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- Question 1 of 40
##### 1. Question

**Directions**(Q. 1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than 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 neither smaller than nor equal to Q’.

**Statements:**B $ K, K @ D, D # M

**Conclusions :**I. B $ M II. B @ M##### Hint

B = K …(i)

K < D …(ii) D > M …(iii)

From (i) and (ii), we get D > K = B …(iv)

From (iii) and (iv), no specific relation can be obtained between B and M. Therefore, B = M (Conclusion I) and B < M (Conclusion II) are not necessarily true. - Question 2 of 40
##### 2. Question

**Directions**(Q. 1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than 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 neither smaller than nor equal to Q’.

**Statements :**H @ N, N © W, W # V

**Conclusions :**I. H @ V II. V @ N##### Hint

H < N … (i) N > W …(ii)

W ≥ V …(iii)

From (ii) and (iii), we get N > W ≥ V …(iv)

From (i) and (iv), no specific relation can be obtained between H and V. Hence, H < V (Conclusion I) is not necessarily true. But V < N (Conclusion II) follows from equation (iv). - Question 3 of 40
##### 3. Question

**Directions**(Q. 1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than 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 neither smaller than nor equal to Q’.

**Statements :**J * D, Q # D, Q @ M

**Conclusions :**I. Q © J II. Q $ J##### Hint

J ≤ D …(i)

Q ≥ D …(ii)

Q < M …(iii) Combining (i) and (ii), we get Q ≥ D ≥ J ⇒ Q > J (Conclusion I) or Q = J (Conclusion II). Hence, either conclusion I or conclusion II is true. - Question 4 of 40
##### 4. Question

**Directions**(Q. 1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than 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 neither smaller than nor equal to Q’.

**Statements :**F # G, N $ G, N © T

**Conclusions :**I. T © F II. N * F##### Hint

F ≥ G …(i)

N = G … (ii)

N > T … (iii)

Combining all, we get F ≥ G = N > T ⇒ N ≤ F (Conclusion II) and T < F. Hence, conclusion I (T > F) is not true but conclusion II is true. - Question 5 of 40
##### 5. Question

**Directions**(Q. 1-5): ‘P # Q’ means ‘P is not smaller than Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than 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 neither smaller than nor equal to Q’.

**Statements :**M © R, R @ K , K $ T

**Conclusions :**I. T © R II. T © M##### Hint

M > R …(i)

R < K …(ii) K = T … (iii) Combining (ii) and (iii), we get K= T > R

⇒ T > R (Conclusion I).

On the basis of the given information no specific relation can be obtained between T and M. Hence, T > M (Conclusion II) is not necessarily true. - Question 6 of 40
##### 6. Question

**Directions**(Q. 6-10): ‘P Q’ means P is not equal to Q. ‘P @ Q’ means P is greater than Q. ‘P + Q’ means P is smaller than Q. ‘P © Q’ means P is either greater than or equal to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.

**Statements :**K © M, M R, R ? T

**Conclusions :**I. K © T II. M ? T##### Hint

K ≥ M … (i)

M ≠ R …(ii); R = T …(iii)

Combining all equations, we get K ≥ M ≠ R = T ⇒ M ≠ T

From this we can’t get any specific relation between K and T. Hence, conclusion I is not true. Conclusion II is false since M ≠ T. - Question 7 of 40
##### 7. Question

**Directions**(Q. 6-10): ‘P Q’ means P is not equal to Q. ‘P @ Q’ means P is greater than Q. ‘P + Q’ means P is smaller than Q. ‘P © Q’ means P is either greater than or equal to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.

**Statements :**B + D, D @ N, N $ H

**Conclusions :**I. M © D II. H © N##### Hint

B < D ...(i) D > N …(ii)

N ≤ H …(iii)

From equations (ii) and (iii), we can’t obtain any specific relation between H and D. Hence, conclusion I (H ≥ D) is not true. But conclusion II (H ≥ N) follows from equation (iii) - Question 8 of 40
##### 8. Question

**Directions**(Q. 6-10): ‘P Q’ means P is not equal to Q. ‘P @ Q’ means P is greater than Q. ‘P + Q’ means P is smaller than Q. ‘P © Q’ means P is either greater than or equal to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.

