BOOST UP PDFS | Reasoning Ability | Inequality-Equality

BOOST UP PDFS | Reasoning Ability | Inequality-Equality Questions (Hard Level Part-1)

Recommend for SBI PO, SBI Clerk, IBPS RRB/PO/Clerk Exams

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Directions (1 – 5): In the following questions the

symbols #, *, @, $ and = are used with the following

meanings:

1) A # B means A is greater than B.

2) A * B means A is greater than or equal to B.

3) A @ B means A is equal to B.

4) A $ B means A is lesser than B.

5) A = B means A is lesser than or equal to B.

Now in each of the following questions, assuming the

three statements to be true, find which of the two

conclusions

I and II given below them is/are true. Give answer.

a) if only conclusion I is true

b) if only conclusion II is true

c) if either conclusion I or conclusion II is true

d) if neither conclusion I nor conclusion II is true

e) if both conclusions I and II are true.

1.Statements: P # Q, R $ P, R * O

Conclusions:

I. Q # R

II. Q $ R

2.Statements: P = Q, T @ R, R # P

Conclusions:

I. T = Q

II. Q $T

3.Statements: P @ Q, L @ M, P # L

Conclusions:

I. Q # M

II. M $ P

4.Statements: P # M # L, L# N @ Q, Q $ S @ R

Conclusions:

I. R @ M

II. L @ R

5.Statements: P * Q, Q@ T, T * L

Conclusions:

I. Q # L

II. T # P

Directions (6-10): Study the following information to

answer the given questions.

If,

P$Q means P is not smaller than Q

P@Q means P is neither smaller than nor equal to Q

P#Q means P is neither greater than nor equal to Q

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BOOST UP PDFS | Reasoning Ability | Inequality-Equality Questions

(Hard Level Part-1) Recommend for SBI PO, SBI Clerk, IBPS RRB/PO/Clerk Exams



P&Q means P is neither greater than nor smaller than Q

P*Q means P is not greater than Q

6. Statements: A $ M, P @ L, K # P, A $ L

Conclusions:

I. K # L

II. A @ P

III. L*A

IV. M # P

A. None is true

B. Only I is true

C. Only II is true

D. Only III is true

E. Only IV is true

7. Statements: W*N, K * V, Y @ V, W @ K

Conclusions:

I. Y @ K

II. W $ N

III. W @ Y

IV. W @ V

A. None is true

B. Only I is true

C. Only II is true

D. Only III is true

E. Only IV is true

8. Statements: T * Y, S # M, Y $ S, M @ K

Conclusions:

I. K # S

II. Y @ M

III. T # M

IV. S @ K

A. None is true

B. Only I is true

C. Only II is true

D. Only III is true

E. Only IV is true

9. Statements: S @ L, L # M, M & B, B * Q

Conclusions:

I. Q $ M

II. B @ L

III. S @ Q

IV. L @ Q

A. I, II and III are true

B. I and II are true

C. I and III are true

D. I, III and IV are true

E. All are true

10. Statements: C # P, P * L, L @ E, E $ M

Conclusions:

I. M # P

II. M @ L

III. P # E

IV. L # C

A. None is true

B. Only I is true








C. Only II is true

D. Only III is true

E. Only IV is true

Directions (11-15): In the following questions, the

symbols +, ×, =, ÷, and - are used with the following

meaning:

1) P + Q means P is greater than Q.

2) P×Q means P is either greater than or equal to Q.

3) P = Q means P is equal to Q.

4) P ÷ Q means P is smaller than Q.

5) P-Q means P is either smaller than or equal to Q.

Now 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

a) if only conclusion I is true,

b) if only conclusion II is true,

c) if either I or II is true.

d) if neither I nor II is true.

e) if both I and II are true.

11. Statements: U + V, W - Y, Y × U

Conclusions:

I. W + U

II. W ÷ V

12. Statements: B ÷ A, D × E, E + A

Conclusions:

I. D + A

II. B ÷ E

13.Statements: S×Q, R+T, R-S

Conclusions:

I. S+T

II. Q=T

14. Statements: M ÷ N, P × Q, P + N

Conclusions:

I. N + Q

II. N – Q

.

15. Statements: G - H, K × L, L – G

Conclusions:

I. G ÷ K

II. L – H

Directions (16-20): In the questions given below,

certain symbols are used with the following meaning:

1) P @ Q means P is greater than Q.

2) P + Q means P is either greater than or equal to Q.

3) P = Q means P is equal to Q.

4) P©Q means P is smaller than Q.

5) P - Q means P is either smaller than or equal to Q.



conclusions








I and II given below them is/are definitely true?

