Mathematical Operations problems
- 1. Statements:
E @ U, U %R, R S F
Conclusions:
I. E S F II. E * 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:
E < U ...(i) U = R ...(ii) R > F ...(iii)
From (i) and (ii) E < R ...(iv)
Now, From (iii) and (iv) E and F can't be compared
Hence neither I nor II follows.
- 2. Statements:
P @ W, W * D, D S J
Conclusions:
I. J @ P II. J @ W
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:
P < W ...(i) W ? D ...(ii) D > J ...(iii)
From (ii) and (iii) W ? D > J or J < W ...(iv)
Hence II follows. However, from (i) and (iv) we can conclude that J and P can't be compared. Hence I does not follow.
- 3. Statements:
V S I, I * M, M # Q
Conclusions:
I. I # Q II. I * Q
Options- A. if only conclusion I is true
- B. if only conclusion I 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:
V > I ...(i) I ? M ...(ii) M ? Q ...(iii)
From (ii) and (iii) I and Q, can't be compared. But I and II make a complementary pair. Hence either I (I ? Q) or II (I ? Q) follows.
- 4. Statements:
H # T, T @ L, L % F
Conclusions:
I. F S H II. H # L
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:
H ? T ...(i) T < L ...(ii) L = F ...(iii)
Combining these we get H ? T < L = F.
Hence F > H and I follows.
But H < L and Hence II (H ? L ) does not follow.
- 5. Statements:
H ? G < I; F ? G > Z
Conclusions:
I. F ? H II. Z < I
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:
H ? G < I; F ? G > Z
Check for I:
F ? G ? H is definitely follows
Check for II:
Z < G < I
? Z < I also follows
Hence, both I and II follows
- 6. Conclusions:
I. R ? S II. W < G
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:
S ? T < U ? W; T ? R, G > U
Check for I:
S ? T ? R
? R ? S follows
Check for II:
G > U ? W
? W < G follows
Hence, both I and II follows
- 7. Statements:
C ? D = E ? F; Y < D ? W
Conclusions:
I. C ? Y II. F ? Y
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:
C ? D = E ? F, Y < D ? W
Check for I:
C ? D > Y
It means C > Y. Thus, I does stand true. check for II:
Y < D ? F
It means F > Y. Thus, II also does not stand true.
- 8. Statements:
N < O ? R > T; R < A; B ? T
Conclusions:
I. N < A II. B < A
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:
N < O ? R > T; R < A; B ? T
Check for I:
N < O ? R > T
? No definite relation can be found between N and A.
Check for II:
- 9. Statements:
R © F, F # D, D @ M
Conclusions:
I. R © D II. M % F III. M S R
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:
R < F ...(i) F ? D ...(ii) D ? M ...(iii)
From (i) and (ii) R and D can't be compared. Hence neight I nor III follows.
From (ii) and (iii) M and F can't be compared. Hence II does not follows.
- 10. 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 definitely true.
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