**Statements :**M © K, [email protected] P, P $ N

**Conclusions :**I. M @ NII. M ? N##### Hint

M ≥ K … (i)

K > P …(ii)

P ≤ N …(iii)

Combining (i) and (ii), we get M ≥ K > P …(iv)

From (iii) and (iv), no specific relation can be obtained between M and N. Hence, conclusion I (M > N) and conclusion II (M = N) are not true. - Question 9 of 40
##### 9. Question

**Directions**(Q. 6-10): ‘P Q’ means P is not equal to Q. ‘P @ Q’ means P is greater than Q. ‘P + Q’ means P is smaller than Q. ‘P © Q’ means P is either greater than or equal to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.

**Statements :**T $ M, M ? Q, Q + R

**Conclusions :**I. Q @ TII. Q ? T##### Hint

T ≤ M …(i)

M = Q …(ii)

Q < R ...(iii) Combining (i) and (ii) we getM = Q ≥ T ⇒ Q > T (Conclusion I) or Q = T (Conclusion II) - Question 10 of 40
##### 10. Question

**Directions**(Q. 6-10): ‘P Q’ means P is not equal to Q. ‘P @ Q’ means P is greater than Q. ‘P + Q’ means P is smaller than Q. ‘P © Q’ means P is either greater than or equal to Q. ‘P $ Q’ means P is either smaller than or equal to Q. ‘P ? Q’ means P is equal to Q.

**Statements :**D @ B, B $ T, T + M

**Conclusions :**I. M @ BII. T © B##### Hint

D > B … (i)

B ≤ T …(ii)

T < M ...(iii) Combining (ii) and (iii), we get M > T ≥ B ⇒ M > B (Conclusion I) and T ≥ B (Conclusion II). - Question 11 of 40
##### 11. Question

**Directions**(Q. 11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater 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.

**Statements :**Z $ K, K × T, T © F

**Conclusions :**I. F # ZII. Z × T - Question 12 of 40
##### 12. Question

**Directions**(Q. 11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater 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.

**Statements :**K × B, B @ D, D # K

**Conclusions :**I. B @ KII. B # K##### Hint

K > B …(i)

B ≤ D …(ii)

D < K …(iii) From (i), B < K. Hence II is true but I is not true. - Question 13 of 40
##### 13. Question

**Directions**(Q. 11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater 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.

**Statements :**N © R, R @ M, M $ J

**Conclusions :**I. N © MII. N # M##### Hint

N = R …(i),

R ≤ M …(ii)

M ≥ J …(iii)

From (i) and (ii), we get N = R ≤ M ⇒ N ≤ M. Hence either I or II is true. - Question 14 of 40
##### 14. Question

**Directions**(Q. 11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater 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.

**Statements :**S $ T, T @ R, R # M

**Conclusions :**I. M × TII. M© T##### Hint

S ≥ T …(i),

T ≤ R … (ii)

R < M ... (iii) From (ii) and (iii), we get T ≤ R < M ⇒ T < M or M > T. Hence I is true and II is not true. - Question 15 of 40
##### 15. Question

**Directions**(Q. 11-15): ‘P $ Q’ means P is not smaller than Q. ‘P © Q’ means P is neither greater than nor smaller than Q. ‘P @ Q’ means P is not greater 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.

**Statements :**H @ V, V © M, M × R

**Conclusions :**I. R × HII. H × R##### Hint

H ≤ V … (i)

V = M … (ii)

M > R … (iii)

Combining all, we get H ≤ V = M > R ⇒ no relationship between H and R can be established. Since conclusions I and II are not exhaustive, neither of them is true. - Question 16 of 40
##### 16. Question

**Directions**(Q. 16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.

**Statements :**S * K, T & K, K * B

**Conclusions :**I. S $ BII. S @ B##### Hint

S ≥ K… (i); T < K ... (ii) K ≥ B ... (iii) Combining (i) and (iii), we get S ≥ K ≥ B. Hence, S > B or S = B. Therefore either conclusion I or II is true.

- Question 17 of 40
##### 17. Question

**Directions**(Q. 16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.

**Statements :**Y $ Z, H $ D, Z * D

**Conclusions :**I. D £ YII. H £ Z##### Hint

Combining all the three statements, we get Y = Z ≥ D = H. Therefore D ≤ Y and H ≤ Z are true.

- Question 18 of 40
##### 18. Question

**Directions**(Q. 16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.

**Statements :**M @ N, P @ R, P & N

**Conclusions :**I. P £ MII. R & N##### Hint

Combining all the three statements together we get M > N > P > R. Therefore P ≤ M is not true, but R < N is true.

