Mathematical Operations problems
- 1. Statements:
F # K, K S B, B % M
Conclusions:
I. M @ F II. B @ F
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:
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.
- 2. Statements:
R # T, T © M, M @ D
Conclusions:
I. D S T II. R # 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:
Explanation:
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.
- 3. Statements:
J © M, M * K, K % D
Conclusions:
I. J © D, II. D * M III. K © J
Options- A. None of true
- B. Only I is true
- C. Only II is true
- D. Only III is true Discuss
Correct Answer: None of true
Explanation:
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.
- 4. Statements:
R @ K, K S F, F * N
Conclusions:
I. N © R, II. F @ R, III. F © R
Options- A. Only I is true
- B. Only either II or III is true
- C. Only I and either II or III are true
- D. Only III is true Discuss
Correct Answer: Only I and either II or III are true
Explanation:
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.
- 5. Statements:
R S D, D @ N, N © F
Conclusions:
I. F * D II. F * R III. N % R
Options- A. Only I and II are true
- B. Only I and III are true
- C. Only II and III are true
- D. All are true Discuss
Correct Answer: Only I and III are true
Explanation:
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.
- 6. Statements:
H * T, T S B, B © R
Conclusions:
I. R © H II. B © H III. T % R
Options- A. Only i is true
- B. Only I and II are true
- C. Only I and III are true
- D. Only II and III are true Discuss
Correct Answer:
Explanation:
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.
- 7. Statements:
M © T, T # J, J S K
Conclusions:
I. K © T II. M © J III. K @ M
Options- A. None is true
- B. Only III is true
- C. Only II is true
- D. Only I is true Discuss
Correct Answer: Only I is true
Explanation:
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.
- 8. Which of the following expression will be true if the given expression A > B ? C < D < E
Options- A. A ? C
- B. E > C
- C. D ? B
- D. A > D Discuss
Correct Answer: E > C
Explanation:
E > C
- 9. If the expression E < J ? H > Z'. 'H ? Y' and 'E > F' true. Which of the following conclusions will be definitely false?
Options- A. F < Y
- B. Y > E
- C. F < H
- D. J ? Y Discuss
Correct Answer:
Explanation:
F < E < J ? H > Z H ? Y and Z < H
- 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
Options- A. >
- B. ?
- C. ?
- D. Either < or ? Discuss
Correct Answer:
Explanation:
H ? I = J = K ? L < M
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