Q: Statements: P @ W, W * D, D S J Conclusions: I. J @ P II. J @ W

P J ...(iii) From (ii) and (iii) W ≥ D > J or J < W ...(iv) Hence II follows. However, from (i) and (iv) we can conclude that J and P can't be compared. Hence I does not follow.

Q: Statements: V S I, I * M, M # Q Conclusions: I. I # Q II. I * Q

V > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii) From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.

Q: Statements: H ≥ G Z Conclusions: I. F ≤ H II. Z < I

H ≥ G Z Check for I: F ≤ G ≤ H is definitely follows Check for II: Z < G < I ∴ Z < I also follows Hence, both I and II follows

Q: Conclusions: I. R ≥ S II. W < G

S ≤ T U Check for I: S ≤ T ≤ R ∴ R ≥ S follows Check for II: G > U ≥ W ∴ W < G follows Hence, both I and II follows

Q: Statements: C ≥ D = E ≤ F; Y < D ≥ W Conclusions: I. C ≥ Y II. F ≥ Y

C ≥ D = E ≤ F, Y Y It means C > Y. Thus, I does stand true. check for II: Y Y. Thus, II also does not stand true.

Q: Statements: N T; R < A; B ≤ T Conclusions: I. N < A II. B < A

N T; R T ∴ No definite relation can be found between N and A. Check for II:

Q: Statements: R © F, F # D, D @ M Conclusions: I. R © D II. M % F III. M S R

R < F ...(i) F ≥ D ...(ii) D ≤ M ...(iii) From (i) and (ii) R and D can't be compared. Hence neight I nor III follows. From (ii) and (iii) M and F can't be compared. Hence II does not follows.

Question 1

Statements: E @ U, U %R, R S F Conclusions: I. E S F II. E * F

Accepted Answer

E < U ...(i) U = R ...(ii) R > F ...(iii) From (i) and (ii) E < R ...(iv) Now, From (iii) and (iv) E and F can't be compared Hence neither I nor II follows.

Question 2

Statements: P @ W, W * D, D S J Conclusions: I. J @ P II. J @ W

Accepted Answer

P < W ...(i) W ≥ D ...(ii) D > J ...(iii) From (ii) and (iii) W ≥ D > J or J < W ...(iv) Hence II follows. However, from (i) and (iv) we can conclude that J and P can't be compared. Hence I does not follow.

Question 3

Statements: V S I, I * M, M # Q Conclusions: I. I # Q II. I * Q

Accepted Answer

V > I ...(i) I ≥ M ...(ii) M ≤ Q ...(iii) From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ≤ Q) or II (I ≥ Q) follows.

Question 4

Statements: H # T, T @ L, L % F Conclusions: I. F S H II. H # L

Accepted Answer

H ≤ T ...(i) T < L ...(ii) L = F ...(iii) Combining these we get H ≤ T < L = F. Hence F > H and I follows. But H < L and Hence II (H ≤ L ) does not follow.

Question 5

Statements: H ≥ G < I; F ≤ G > Z Conclusions: I. F ≤ H II. Z < I

Accepted Answer

H ≥ G < I; F ≤ G > Z Check for I: F ≤ G ≤ H is definitely follows Check for II: Z < G < I ∴ Z < I also follows Hence, both I and II follows

Question 6

Conclusions: I. R ≥ S II. W < G

Accepted Answer

S ≤ T < U ≥ W; T ≤ R, G > U Check for I: S ≤ T ≤ R ∴ R ≥ S follows Check for II: G > U ≥ W ∴ W < G follows Hence, both I and II follows

Question 7

Statements: C ≥ D = E ≤ F; Y < D ≥ W Conclusions: I. C ≥ Y II. F ≥ Y

Accepted Answer

C ≥ D = E ≤ F, Y < D ≥ W Check for I: C ≥ D > Y It means C > Y. Thus, I does stand true. check for II: Y < D ≤ F It means F > Y. Thus, II also does not stand true.