Give answer

a) if only conclusion I is true,


c) if either I or II is true,

d) if neither 1 nor II is true, and


16. Statements: B @ V , K © C, C - B

Conclusions:

I. V @ C

II. B @ K

17. Statements: K@T, S=K, T-R

Conclusions:

I. S© R

II. S@ R

18. Statements: U = M, P + U, M @ B

Conclusions:

I. P = B

II. P @ B

19. Statements: L + N, J - P, P + L

Conclusions:

I. J = L

II. P = N

20. Statements: H + G, D @ E, H = E

Conclusions:

I. D @ H

II. G © D.

Directions (21-25): In the following questions the

symbols @, c, £, ?and $ are used with the following

meanings:

1. A @ B means A is neither equal to nor smaller than B.

2. A c B means A is neither greater nor smaller than B.

3. A £ B means A is not equal to B.

4. A ? B means A is neither greater than nor equal to B.

5. A $ B means A is either greater or equal to B.

Now, in each of the following questions, assuming the


conclusions I and II given below them is/are definitely

true. Give answer

a) if only conclusion I is true

b) if only conclusion II is true

c) if either I or II is true

d) if neither I nor II is true

e) if both I and II are true

21. Statements: N ? S, S @ P, P £ M

Conclusions:

I. S@M

II. PcN

22. Statements: JcP, P$N, J£H

Conclusions:

I. JcN








II. H@P

23. Statements: Z @ D, F c D, F $ G

Conclusions:

I. DcG

II. Z@G

24. Statements: L @ T, P ? T, K$L

Conclusions:

I. L@P

II. K@T

25. Statements: R c U, U ? Q, W $ R

Conclusions:

I. WcU

II. W@U

Directions (26-30): In the questions given below,

certain symbols are used with the following meaning:

1) A @ B means A is greater than B.

2) A + B means A is either greater than or equal to B.

3) A # B means A is smaller than B

4) A % B means A is either smaller than or equal to B.

5) A $ B means A is equal to B


given statements to be true find which of the two


true? Give answer

a) if only conclusion I is true.





26.Statements: T $ G, K @ P, M # T, P + M

Conclusions:

I. K @ T

II. G $ P

27.Statements: R + N, S % B, A @ R, B $ A

Conclusions:

I. S $ N

II. A @ N

28.Statements: G $ K, F @ J, K + Q, Q + F

Conclusions:

I. K $ F

II. F # K

29.Statements: W @ S, K % Z, U + W, S $ K

Conclusions:

I. U @ K

II. Z @ S

30. Statements: G $ E, D # K, E # S, K # G

Conclusions:

I. S @ D

II. D# E









symbols $, @, %, & and # are used with the following

meanings as illustrated below:

‘A $ B' means A is neither greater nor smaller than B

‘A @ B' means A is neither greater than nor equal to B

`A % B' means A is neither smaller than nor equal to B

‘A& B' means A is not smaller than B

‘A # B' means A is not greater than B

In each of the following questions, assuming the given

statements to be true, find out which of the two


true. Give answer


b) if only conclusion II is true.

c) if either conclusion I or II is true.

d) if neither conclusion I nor II is true.

e) if both conclusions I and II are true.

31.Statements: W&P, P %G, G @ I, I # N

Conclusions:

I. N%W

II. II. N # W

32.Statements: U @ D, D $ E, E % Y, Y& W

Conclusions:

I. U @ Y

II. II. W %D

33.Statements: Z % N, N # K, K $ M, M @ R

Conclusions:

I. M $ N

II. II. M% N

34.Statements: V&D, D %T, K $ T, K # F

Conclusions:

I. V% F

II. II. V% K

35.Statements: S $ Q, Q @ B, B &K, K # W

Conclusions:

I. W%K

II. II. S @ B


symbol $, @, *, ** and # are used with the following

meaning.

1) A $ B means A is greater than B

2) A @ B means A is either greater than or equal to B

3) A * B means A is equal to B

4) A ** B means A is smaller than B

5) A # B means A is either smaller than or equal to B



conclusions

I and II given below them is/are definitely True? Give

answer


b) if only conclusion II is true.











36.Statements: P @ Q, M # N, N**Q

Conclusions:

I. P $ M

II. N # P

37. Statements: D**X, F @ Y, D $ F

Conclusions:

I. X @ Y

II. Y # D

38.Statements: M**P, S $ T, M @ T

Conclusions:

I. S * M

II. T ** P

39.Statements: U*V, X $ W, U**W

Conclusions:

I. W $ V

II. U ** X

40.Statements: G $ H, J # K, H * K

Conclusions:

I. H $ J

II. J * H


symbols !, @, ©, % and * are used with the following

meaning as illustrated below:

‘P ! Q’ means ‘Q is not smaller than P’.

‘P * Q’ means ‘Q is neither smaller than nor equal to P’.

‘P % Q’ means ‘Q is neither greater than nor equal to P’.

‘P ©Q’ means ‘Q is not greater than P’.

‘P @ Q’ means ‘Q is neither greater than nor smaller

than P’.

