Reasoning Quiz - Coded Inequalities - 4

Hello and welcome to exampundit. Here is a set of Reasoning Quiz on Coded Inequalities.   Directions (Qs.1-5): In the following questions, the symbols @, #, $, * and % are used as illustrated below: ‘P @ Q’ means ‘P is not smaller than Q’. ‘P # Q’ means ‘P is neither greater than nor equal to Q’. ‘P $ Q’ means ‘P is neither smaller than nor greater than Q’. ‘P * Q’ means ‘P is not greater than Q’. ‘P % Q’ means ‘P is neither smaller than nor equal to Q’. Now, in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true? Give answer (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. (e) if both Conclusions I and II are true.  

1. Statements:

M $ K, D * K, R # K Conclusions:

1. D $ M
2. M % D

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: C Explanation: M = K .…. (i); D ≤ K ….. (ii); R < K ..… (iii) From (i) and (ii), we get M = K ≥ D --> M ≥ D Hence, either M > D (conclusion II) or M = D (conclusion I) is true [/su_spoiler]  

2. Statements:

F * M, M % R, E @ F Conclusions:

1. M % E
2. R @ E

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: D Explanation: F ≤ M… (i); M > R… (ii); E ≥ F… (iii) From (i) and (iii), no specific relation can be obtained between M and E. Similarly, no specific relation can be obtained between R and E. [/su_spoiler]    

3. Statements:

H $ K, T # H, W * T Conclusions:

1. K % W
2. T # K

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: E Explanation: H = K… (i); T < H…(ii), W ≤ T …(iii) From (i), (ii) and (iii), we get K = H > T ≥ W --> K > W (conclusion I) and T < K (conclusion II). [/su_spoiler]    

4. Statements:

N % A, A # L, F $ N Conclusions:

1. L % F
2. F % A

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: B Explanation: N > A… (i), A < L… (ii), F = N…(iii) From (i) and (iii), we get F = N > A--> F > A (conclusion II). But no specific relation can be obtained between L and F. Hence, conclusion I is not necessarily true. [/su_spoiler]    

5. Statements:

B * D, D $ M, F % M Conclusions:

1. B # M
2. F % B

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: B Explanation: B ≤ D…(i); D = M…(ii); F > M …(iii) From (i), (ii) and (iii), we get F > M = D ≥ B --> B < M and F > B (conclusion II). Since, B < M, therefore, conclusion I is not necessarily true. [/su_spoiler]       Directions (Qs. 6-11): In the following questions the symbols +, ×, ?, @ and $ are used with the following meanings: P + Q means P is neither smaller nor greater than Q. P × Q means P is neither equal to nor smaller than Q. P ? Q means P is neither greater than nor equal to Q. P @ Q means P is either greater than or equal to Q. P $ Q means P is not equal to Q. Now, in each of the following questions assuming the given statements to be true, find which of the two conclusions I and II given below them is/are definitely true. Give answer (a) if only conclusion I is true; (b) if only conclusion II is true; (c) if either I or II is true: (d) if neither I nor II is true; and (e) if both I and II are true.    

6. Statements:

P $ Q, Q × R, P + R Conclusions:

1. Q × P
2. P ? Q

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: E Explanation: P ≠ Q ...(i), Q > R ... (ii), P = R ...(iii) From (ii) and (iii), we get Q > R = P --> Q > P. Hence, both I and II are true. [/su_spoiler]    

7. Statements:

A + B, B $ C, C ? A Conclusions:

1. C $ A
2. B + C

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: A Explanation: A = B ... (i), B ≠ C ... (ii), C < A ... (iii) From (iii), conclusion I is true. II contradicts statement (ii), hence, it is not true. [/su_spoiler]    

8. Statements:

Y @ Z, Z × Q, Q $ P Conclusions:

1. Y ? Q
2. Y ? P

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: D Explanation: Y ≥ Z ...(i), Z > Q ... (ii), Q ≠ P ...(iii) From (i) and (ii), we get Y > Z > Q --> Y > Q ... (A) Hence, I is not true. From (iii), two possible relationships between P and Q are; Case I: When P > Q Now, using (A), we get Y > Q < P --> no conclusion. Case II: When Q > P using (A), we get Y > Q > P --> Y > P. Hence, II is not true. [/su_spoiler]    

9. Statements:

E × F, F @ L, L+ N Conclusions:

1. N + F
2. E × L

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: B Explanation: E > F .... (i), F ≥ L ... (ii), L = N ...(iii) From (ii) and (iii), we get F ≥ L= N --> F ≥ N or N′ F. Hence, I may be true but not necessarily so. From (i) and (ii), we get E > F ≥ L --> E > L Hence, II is true. [/su_spoiler]    

10. Statements:

H @ J. J ? K, K × M Conclusions:

1. H @ M
2. M × J

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: D Explanation: H ≥ J ... (i), J < K ... (ii), K > M ... (iii) From (ii) and (iii), we get J < K > M fi no relationship between J and M can be established. Hence, II can’t be established. Again, combining all we can’t conclude the relationship between H and M. Hence, I is not true. [/su_spoiler]  

11. Statements:

M @ T, T + V, V ? E Conclusions:

1. V + M
2. V ? M

[su_spoiler title="Show Answer" style="fancy" icon="arrow-circle-1"] Option: C Explanation: M ≥ T ... (i), T = V .... (ii), V < E ...(iii) From (i) and (ii), we get M ≥ T = V --> M ≥ V --> either V = M or V < M is true. [/su_spoiler]   Regards Team EP