# Reasoning Quiz On Inequality Day 1 Bag

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Que. 1

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given five conclusions is/are definitely true and then give your answers accordingly.

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Conclusions:

1. R < I
2. O < Z

III.  Z < M

1. G ≤ Z
2. M = N

1.Both conclusions I and II are true.

2.Conclusion I, III and IV are true.

3.Both conclusion III and IV are true.

4.Either conclusion I or III is true.

5.Only conclusion V is true.

Answer:

Given statements: M ≥ O = N; I ≥ G > R; N > Z; Z ≥ I

On combining: M ≥ O = N > Z ≥ I ≥ G > R

Conclusion:

1. R < I → True as it is given that I ≥ G > R.
2. O < Z → Not true as it is given that O = N > Z

III. Z < M → True as it is given M ≥ O = N > Z.

1. G ≤ Z → True as it is given that Z ≥ I ≥ G,
2. M = N → Not true as it is given that M ≥ O = N therefore N can be smaller than M as well.

Hence, conclusion I, III and IV are true.

Que. 2

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given three conclusions is /are definitely true and then give your answers accordingly.

Statements: T < S; S ≤ U; L > U; R ≥ U

Conclusions:

1. R ≥ S
2. L > S

III. T < U

1.Only III is true

2.Only I is true

3.Only I and III are true

4.Either II or III is true

5.All are true

Answer:5

Given statements: T < S; S ≤ U; L > U; R ≥ U

On combining: T < S ≤ U < L; T < S ≤ U ≤ R

Conclusions:

1. R ≥ S → True (as T < S ≤ U ≤ R → R ≥ S)
2. L > S → True (as S ≤ U < L → L > S)

III. T < U → True (as T < S ≤ U → T < U)

Therefore, all conclusions are true.

Que. 3

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given three conclusions is /are definitely true and then give your answers accordingly.

Statements: A ≤ K; K > P; P = O

Conclusions:

1. A ≥ P
2. K > O

III. O > A

1.Only III is true

2.Only I and II are true

3.Only II is true

4.None is true

5.All are true

Answer:3

Given statements: A ≤ K; K > P; P = O

On combining: A ≤ K > P = O

Conclusions:

1. A ≥ P → False (as A ≤ K > P → thus clear relation between A and P cannot be determined)
2. K > O → True (as K > P = O)

III. O > A → False (as A ≤ K > P = O → thus clear relation between A and O cannot be determined)

Therefore, only conclusion II is true.

Que. 4

Directions: In the following questions, the symbols \$, %, *, & and © are used with the following meaning as illustrated below:

‘A % B’ means ‘A is greater than B’.

‘A \$ B’ means ‘A is not greater than B’.

‘A * B’ means ‘A is neither greater than nor equal to B’.

‘A & B’ means ‘A is either greater than or equal to B’.

‘A © B’ means ‘A is neither smaller than nor greater than B’.

Now in each of the following questions assuming the given statements to be true, find which of the conclusion/s given below them is/are definitely true?

Statements:

R * A, A \$ M, P & M, M \$ C

Conclusions:

1. P % R
2. A \$ P

III. P % C

1.Only Conclusion I is true.

2.Both Conclusions I and II are true.

3.Either Conclusion I or III is true.

4.Neither Conclusion I nor III is true.

5.Either Conclusions I or II and III are true.

Answer:2

According to the given information,

 A is Symbol % \$ * & © Meaning > ≤ ≥ = Than B

Statements:

R * A, A \$ M, P & M, M \$ C

→ R

→ P ≥ M ≥ A > R and C ≥ M ≥ A > R

Conclusions:

1. P % R ⇒ P > R (True)
2. A \$ P ⇒ A ≤ P (True)

III. P % C ⇒ P > C (Can’t be determined since P ≥ M and C ≥ M)

Hence, both the conclusions I and II follow.

Que. 5

Statements:

A \$ S © D, Z & X © A, C % S

Conclusions:

1. S % Z
2. D * C

III. X * C

1.Only Conclusion I is true.

2.Both Conclusions II and III are true.

3.Either Conclusion II or III is true.

4.Neither Conclusion I nor III is true.

5.Either Conclusions I or II and III are true.