41. Statements: B © T, T * R, R % F, F @ K

Conclusions:

I. B % R

II. F * T

III. R % K

IV. K @ T

a. None follows

b. Only I follow

c. Only III follows

d. Only II follows

e. Only IV follows

42. Statements: D ! T, T @ R, R © M, M % K

Conclusions:

I. R @ D

II. R % D

III. K * T

IV. M ! T

a. Only either I or II follows








b. Only III and IV follow

c. Only either I or II and III follows

d. Only either I or II and IV follows

e. Only either I or II and III and IV follows

43.Statements: F % N, N © W, W ! Y, Y * T

Conclusions:

I. F % W

II. T % N

III. N % Y

IV. T % W

a. Only I and III follow

b. Only I and IV follow

c. Only II and III follow

d. Only I, II and IV follows

e. None of these

44. Statements: J @ F, F ! N, N % H, H © G

Conclusions:

I. G * N

II. N © J

III. F * J

IV. J ! G

a. Only I and II follows

b. Only I, II and III follows

c. Only II, III and IV follow

d. All I, II, III and IV follows

e. None of these

45. Statements: R * K, K % D, D @ V, V ! M

Conclusions:

I. R * D

II. V * R

III. D @ M

IV. M % D

a. None follows

b. Only III follows

c. Only IV follows

d. Only either III or IV follows

e. None of these


symbols $, #, @, % and * are used with the following

meanings illustrated as below:

‘A $ B’ means ‘A is not smaller than B’

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

‘A % B’ means ‘A is not greater than B’

‘A # B’ means ‘B is neither smaller than nor equal to A’

‘A * B’ means ‘B is neither greater than nor smaller than

A’

46. Statements: D * Q, Q @ L, L $ B, B # G

Conclusions:

I.D @ B

II.B * D

III.G @ L

a. Either I or II only follow

b. I and II only follow








c. I only follow

d. II and III only follow

e. None follows

47. Statements: P # M, M % R, R * T, T # L

Conclusions:

I.P # R

II.P * R

III.M % L

a. I only follow

b. Either I or II only follow

c. III only follows

d. All I, II and III follow

e. None is true

48. Statements: Z @ Y, Y # K, K % M, M @ T

Conclusions:

I.Z @ M

II.Y @ T

III.Z # K

a. I only follow

b. II and III only follow

c. Either I or III only follow

d. All I, II and III follow

e. None follows

49. Statements: K @ T, T # D, D * F, F % G

Conclusions:

I.G @ K

II.G * T

III.G @ T

a. I and II only follow

b. II and III only follow

c. Either II or III only follow

d. III only follows

e. None follows

50. Statements: F @ H, M % H, M $ R, G * M

Conclusions:

I.F $ R

II.F @ R

III.H $ G

a. II and III only follow

b. II only follows

c. III only follows

d. III and either I or II follow

e. None follows

Answer Key with Explanation

Solution (1-5) 1. D








2. C

3. E

4. D

5. D

Solution (6-10)

6. D

7. B

8. A

9. B

10. A

Solution (11-15)

11. D

12. E

13. A

14. C

15. B

Solution (16-20)

16. B

17. D

18. B

19. D

20. E

Solution (21-25)

21. D

22. D

23. B

24. E

25. C

Solution (26-30)

26. D

27. B

28. C

29. A

30. E

Solution (31-35)

31. C

32. D

33. C

34. B

35. B

Solution (36-40)

36. A

37. D

38. B

39. E

40. C

Solution (41-45)

41. C

B ≥ T, T < R, R > F, F = K

B > R not follows

F < T not follows

R > K follows

K = T not follows

42. E

D ≤ T, T = R, R ≥ M, M > K

R = D

R > D








K < T

M ≤ T

Only either I or II and III and IV follows

43. B

F > N, N ≥ W, W ≤ Y, Y < T

F > W follows

T > N not follows

N > Y not follows

T > W follows

44. A

J = F, F ≤ N, N > H, H ≥ G

G < N follows

N ≥ J follows

F < J not follows

J ≤ G not follows

45. D

R < K, K > D, D = V, V ≤ M

R < D

V < R

D = M

M > D

Only either III or IV follows

Solution (46-50)

46. C

D = Q

Q > L

L ≥ B

B < G

Therefore,

D = Q > L ≥ B < G

D > B : follow

B = D : Not follow

G > L : Not follow

47. A

P < M

M ≤ R

R = T

T < L

Therefore, P < M ≤ R = T < L

P < R : follows

P = R : Not follow

M ≤ L : Not follow

48. E

Z > Y

Y < K

K ≤ M

M > T

Therefore,

Z > Y < K ≤ M > T

Z > M : Not follow

Y > T : Not follow

Z < K : Not follow

49. D

K > T

T < D

D = F

F ≤ G

Therefore, K > T < D = F ≤ G








G > K : Not follow

G = T : Not follow

G > T : follow

50. A

F > H

M ≤ H

M ≥ R

G = M

Therefore,

F > H ≥ M = G ≥ R

F ≥ R : Not follow

F > R : follow

H ≥ G : follow




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BOOST UP PDFS | Reasoning Ability | Inequality-Equality