Mathematical Operations problems
- 1. Statements:
V @ M, A S M, R # V
Conclusions:
I. R # A II/. V @ A III. R S M
Options- A. Only I follows
- B. Only II follows
- C. Only III follows
- D. None follows Discuss
Correct Answer: None follows
Explanation:
V ? M ...(i) A > M ...(ii) R ? V ...(iii)
These lead us to no relationship by combination.
- 2. Statements:
T S K, K # R, R * M
Conclusions:
I. M * K II. M % T III. M S K
Options- A. All follow
- B. Only either I and III follows
- C. Only either I and II follows
- D. Only either II and III follows Discuss
Correct Answer: Only either I and III follows
Explanation:
D > K ...(i) K ? R ...(ii) R = M ...(iii)
From (ii) and (iii) M ? K ...(iv)
Hence either I (M = K) or III (M > K) follow. But M and T can't be compared from (i) and (iv).
Hence II does not follow.
- 3. Statements:
B * D, D @ H, H % F
Conclusions:
I. B * F II B S F III. D S F
Options- A. None follow
- B. Only either I or III follows
- C. Only either I or II follows
- D. Only either II or III follows Discuss
Correct Answer: None follow
Explanation:
B = D ...(i) D ? H ...(ii) H > F ...(iii)
D and F can't be compared from (i) and (ii). And from the same reason, if we bear (i) an mind. B and F can't be compared. Hence none follows.
- 4. Statements:
I # N
Conclusions:
I. J % T II. T S N III. N @ J
Options- A. None follow
- B. Only I and II follow
- C. Only I and III follow
- D. Only II and III follow Discuss
Correct Answer:
Explanation:
J ? N ...(i) K ? N ...(ii) T > K ...(iii)
Combining these we get T > K ? N ? J
Hence J < T and I follows. Also T > N and II follows.
Beside N ? J and III follows
- 5. Statements:
M % R, R # T, T * N
Conclusions:
I. N * R, II. NSR, II. NSM
Options- A. All follow
- B. Only either I or II follows
- C. Only either I or II and III follow
- D. Only either I or III and II follow Discuss
Correct Answer: Only either I or II and III follow
Explanation:
M < R ...(i) R ? T ...(ii) T = N ...(iii)
Combining these we get M < R ? T = N
Hence N ? R
Which means either I (N = R) or II (N > R) follows.
Again N > M. Hence III follows
- 6. Statements:
M % R, R S T, T © K
Conclusions:
I. T ? M II. R S T
Options- A. if only conclusion I is true
- 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 Discuss
Correct Answer: if only conclusion I is true
Explanation:
M ? R ...(i) R < T ...(ii) T ? K ...(iii)
From (ii) and (iii) M ? R < T or T > M
Hence I follows
From (ii) and (iii) R and K can't be compared. Hence II does not follow
- 7. Statements:
W % V, V @ Z, Z © D
Conclusions:
I. D % V II. W % Z
Options- A. if only conclusion I is true
- 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 Discuss
Correct Answer:
Explanation:
W ? V ..(i) V = Z ...(ii) Z ? D ...(iii)
From (ii) and (iii) V = Z ? D or D ? V
Hence I follows.
From (i) and (ii) W ? V = Z or W ? Z
Hence II follows.
- 8. Statements:
B ? T, T S H, H @ M
Conclusions:
I. M ? T II. B ? H
Options- A. if only conclusion I is true
- 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 Discuss
Correct Answer: if only conclusion I is true
Explanation:
B > T ...(i) T < H ...(ii) H = M ...(iii)
From (ii) and (iii) T < H = M or M > I
Hence I follow
From (i) and (ii) B and H can't be compared. Hence II does not follow
- 9. Statements:
J ? D, D @ N, N % F
Conclusions:
I. J ? F II. F © D
Options- A. if only conclusion I is true
- 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 Discuss
Correct Answer: if only conclusion II is true
Explanation:
J > D ...(i) D = N ...(ii) N ? F ...(iii)
From (ii) and (iii) D = N ? F or F ? D ...(iv)
Hence II follows.
From (i) and (iv) R and (iv) J and F can't be compared.
Hence I does not follow.
- 10. Statements:
R S J, J ? F, F % H
Conclusions:
I. H ? J II. R S F
Options- A. if only conclusion I is true
- 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 Discuss
Correct Answer: if neither conclusion I nor II is true
Explanation:
R < J ...(i) J > F ...(ii) F ? H ...(iii)
From (ii) and (iii) H and J can't be compared.
Hence I does not follow
From (i) and (ii) R and F can't be compared.
Hence II does not follow
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