Answer:2

According to the given information,

 A is Symbol % \$ * & © Meaning > ≤ ≥ = Than B

Statement:

A \$ S © D, Z & X © A, C % S

→ A ≤ S = D, Z ≥ X = A, C > S

→ Z ≥ X = A ≤ S = D

Conclusions:

1. S % Z ⇒ S > Z → false (as Z ≥ X = A ≤ S → relation between S and Z cannot be established)
2. D * C ⇒ D

III. X * C ⇒ X Hence both the conclusion II and III follows.

Que. 6

Statements:

F © G, F % H & V, B \$ H

Conclusions:

1. F % V
2. G © H

III. V % B

1.Only Conclusion I is true.

2.Both Conclusions I and II are true.

3.Either Conclusion I or III is true.

4.Neither Conclusion I nor III is true.

5.Either Conclusions I or II and III are true.

Answer:1

According to the given information,

 A is Symbol % \$ * & © Meaning > ≤ ≥ = Than B

Statement:

F © G, F % H & V, B \$ H

→ F = H, F > H ≥ V, B ≤ H

→ G = F > H ≥ V, B ≤ H

Conclusions:

1. F % V ⇒ F > V → true
2. G © H ⇒ G = H → false (as G = F > H → G > H)

III. V % B ⇒ V > B → false (as H ≥ V and B ≤ H → B ≤ H ≥ V → relation between V and B cannot be established)

Hence only conclusion I follows.

Que. 7

Statements:

E % J; J & H; H © D; D \$ C; D % F

Conclusions:

1. E % C
2. F * E

III. J % F

1.Only Conclusion I is true.

2.Both Conclusions I and II are true.

3.Both Conclusions II and III are true.

4.Neither Conclusion I nor III is true.

5.Either Conclusions I or II and III are true.

Answer:3

According to the given information,

 A is Symbol % \$ * & © Meaning > ≤ ≥ = Than B

Statements:

E % J; H © D; D \$ C; D % F; J & H

→ E > J; H = D; D ≤ C; D > F; J ≥ H

→ E > J ≥ H = D > F ≤ C

Conclusions:

1. E % C ⇒ E > C → False (as E > J ≥ H → E > H and H = D → E > D and D ≤ C → thus clear relation between E and C cannot be determined)
2. F * E ⇒ F

III. J % F ⇒ J > F → True

Therefore, only conclusions II and III are true.

Que. 8

Statements:

Z © Y; Y & V; W % V; W \$ R

Conclusions:

1. W & Y
2. R % V

III. V \$ Z

1.Only Conclusion I is true.

2.Both Conclusions I and II are true.

3.Both Conclusions II and III are true.

4.Neither Conclusion I nor III is true.

5.Either Conclusions I or II and III are true.

Answer:3

According to the given information,

 A is Symbol % \$ * & © Meaning > ≤ ≥ = Than B

Statements:

Z © Y; Y & V; W % V; W \$ R

→ Z = Y; Y ≥ V; W > V; W ≤ R

→ Z = Y ≥ V

Conclusions:

1. W & Y ⇒ W ≥ Y → False (as Y ≥ V
2. R % V ⇒ R > V → True

III. V \$ Z ⇒ V ≤ Z → True

Therefore, only conclusions II and III are true.

Que. 9

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given three conclusions is /are definitely true and then give your answers accordingly.

Statements: 6 < 2; 5> 2; 7 = 6; 8 > 6

Conclusions:

1. 8 > 7
2. 8 > 5

III. 6 > 2

1.None is true

2.Only I is true

3.Only II is true

4.Only III is true

5.All are true

Answer:2

Given statements: 6 < 2; 5 > 2; 7 = 6; 8 > 6

On combining: 5 > 2 > 6 = 7 < 8

Conclusions:

1. 8 > 7→ True (as 8 > 7)
2. 8 > 5→ False (as 8 > 7 < 5 → No direct relationship between 5 & 8 can be obtained)

III. 6 > 2→ False (as 2 > 6)

Therefore, only conclusion 1 is true.

Que. 10

Directions: In the following question assuming the given statements to be true, find which of the conclusion among given three conclusions is /are definitely true and then give your answers accordingly.

Statements: \$ < @; @ > %; % = &; &< 4

Conclusions:

1. \$ ≥ 4
2. @ >&

III. 4 > %

1.None is true

2.Only I& II are true

3.Only II is true

4.Only II & III are true

5.All are true

Answer:4

Given statements: \$ < @; @ > %; % = &; &<4

On combining: \$ < @ > % = &< 4

Conclusions:

1. \$ ≥ 4→ False (as \$ < @ > % = &< 4→ no direct relationship can be obtained between the two)
2. @ >&→ True (as @ > % = & → @ >&)

III. 4 > % → True (as % = &< 4→ 4 > %)

Therefore, only conclusion II& III are true.

