Q: Statements: J © M, M * K, K % D Conclusions: I. J © D, II. D * M III. K © J

J > M ...(i) M < K ...(ii) K ≥ D ...(iii) From (i) and (ii) J and K can't be compared and consequently J and D can't be compared. Hence neither III nor I follows. From (ii) and (iii) D and M can't be compared Hence II does not follow.

Q: Statements: R @ K, K S F, F * N Conclusions: I. N © R, II. F @ R, III. F © R

R = K ...(i) K ≤ F ... (ii) F R and I follow. Also F ≥ R. Hence either II (F = R) or III (F = R) and follows.

Q: Statements: H * T, T S B, B © R Conclusions: I. R © H II. B © H III. T % R

H R ...(iii) From (i) and (ii) we get H H. Hence III does not follow.

Q: Statements: D * R, R % F, F S T Conclusions: I. F % D II. F S D III. T © R

D ≤ N ...(i) R = F ...(ii) F > T ...(ii) From (i) and (ii) D ≥ R = F or D ≤ F or F ≥ D. Hence either I (F = D ) or II (F > D) follows From (ii) and (iii) R = F > T or R > T or T < R. Hence III follows.

Question 1

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

Accepted Answer

F ≥ K ...(i) K > B ....(ii) B ≤ M ...(iii) From (i) and (ii) F can't be compared with B and consequently with M. Hence neither II nor I follows.

Question 2

Statements: R # T, T © M, M @ D Conclusions: I. D S T II. R # M

Accepted Answer

R ≥ T ...(i) T = M ...(ii) M > D ...(iii) Combining these we get R ≥ T = M > D. Hence D > T and I follows. Also R J≥ T and II follows.

Question 3

Statements: J © M, M * K, K % D Conclusions: I. J © D, II. D * M III. K © J

Accepted Answer

J > M ...(i) M < K ...(ii) K ≥ D ...(iii) From (i) and (ii) J and K can't be compared and consequently J and D can't be compared. Hence neither III nor I follows. From (ii) and (iii) D and M can't be compared Hence II does not follow.

Question 4

Statements: R @ K, K S F, F * N Conclusions: I. N © R, II. F @ R, III. F © R

Accepted Answer

R = K ...(i) K ≤ F ... (ii) F < K ...(iii) Combining these we get R = K ≤ F < N. Hence K > R and I follow. Also F ≥ R. Hence either II (F = R) or III (F = R) and follows.

Question 5

Statements: R S D, D @ N, N © F Conclusions: I. F * D II. F * R III. N % R

Accepted Answer

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

Question 6

Statements: H * T, T S B, B © R Conclusions: I. R © H II. B © H III. T % R

Accepted Answer

H < T ...(i) T ≤ B ...(ii) B > R ...(iii) From (i) and (ii) we get H < T ≤ B or B > H. Hence III does not follow.

Question 7

Statements: M © T, T # J, J S K Conclusions: I. K © T II. M © J III. K @ M

Accepted Answer

M < T ...(i) T ≥ J ...(ii) J > K ...(iii) From (ii) and (iii) T ≥ J > K or K < T. Hence I follows. From (i) and (ii) M and J can't be compared. Hence II does not follows.Nor can III follows.

Question 8

Which of the following expression will be true if the given expression A > B ≥ C < D < E

Accepted Answer

E > C

Question 9

If the expression E < J ≤ H > Z'. 'H ≤ Y' and 'E > F' true. Which of the following conclusions will be definitely false?

Accepted Answer

F < E < J ≤ H > Z H ≤ Y and Z < H

Question 10

Which of the following symbols should replace the question mark in the given expression in order to make the expression 'K ≤ H' and 'M > J' definitely true? H ≥ I = J? K ≤ L < M

Accepted Answer

H ≥ I = J = K ≤ L < M

Question 11

In which of the following expressions will be expression 'P > S' definitely false?

Accepted Answer

From this expression we cannot deduce any relation between P and S

Question 12

Which of the following symbols should be placed in the blank space respectively (in the same order from left to right) in order to complete the given expressions in a such a manner that 'N < K' definitely holds true? K - L - M - N

Accepted Answer

K ≥ L = M > N

Question 13

Statements: V © K, K @ B, B S M Conclusions: I. V © B II. M © K III. M © R

Accepted Answer

V < K ...(i) K ≥ B ...(ii) B > M ...(iii) From (i) and (ii) V and B can't be compared. Hence I does not follow. From (ii) and (iii) K ≥ B > M or K > M or M < K Hence II follows. From (i) and (iv) V and M can't be compared. Hence III does not follow.

Question 14

Accepted Answer

D ≤ N ...(i) R = F ...(ii) F > T ...(ii) From (i) and (ii) D ≥ R = F or D ≤ F or F ≥ D. Hence either I (F = D ) or II (F > D) follows From (ii) and (iii) R = F > T or R > T or T < R. Hence III follows.

Question 15

Accepted Answer

N ≥ D ...(i) D ≤ N ...(ii) K > A ...(iii) Obviously none of these in equations can be combined.

Question 16

Accepted Answer

N ≥ T ...(i) T > N ...(ii) N < R ...(iii) From (i) and (ii) N ≥ T. Hence II (N ≤ K) does not follow. From (iii) and (iv) no relationship can be established a between K and R. Hence I does not follow.

Question 17

Accepted Answer

W = K ....(i) K < F ...(ii) D > F ...(iii) Combining these we get W = K < F < D Hence D > K and I follows Again D > W and II follows. Also, F > W Hence III (F ≥ W) does not follow.

Question 18

Accepted Answer

B ≤ K ...(i) K < F ...(ii) F = W ...(iii) Combining these we get B ≤ K < F = R Hence R > K and I follows Again R > B and II follows. Also, F > B III follow.

Question 19

Accepted Answer

R ≥ K ...(i) K > M ...(ii) M ≤ J ...(iii) From (i) and (ii) J and K can't be compared. Hence I does not follow. From (i) and (ii) R ≥ K > M or K > M or M < R. Hence II is true but III (M = R) is not.

Question 20

Accepted Answer

R > B ...(i) B ≥ N ...(ii) N < T ...(iii) From (i) and (ii) R > B ≥ N or N < R Hence I is true From (ii) and (iii) B and T can't be compared. Hence III does not follow. Nor does III subsequently.

Mathematical Operations Questions