Question 8

Statements: N < O ≥ R > T; R < A; B ≤ T Conclusions: I. N < A II. B < A

Accepted Answer

N < O ≥ R > T; R < A; B ≤ T Check for I: N < O ≥ R > T ∴ No definite relation can be found between N and A. Check for II:

Question 9

Statements: R © F, F # D, D @ M Conclusions: I. R © D II. M % F III. M S R

Accepted Answer

R < F ...(i) F ≥ D ...(ii) D ≤ M ...(iii) From (i) and (ii) R and D can't be compared. Hence neight I nor III follows. From (ii) and (iii) M and F can't be compared. Hence II does not follows.

Question 10

Statements: M # W, W % N, N S B Conclusions: I. N % M II. N © M III. M S B

Accepted Answer

M ≥ W ...(i) W = N ...(ii) N > B ...(iii) Combining these we get M ≥ W = N > B. Hence M ≥ N or N ≤ M, Which means either I (N = M) or II (N < M) follows. Also M > B and II (M ≤ D) Hence III definitely true.

Question 11

Statements: M # W, W % N, N S B Conclusions: I. N % M II. N © M III. M S B

Accepted Answer

M ≥ W ...(i) W = N ...(ii) N > B ...(iii) Combining these we get M ≥ W = N > B. Hence M ≥ N or N ≤ M, Which means either I (N = M) or II (N < M) follows. Also M > B and II (M ≤ D) Hence III deficitely true.

Question 12

Statements: W @ F, F S M, M © D Conclusions: I. D S F II. W © B III. F S D

Accepted Answer

W ≥ F ...(i) F > M ...(ii) M < D ...(iii) From (i) and (ii) W and M can't be compared. Hence II does not follow. From (ii) and (iii) F and D can't be compared. Hence neither I or III follows.

Question 13

Statements: B % H, H S E, E @ K Conclusions: I. K S H II. K S B III. E © B

Accepted Answer

B = H ...(i) H > E ...(ii) E ≤ K ...(iii) From (i) and (ii) B = H > E or E < B Hence III follows. From (ii) and (iii) H and K can't be compared. Hence I does not follow. Nor can II follow.

Question 14

Accepted Answer

F ≥ N ...(i) N < D ...(ii) D ≤ R ...(iii) From (i) and (ii) F and can't be compared. Hence I does not follow. From (ii) and (iii) N < D ≤ R or R > N ...(iv) Hence II follows. From (i) and (iv) R and F can't be compared. Hence III does not follow.

Question 15

Statements: F S B, B @ H, H % K Conclusions: I. B % F II. K @ F II. K S B

Accepted Answer

F ≤ B ...(i) B = H ...(ii) H ≥ K ... (iii) From (i) B F. Hence I follows. From (ii) and (iii) B = H ≥ K or B ≥ K or K ≤ B can't be compared. Hence II does not follow.

Question 16

Accepted Answer

M ≥ D ...(i) D< K ...(ii) K ≤ N ...(iii) From (i) and (ii) K and M can't be compared. Hence I does not follow. From (ii) and (iii) D < K ≤ N or N > D. Hence II follows. From (i) and II, M and N can't be compared. Hence III does not follow.

Question 17

Accepted Answer

R ≤ N ...(i) N ≥ F ...(ii) F > B ...(iii) From (i) and (ii) F and R can't be compared. Hence I does not follow. Combing (ii) and (iii) we get N ≥ F > B or N > B or B < N. Hence II follows.

Question 18

Accepted Answer

H = W ...(i) W ≤ R ...(ii) R > F ...(iii) From (i) and (ii) H = W ≤ R or R ≥ H, Hence either I (R = H) or II (R > H) follows.

Question 19

Accepted Answer

M < T ... (i) T > K ...(ii) K = D ...(iii) From (ii) and (iii) T > K = D or D < T. Hence I follow From (i) and (ii) K and M can't be compared Hence II does not follow

Question 20

Statements: H @ W, W S M, M # K Conclusions: I. K S W II. H @ M

Accepted Answer

H > W ...(i) W > M ..(ii) M ≥ K ....(iii) From (ii) and (iii) K and W can't be compared Hence I does not follow. From (i) and (ii) H and M can't be compared Hence II does not follow

Mathematical Operations Questions