1. In which of these expressions ‘I > E’ be definitely false?

A. I>P≥Q=G≥R>E
B. P<A≤I≤T;E≥O>T
C. E≤A≤L=R<I
D. I>C>=F≤H; E<F
E. I>T=O≥P; E<J=P

Answer & Explanation

Answer – B. P<A≤I≤T;E≥O>T

1. Which of the following symbols 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 both ‘H≥F’ as well as ‘G≤H’ definitely holds true? H _ A _ F _ G _ I
A. >, ≥, <, =
B. >, >, ≥, <
C. ≥, ≥, ≤,≤
D. ≥, =, ≥,<
E. Other than those given as options

Answer & Explanation

Answer – D. ≥, =, ≥,<

1. In Which of the following expressions does the expression ‘I≤Z’ to definitely hold true?
A. K ≥ I ≤ R = P < S ≤ Z
B. U ≥ Z ≥ M = F ≤ A ≥ I
C. I ≥ C > Q ≥ B = N ≤ Z
D. G ≥ I = A < B ≤ S ≤ Z
E. Z ≥ E = G ≥ W = Y ≥ I

Answer & Explanation

Answer – E. Z ≥ E = G ≥ W = Y ≥ I

Directions (14 – 18): In the following questions, the symbols @, #, %, \$ and © are used with the following meaning as illustrated below:
[email protected]’ means ‘P is neither smaller than nor equal to Q’.
‘P#Q’ means ‘P is neither greater than nor equal to Q’.
‘P%Q’ means ‘P is not greater than Q’.
‘P\$Q’ means ‘P is not smaller than Q’.
‘P©Q’ means ‘P is neither smaller than nor greater than Q’.

In each of the following questions, mark answer according to above symbols and their meaning.

1. Which of the following does not make P @ S and V # S definitely not true?
A) P @ Q © R \$ S \$ T @ U © V
B) P \$ Q @ R @ V # T © S % U
C) P # Q % R © S \$ T © U \$ V
D) P © Q @ R © S @ T \$ U © V
E) None of these

View Answer

Option C
Check all the options. And find in which both P > S and V < S are false
In C option, P < Q ≤ R = S ≥ T = U ≥ V. In this P < S and V ≤ S

1. What will come in place of blank in following below such that both P @ S and V % R are definitely true?
P \$ Q @ R _ S \$ T © U \$ V
i) @
ii) ©
iii) %
iv) \$
A) Only (i)
B) Either (i) or (iii)
C) Either (i) or (ii) or (iv)
D) Either (ii) or (iv)
E) All are true

View Answer

Option D
With option D we get,
P ≥ Q > R ≥ S ≥ T = U ≥ V OR P ≥ Q > R = S ≥ T = U ≥ V
With both these we get, P > S and V ≤ R definitely true

1. Which of the following makes C \$ E or B % E definitely true?
A) A © B \$ C @ D % E # F
B) A # B % C \$ D @ E # F
C) A # B © C % D % E \$ F
D) A @ B % C © D # E @ F
E) None of these

View Answer

Option C
Check all the options and find in which both or at least one of B ≤ E and C ≥ E is true. (because or is given)
In C) option B ≤ E  is true. In all other options, both are false.

1. If “A % B # C © D @ E © F \$ G” is true then which of the following is definitely not true?
(i) A # D
(ii) C © F
(iii) B @ D
(iv) E % G
A) Only (i)
B) Only (ii) and (iv)
C) Only (ii) and (iii)
D) Only (i), (iii) and (iv)
E) All are true

View Answer

Option B
In A % B # C © D @ E © F \$ G,
A < D so A # D is true
C > D so C © F is false (means not true)
We do not have sufficient information about B and D to know relationship, so B @ D cannot be said definitely not true.
E ≥ G so E % G is definitely false or not true

1. Which of the following makes A \$ C and E # B definitely true?
A) A \$ B \$ C @ D % E # F
B) A \$ D \$ B @ C @ E # F
C) A © B # C % D @ E \$ F
D) A © B \$ D © C @ E @ F
E) None of these

View Answer

Option D
In D option both A \$ C and E # B are true

Direction (19-23): Relationship between different elements is shown in the statements. Find if the conclusions also follow or not.

