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

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

1. Statements:

F * M, M % R, E @ F

Conclusions:

1. M % E
2. R @ E

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.

1. Statements:

H \$ K, T # H, W * T

Conclusions:

1. K % W
2. T # K

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).

1. Statements:

N % A, A # L, F \$ N

Conclusions:

1. L % F
2. F % A

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.

1. Statements:

B * D, D \$ M, F % M

Conclusions:

1. B # M
2. F % B

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.

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.

1. Statements:

P \$ Q, Q × R, P + R

Conclusions:

1. Q × P
2. P ? Q

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.

1. Statements:

A + B, B \$ C, C ? A

Conclusions:

1. C \$ A
2. B + C

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.

1. Statements:

Y @ Z, Z × Q, Q \$ P

Conclusions:

1. Y ? Q
2. Y ? P

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.

1. Statements:

E × F, F @ L, L+ N

Conclusions:

1. N + F
2. E × L

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.

1. Statements:

H @ J. J ? K, K × M

Conclusions:

1. H @ M
2. M × J

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.

1. Statements:

M @ T, T + V, V ? E

Conclusions:

1. V + M
2. V ? M

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.

Regards

Team EP

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