Mathematical Operations problems
- 1. Statements:
M # W, W % N, N S B
Conclusions:
I. N % M II. N © M III. M S B
Options- A. Only either I or II is true
- B. Only either I or III is true
- C. Only either I or II and III are true
- D. Only III is true Discuss
Correct Answer: Only either I or II and III are true
Explanation:
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.
- 2. Statements:
W @ F, F S M, M © D
Conclusions:
I. D S F II. W © B III. F S D
Options- A. None is true
- B. Only I is true
- C. Only II is true
- D. Only III is true Discuss
Correct Answer: None is true
Explanation:
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.
- 3. Statements:
B % H, H S E, E @ K
Conclusions:
I. K S H II. K S B III. E © B
Options- A. None is true
- B. Only III is true
- C. Only II is true
- D. Only I is true Discuss
Correct Answer: Only III is true
Explanation:
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.
- 4. Statements:
F @ N, N © D, D @ R
Conclusions:
I. D # F II. R S N III. R S F
Options- A. None is true
- B. Only I is true
- C. Only II is true
- D. Only III is true Discuss
Correct Answer: Only II is true
Explanation:
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.
- 5. Statements:
F S B, B @ H, H % K
Conclusions:
I. B % F II. K @ F II. K S B
Options- A. Only I is true
- B. Only II is true
- C. Only III is true
- D. Only I and III are true Discuss
Correct Answer: Only I and III are true
Explanation:
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.
- 6. Statements:
M % D, D * K, K S N
Conclusions:
I. K © M II. N © D III. M © N
Options- A. Only I is true
- B. Only II is true
- C. Only III is true
- D. Only I and II are true Discuss
Correct Answer: Only II is true
Explanation:
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.
- 7. Statements:
R % N, N # F, F @ B
Conclusions:
I. F © R II. B S N
Options- 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 Discuss
Correct Answer: if only conclusion II is true
Explanation:
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.
- 8. Statements:
H © W, W % R, R @ F
Conclusions:
I. R © H II. R @ H
Options- 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 Discuss
Correct Answer: if either conclusion I or conclusion II is true
Explanation:
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.
- 9. Statements:
M S T, T @ K, K © D
Conclusions:
I. D S T II. K S M
Options- 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 Discuss
Correct Answer: if only conclusion I is true
Explanation:
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
- 10. Statements:
H @ W, W S M, M # K
Conclusions:
I. K S W II. H @ M
Options- 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 Discuss
Correct Answer: if neither conclusion I nor conclusion II is true
Explanation:
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
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