- Question 19 of 40
##### 19. Question

**Directions**(Q. 16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.

**Statements :**T & K, K * B, S * K

**Conclusions :**I. B * TII. S £ T##### Hint

Combining I and III, we get S ≥ K > T. Therefore S ≤ T is not true. We have no information about the relationship between B and T.

- Question 20 of 40
##### 20. Question

**Directions**(Q. 16-20): ‘A * B’ means A is either equal to or greater than B. ‘A $ B’ means A is equal to B. ‘A £ B’ means A is either equal to or smaller than B. ‘A & B’ means A is smaller than B. ‘A @ B’ means A is greater than B.

**Statements :**P @ R, M @ N, P & N

**Conclusions :**I. N @ RII. P & M##### Hint

Combining all the three statements, we get M > N > P > R. Therefore N > R and P < M are true.

- Question 21 of 40
##### 21. Question

**Directions**(Q. 21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.

**Statements :**M $ K,D * K,R # K

**Conclusions :**I. D $ MII. M % D##### Hint

M = K .…. (i)

D ≤ K ….. (ii)

R < K ..… (iii) From (i) and (ii), we get M = K ≥ D ⇒ M ≥ D Hence, either M > D (conclusion II) or M = D (conclusion I) is true - Question 22 of 40
##### 22. Question

**Directions**(Q. 21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.

**Statements :**F * M, M % R, E @ F

**Conclusions :**I. M % EII. R @ E##### Hint

F ≤ M … (i)

M > R … (ii)

E ≥ F … (iii)

From (i) and (iii), no specific relation can be obtained between M and E. Similarly, no specific relation can be obtained between R and E. - Question 23 of 40
##### 23. Question

**Directions**(Q. 21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.

**Statements :**H $ K, T # H, W * T

**Conclusions :**I. K % WII. T # K##### Hint

H = K … (i)

T < H …(ii) W ≤ T …(iii) From (i), (ii) and (iii), we get K = H > T ≥ W ⇒ K > W (conclusion I) and T < K (conclusion II). - Question 24 of 40
##### 24. Question

**Directions**(Q. 21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.

**Statements :**N % A, A # L, F $ N

**Conclusions :**I. L % FII. F % A##### Hint

N > A … (i)

A < L … (ii) F = N …(iii) From (i) and (iii), we get F = N > A ⇒ F > A (conclusion II). But no specific relation can be obtained between L and F. Hence, conclusion I is not necessarily true. - Question 25 of 40
##### 25. Question

**Directions**(Q. 21-25): ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’.

**Statements :**B * D,D $ M, F % M

**Conclusions :**I. B # MII. F % B##### Hint

B ≤ D …(i)

D = M …(ii)

F > M …(iii)

From (i), (ii) and (iii), we get F > M = D ≥ B ⇒ B ≤ M and F > B (conclusion II). Since, B ≤ M, therefore, conclusion I is not necessarily true. - Question 26 of 40
##### 26. Question

**Directions**(26-30) : Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?

Statement : W ≥ D < M < P < A = F Conclusion : I. F > DII. P < W##### Hint

W ≥ D < M < P < A = F or F > D

So I follows.

No relation can be established between P and W. So II does not follow. - Question 27 of 40
##### 27. Question

**Directions**(26-30) : Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?

Statement : H ≥ M > F < A = B > S

Conclusion : I. H > BII. F < S##### Hint

H ≥ M > F < A = B > S

No relation can be established between (H, B) and (F, S).

So none follows. - Question 28 of 40
##### 28. Question

**Directions**(26-30) : Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?

Statement : B > T > Q > R = F

**Conclusions :**I. Q ≥ FII. T > F##### Hint

B > T > Q > R = F

or Q > F and T > F

So, only II follows. - Question 29 of 40
##### 29. Question

**Directions**(26-30) : Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?

Statement : S = R ≥ Q, P < Q Conclusion : I. S ≥ PII. R > P##### Hint

S = R ≥ Q > P

or S > P and R > P

So, only II follows. - Question 30 of 40
##### 30. Question

**Directions**(26-30) : Assuming the given statements to be true, find which of the conclusion(s) given below is/are definitely true?

Statement : S ≥ M < Y = Z > F > T

Conclusion : I. S > FII. Y > T##### Hint

S ≥ M < Y = Z > F > T

or Y > T

So, only II follows. - Question 31 of 40
##### 31. Question

**Directions**(Q. 31-35): ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P × Q’ means ‘P is not smaller than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.