1. Statements: P >A ≤ R > S = T; U > R = V ≤ C; S > D ≥ E
Conclusions:
I. E ≤ C
II. T > D
A) only I follows
B) only II follows
C) either I or II follows
D) neither I nor II follow
E) both I and II follow

View Answer

Option B
E < S < R ≤ C so E < C
T = S > D so T > D

1. Statements: A= B ≥ P < T = S; Q > C = D < P < U; E > F < U = V
Conclusions:
I. V > C
II. A > Q
A) only I follows
B) only II follows
C) either I or II follows
D) neither I nor II follow
E) both I and II follow

View Answer

Option A
V = U > C So V > C
A ≥ P > D = C < Q, so relation between A and Q

1. Statements: P ≥ B = A ≥ S < T = Q; C = S > D > R = J
Conclusions:
I. C ≤ P
II. Q > R
A) only I follows
B) only II follows
C) either I or II follows
D) neither I nor II follow
E) both I and II follow

View Answer

Option E

1. Statements: T ≤ S < Q < A = P ≥ M = K; R = D ≥ A ≥ C > S < B = C
Conclusions:
I. K < Q
II. D > T
A) only I follows
B) only II follows
C) either I or II follows
D) neither I nor II follow
E) both I and II follow

View Answer

Option B

1. Statements: P > A ≤ R > S = T; U > R = V ≤ C; S > D ≤ E
Conclusions:
I. U ≥ E
II. U < E
A) only I follows
B) only II follows
C) either I or II follows
D) neither I nor II follow
E) both I and II follow

View Answer

Option C
U > R > S > D ≤ E, so there is no relationship between U and E. But U will be certainly equal to, or greater than, or lesser than E. So these all three symbols are present in options. U ≥ E and U < E. SO eother of them will follow.

1. Which of the following expressions is true, if P > G and F < H are definitely true?
A) Q < P ≥ B > D > F = G < H
B) B ≤ Q < H < D > P > F > G
C) Q ≤ H ≥ B ≥ D < G ≥ P > F
D) D ≤ G > P ≥ F > H ≤ Q ≤ B
E) H ≥ Q > D ≥ B ≥ P = G > F

View Answer

Option A

1. Which of the following is definitely true if P ≤ V < S = G ≥ Q ≥ R > E
A) Q > P
B) S > R
C) V > R
D) S > E
E) P < R

View Answer

Option D
26, Which of the following should replace the question mark so that E > D is definitely true?
C = B > A ≥ D ≤ G ? F ≤ E
A) =
B) >
C) ≤
D) <
E) ≥
View Answer

Option D

1. Which of the following order of letters in the blanks makes the expression D > E is definitely true?
___ < ___ ≤ ___ = ___ > ____
A) B, C, D, E, A
B) A, B, C, E, D
C) D, B, A, C, E
D) E, C, A, B, D
E) C, A, D, B, E

View Answer

Option E

1. What will come in place of question mark in following below such that both E < B and D ≥ G are definitely true? A > B = C > D ? E ≥ F = G
A) ≤
B) ≥
C) =
D) >
E) Both B and C

View Answer

Option E
Directions (29-33): In the following questions, the symbols * , \$, #, δ and % are used with the following meaning as illustrated below:
‘P \$ Q’ means ‘P is neither greater than nor smaller than Q’.
‘P δ Q’ means ‘P is neither greater than nor equal to Q’.
‘P % Q’ means ‘P is neither smaller than nor equal to Q’.
‘P*Q’ means ‘P is not smaller than Q’.
‘P # Q’ means ‘P is not greater than Q’.
Now in each of the following question assuming the given statements to be true, find which of the conclusions I, II, III and IV given below them is/are definitely true and give your answer accordingly.

