of girls to the right of Swati = (40 – 17) = 23.
Thus, Swati is 24th from the right end of the row.
Ans. (5)
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DIRECTION AND DISTANCE
This test is meant to judge the candidate’s ability to trace and follow correctly and sense the direction correctly.
There are four main directions:
North, East, South, West
There are four subordinate directions:
North-East (N-E), South - East (S-E), South-West (S-W) & North-West (N-W) those are also called sub directions and these sub directions are between prime directions like NE is between North and East, SE is between South & East & so on,....
North-East (N-E), South - East (S-E), South-West (S-W) & North-West (N-W) those are also called sub directions and these sub directions are between prime directions like NE is between North and East, SE is between South & East & so on,....
Examples:
Type - 1
Q.1. Shyam travels 7 km. toward North, then he turn to his right and walks 3 km. He again turns to his right and moves 7 km forward. Now in which direction is he from his starting point?
(1) North (2) South (3) East (4) West (5) Can’t be determined
EXPLANATION: Ans.3
Type - 1
Q.1. Shyam travels 7 km. toward North, then he turn to his right and walks 3 km. He again turns to his right and moves 7 km forward. Now in which direction is he from his starting point?
(1) North (2) South (3) East (4) West (5) Can’t be determined
EXPLANATION: Ans.3
Q.2. Lucky walks 7 km. in the east. Then he turns to his right and moves 20 km, then he turns to his left and moves 5 km, then he turns to his left and moves 11 km. and then again he turned to his left and move 12 km. Now in which direction is he from his starting point and how far?
(1) 9 km South (2) 64 km East (3) 20 km west (4) 7 km south (5) None of these
(1) 9 km South (2) 64 km East (3) 20 km west (4) 7 km south (5) None of these
Q.1. A man is facing North. He turns to 1800 in clockwise direction and another 450 in the same direction and the 2700 in the anticlockwise direction. Which direction is he facing now ?
(1) South-West (2) South-East (3) North-East (4) North-West (5) North
EXPLANATION: Ans. 4
Final Direction North-West Degrees can only be judged towards the direction in which a person is facing instead of the path covered by him.
Type - 3
Q.1. One evening before sunset Rekha and Hema were talking to each other face to face. If Hema’s shadow was exactly to the right of Hema, which direction was Rekha facing?
(1) North (2) South (3) East (4) Data is inadequate (5) None of these
EXPLANATION: Ans. 2
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       CLOCKQ 1) How often the hour hand and minute hand of a clock coincide ?A 65 minutes B 65(4/11) minute C 65(10/11) minute D 65(5/11) minute Ans (D) Q 2) If the minute hand of a clock has moved 3120 , how many degrees has the hour hand moved ? A 350 B 250 C 260 D 270 Ans (C) Q3) How many time in a day do the hands of the clock lie in opposite direction forming a straight line? A 21 B 22 C 24 D 11 Ans (B) Q4) A clock show 7:15 when see through a mirror, what time does it show? A 4:45 B 6:45 C 7:45 D 3:45 Ans (A) |
Read the instructions carefully and answer the given questionA-B means A is mother B A*B means A is son of B A%B means A is sister of B Q- P+Q-R%S*T Then how is T related to P? 1)Daughter-in-law 2)Son-in-law 3)Either 1 or 2 4)Can not determine 5)None of these Solution- 2)Son-in-law Note- This is a simple question but when ever we use short trick we got confused and we use to mark option 4)Can not determine just because here after T there is not any syomble so we think that gender of T we cant determine BUT if the sequence of relation is in such a way (1.Mother/father-2.sister/brother-3.son/doughter ) then gendre of last elment will be dependent on 1st relation and they will be in relation of Husband-Wife. |
| RANKING: Q 1. Some boys are sitting in a row.R is sitting fourteen from the left and S is seventh from the right .If there are four boy R and S. How many boys are there In the row ? Ans : (1) 34 (2) 33 (3) 25 (4) 24 (5) 26 Explanation :- Total number of boy in the row = no. of boy uptil R + no. of boy including S + no. of boys between R and S Total boy = 14 + 7 + 4 = 25 Q 2. In a class of boys stands in a single line one boy in nineteenth in order from both the end .How many boys are there in the class Ans : (1) 34 (2) 35 (3) 37 (4) 36 (5) 33 Explanation: no . of boy = ( 19 +19 -1 ) |
| DATA SUFFICIENCY About Data Sufficiency This topic covers most of the topics of reasoning i.e. alphabetical series, coding and decoding, blood relation, direction, ranking etc.
(1) If statement I alone is sufficient but statement II alone is not sufficient. (2) If statement II alone is sufficient but statement I alone is not sufficient. (3) If each statement alone (either I or II) is sufficient. (4) If statement I and II together are not sufficient. (5) If both statement together are sufficient, but neither statement alone is sufficient. Examples Q.1. Who scored highest among P, Q, R, S and T ? (I) Q scored more than S, but not as much as R. (II) T scored more than R, but not more than P. Explanation: According to question- (I) R>Q>S, (II) P>T>R So, P>T>R>Q>S P scored the highest. So, both statements are needed to arrive at answer. Ans.(5) Q.2. Five friends P, Q, R, S and T are standing in a row facing East. Who is standing at extreme left end ? (1) R is between T and Q (2) Only P is between S and T. R is immediately right of T. Explanation: According to question : S is extreme left end. So, both statements are needed to arrive at answer. S P T R Q Ans.(5) |