**Statements :**J © T, T * B, B @ R

**Conclusions :**I. J @ RII. R % T III. J @ B##### Hint

J > T …(i)

T ≤ B ….(ii)

B < R ... (iii) From (ii) and (iii), we get R > B ≥ T … (iv)

Hence, no specific relation can be obtained between (i) J and R or (ii) J and B. Hence, neither I nor III follows. From equation (iv) we get R > T. Therefore, conclusion II does not follow. - Question 32 of 40
##### 32. Question

**Directions**(Q. 31-35): ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P × Q’ means ‘P is not smaller than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.

In each of the following questions assuming the given statements to be true, find which of the conclusions given below are definitely true.

**Statements :**T * M, K @ M, K × Z

**Conclusions :**I. T @ Z II. Z @ M III. M % Z##### Hint

T ≤ M … (i)

K< M ...(ii) K ≥ Z ... (iii) From (ii) and (iii), we get M > K ≥ Z …(iv).

⇒ M > Z Hence, conclusion II (Z < M) follows. But conclusion III (M = Z) does not follow. Again, no specific relation can be obtained between T and Z. Hence, conclusion I does not follow. - Question 33 of 40
##### 33. Question

**Directions**(Q. 31-35): ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P × Q’ means ‘P is not smaller than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.

**Statements :**K * N, N% T, R @ T

**Conclusions :**I. K @ R II. T © K III. R % K##### Hint

K ≤ N …(i)

N = T …(ii)

R < T ...(iii) From (i) and (ii), we get T = N ≥ K ...(iv) From (ii) and (iii), we get T = N > R …(v)

From equation (iv), we get T ≥ K. Hence, conclusion II (T > K) is not necessarily true.

From equations (iv) and (v) we can’t obtain any specific relation between K and R. There fore, conclusion I and conclusion III do not follow. Thus, no conclusion follows. - Question 34 of 40
##### 34. Question

**Directions**(Q. 31-35): ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P × Q’ means ‘P is not smaller than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.

**Statements :**H © M, M × D, T @ D

**Conclusions :**I. T @ MII. H © D III. H % D##### Hint

H > M … (i)

M ≥ D … (ii)

T < D ... (iii) From (i), (ii) and (iii), we get H > M ≥ D > T…(iv)

From equation (iv), we get H > T. This implies T < M. Hence, conclusion I follows. Again, H > D. Hence II follows but III does not. - Question 35 of 40
##### 35. Question

**Directions**(Q. 31-35): ‘P @ Q’ means ‘P is neither greater than nor equal to Q’. ‘P × Q’ means ‘P is not smaller than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P © Q’ means ‘P is neither smaller than nor equal to Q’. ‘P % Q’ means ‘P is neither greater than nor smaller than Q’.

**Statements :**W × M, M © F, D * F

**Conclusions :**I. [email protected] M©D III. [email protected]##### Hint

W ≥ M … (i)

M > F … (ii)

D ≤ F …(iii)

From (i), (ii) and (iii), we get W ≥ M > F ≥ D…(iv)

From (iv); we get W > D. Hence, conclusion I (D < W) follows. Again, from the equation (iv), we get M > D. Hence, conclusion II (M > D) follows. Again, from the equation (iv), we get W > F. Hence, conclusion III (F < W) follows. - Question 36 of 40
##### 36. Question

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 ‘V > Z’ definitely holds true ?

V__ W__ X__ Z##### Hint

V > W ≥ X > Z

or V > Z - Question 37 of 40
##### 37. Question

Which of the following symbols should replace the question mark in the given expression in order to make the expressions ‘M ≤ K’ as well as ‘L > P’ definitely true ?

K ≥ L ? M > N > P##### Hint

K ≥ L = M > N > P

or M ≤ K and L > P - Question 38 of 40
##### 38. Question

In which of the following expressions will the expressions ‘H < F’ as well as ‘J > H’ be definitely true ?

##### Hint

F ≥ G = H ≤ I < J or H ≤ F and J > H

- Question 39 of 40
##### 39. Question

Which of the following expressions will be true if the given expression ‘A < C ≥ B = D ≤ E’ is definitely true ?

##### Hint

A < C ≥ B = D ≤ E None of the four is true.

- Question 40 of 40
##### 40. Question

In which of the following expressions will the expression ‘L > P’ be definitely false ?

##### Hint

P = N ≥ L > M

or L ≤ P

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