1. Statements: A * P, P % E, E δ F, F # S
Conclusions:
I. S % E
II. A % E
III.F % P
A) Only I and III are true
B) Only II is true
C) Only I and II are true
D) Only II and III are true
E) None of these

View Answer

Option C
A ≥ P > E < F ≤ S

1. Statements: P δ W, W \$ Q, Q % S, S * A
Conclusions:
I. A δ Q
II. Q % P
III. W % A
A) Only I is true
B) Only I and III are true
C) Only I and II are true
D) All I, II and III are true
E) None of these

View Answer

Option D
P < W = Q > S ≥ A

1. Statements: L % N, N # T, T \$ D, D δ A
Conclusions:
I. L % A
II. L # A
III. A % N
A) Only either I or II and III are true
B) Only I is true
C) Only either I or II is true
D) Only III is true
E) None of these

View Answer

Option A
L > N ≤ T = D < A No relation between L and A, so L > A or L ≤ A

1. Statements: M # Q, Q \$ K, A % K, V * A
Conclusions:
I. K * M
II. A % Q
III. A % M
A) None is true
B) Only I and II are true
C) Only I and III are true
D) Only II and III are true
E) All I, II and III are true

View Answer

Option E
M ≤ Q = K < A ≤ V

1. Statements: E \$ C, C δ A, A * R, R # S
Conclusions:
I. S % A
II. R δ C
III. R # E
A) None is true
B) Only I and II true
C) Only II is true
D) Only III is true
E) All I, II and III are true

View Answer

Option A
E = C < A ≥ R ≤ S

Directions (34 – 40): In the following questions, the symbols %, @, #, \$ and * are used with the following meaning as illustrated below:
‘P#Q’ means ‘P is neither smaller than nor equal to Q’.
‘P*Q’ means ‘P is neither greater than nor equal to Q’.
‘P\$Q’ means ‘P is not greater than Q’.
‘P%Q’ means ‘P is not smaller than Q’.
[email protected]’ means ‘P is neither smaller than nor greater than Q’.
In each of the following questions, mark answer according to above symbols and their meaning.

1. Which of the following does not make A # C and D \$ F definitely not true?
A) A % B # C @ D \$ E \$ F
B) A # B @ C \$ D \$ E @ F
C) A % B # C @ D \$ E * F
D) A % B # C # D @ E \$ F

View Answer

Option C
Check all the options and find in which both A > C and D ≤ F are false
C) option is A = B ≥ C = D ≤ E < F. In this A ≥ C but D < F

1. Which of the following makes C \$ E or B % E definitely true?
A) A * B \$ C @ D % E # F
B) A # B * C \$ D @ E # F
C) A # B # C % D % E * F
D) A @ B % C @ D * E * F

View Answer

Option B
Check all the options and find in which both or at least one of C ≤ E and B ≥ E is true. (because or is given between C \$ E or B % E
B) option is A > B < C ≤ D = E > F. In this C ≤ = E. In all other options, both are false.

1. If “A % B % C * D @ E \$ F” is true then which of the following is definitely not true?
(i) A # D
(ii) C * F
(iii) B # D
(iv) D # F
A) Only (i)
B) Only (ii) and (iv)
C) Only (i) and (iii)
D) Only (i), (iii) and (iv)
E) All are true

View Answer

Option C
Questions asks definitely not true or definitely false. We do not have sufficient information about relation between B and D, so cannot be said for (iii)

1. What will come in place of blank in following below such that both A % D and C # F are definitely true?
A % B % C _ D # E % F
i) @
ii) *
iii) %
iv) \$
A) Only (i)
B) Only (ii) and (iv)
C) Only (i) and (iii)
D) Only (i), (iii) and (iv)
E) All are true

View Answer

Option C
With (i) – A ≥ B ≥ C = D > E ≥ F
With (iii) – A ≥ B ≥ C ≥ D > E ≥ F
In both of these A ≥ D and C > F

1. Which of the following makes F # D \$ B definitely true?
A) A @ B \$ C * D # E * F
B) A * B @ C % D # E * F
C) A % B * C \$ D @ E * F
D) A # B % C @ D * E * F

View Answer

Option D

D) Option: A > B ≥ C = D < E < F

1. Which of the following is definitely true if A # B @ C # D @ E \$ F is true?
(i) C # F
(ii) F % D
(iii) B % E
(iv) E # A)
A) Only (i)
B) Only (ii) and (iii)
C) Only (iv)
D) Only (ii)
E) Only (i), (ii) and (iii)

View Answer

Option D
A > B = C > D = E ≤ F so F ≥ D is true

1. Which of the following does not make A % B and D * F definitely not true?
A) A % B % C * D \$ E # F
B) A % B % C @ D * E * F
C) A * B % C @ D \$ E \$ F
D) A % B @ C \$ D @ E * F

View Answer

Option C
Check all the options and find in which both A ≥ B and D < F are false
In C option, both are false

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