Mathematical Operations problems
- 1. In which of the following expressions will be expression 'P > S' definitely false?
Options- A. P > Q ? R = S
- B. S ? R ? Q < P
- C. R = P > Q ? S
- D. S > Q ? R < P Discuss
Correct Answer: S > Q ? R < P
Explanation:
From this expression we cannot deduce any relation between P and S
- 2. 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
Options- A. ? , =, >
- B. ? , <, =
- C. ? , =, <
- D. > ? , < Discuss
Correct Answer: ? , =, >
Explanation:
K ? L = M > N
- 3. Statements:
V © K, K @ B, B S M
Conclusions:
I. V © B II. M © K III. M © R
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:
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.
- 4. Statements:
D * R, R % F, F S T
Conclusions:
I. F % D II. F S D III. T © R
Options- A. Only I is true
- B. Only II is true
- C. Only III is true
- D. Only either I or II is true Discuss
Correct Answer:
Explanation:
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.
- 5. Statements:
N @ D, D * K, K S A
Conclusions:
I. K @ N II. A © D III. N S A
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:
N ? D ...(i) D ? N ...(ii) K > A ...(iii)
Obviously none of these in equations can be combined.
- 6. Statements:
K @ T, T S N, N © R
Conclusions:
I. R S K II. N * K III. K S N
Options- A. None is true
- B. Only I is true
- C. Only II is true
- D. Only III is true Discuss
Correct Answer: Only III is true
Explanation:
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.
- 7. Statements:
W % K, K © T, D S F
Conclusions:
I. D S K II. D S W III. F @ W
Options- A. Only I and III are true
- B. Only I and II are true
- C. Only II and III are true
- D. All I, II and III are true Discuss
Correct Answer: All I, II and III are true
Explanation:
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.
- 8. Statements:
B * K, K © F, F % R
Conclusions:
I. R $ K II. R $ B III. F $ B
Options- A. Only I and III are true
- B. Only I and II are true
- C. Only II and III are true
- D. All I, II and III are true Discuss
Correct Answer: Only I and II are true
Explanation:
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.
- 9. Statements:
R © K, K ? M, M *
Conclusions:
I. J ? K II. M @ R III. M % R
Options- A. None is true
- B. Only I is true
- C. Only II is true
- D. Only either II and III are true Discuss
Correct Answer: Only II is true
Explanation:
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.
- 10. Statements:
R ? B, B © N, N @ T
Conclusions:
I. N @ R II. T ? B III. T ? R
Options- A. None is true
- B. Only I is true
- C. Only II is true
- D. Only III is true Discuss
Correct Answer: Only I is true
Explanation:
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.
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