   Directions: In these questions, relationship between different elements is shown in the statements. The statements are followed by two conclusions. Choose the correct answer for inequality given below:
Important for :
1
Statements:  H = I < J,     I = K > L ≥ M,     L > F ≤ S < T

Conclusions:   I. H > M          II. K > S
» Explain it
A
Only conclusion I follows.

Option A, is hence the correct answer.

Common explanation:

There is a priority order of the symbols according to which the priority of the symbol is decided to reach the conclusion. Whenever there are two or more type of symbols are there between two objects whose relation is to be determine we have to use this order.

If the direction of sign is opposite between that two objects, no relation can be stated perfectly and we have to say that it does not follow.

Priority Order:

1.      > and <
2.      ≥ and  ≤
3.           =

For conclusion I: H > M

Combining statements I and II:

H = I = K > L ≥ M

As, “>”, is the highest priority sign in the combination so, “H > M”, is the true relation between H and M.

Hence, Conclusion I follows.

For conclusion II: K > S

Combining statements II and III:

K > L > F ≤ S

As, sign between “K” and “S” are in different direction so, this conclusion does not follow.
2
Statements:  A > B ≥ C = D,    C < E = F > G ≥ H,    F < K ≤ L

Conclusions: I. C ≤ L                  II. D < E
» Explain it
B
Only conclusion II follows.

Option B, is hence the correct answer.

Common explanation:

There is a priority order of the symbols according to which the priority of the symbol is decided to reach the conclusion. Whenever there are two or more type of symbols are there between two objects whose relation is to be determine we have to use this order.
If the direction of sign is opposite between that two objects, no relation can be stated perfectly and we have to say that it does not follow.

Priority Order:
1.      > and <
2.      ≥ and  ≤
3.           =

For conclusion I: C ≤ L

Combining statements II and III:

C < E = F < K ≤ L

As, “<”, is having highest priority, therefore, this conclusion does not follow.

For conclusion II: D < E

Combining statements I and II

E > C = D

As, “<”, is having highest priority, so the conclusion follows.
3
Statements:  A = B ≤ X ≤ Y,     P ≥ X = Z,     X ≤ N < O > P

Conclusions:  I.   P > B                  II.  P = B
» Explain it
D
Either conclusion I or conclusion II follows.

Option D, is hence the correct answer.

Common explanation:

There is a priority order of the symbols according to which the priority of the symbol is decided to reach the conclusion. Whenever there are two or more type of symbols are there between two objects whose relation is to be determine we have to use this order.

If the direction of sign is opposite between that two objects, no relation can be stated perfectly and we have to say that it does not follow.

Priority Order:
1.      > and <
2.      ≥ and  ≤
3.           =

For conclusion I: P > B

Combining statements I and II:

B ≤ X ≤ P

So, P > B, does not follow.

For conclusion II: P = B

Combining statements I and II:

B ≤ X ≤ P

So, P = B, does not follow.

Now, we can see that:

Both the objects of conclusions I and II are same i.e. ‘P’ and ‘B’.
Both the conclusions I and II are wrong.
On combining both the relations we get the actual relation i.e. P ≥ B

So,

Either conclusion I or conclusion II follows.
4
Statements: L = P ≤ M ≤ V ≤ A,  Q ≥ R = N > P

Conclusions:  I. Q > L    II. N ≤ A
» Explain it
D
Given Statements: X = S ≤ T ≤ W ≤ A,  Q ≥ C = E > S

Conclusions:  I. Q > X    II. E ≤ A

For Conclustion I , combining both the equations, we get

Q ≥ C = E > S = X ≤ T ≤ W ≤ A  .................... (i)

We can observe that between Q and X, the common sign of inequality is of '>' which confirms Q > X which is given as conclusion I.

For Conclustion II,

We can observe that between E and A the signs are getting reversed and hence we can't derive a definite conclusion between these two elements. Conclustion II, hence, doesn't follow.

Option D is hence the correct answer.
5
Statements: S ≤ D > Q > V;   M ≤ N < Q = W

Conclusions: I. D ≥ M        II. N < D

» Explain it
C
Statements: S ≤ D > Q > V;     M ≤ N < Q = W
Conclusions: I. D ≥ M        II. N < D

Combining eq (i) and (ii) for the relation between B and L & K and B, we get
D > Q > N ≥ M and
N < Q < D

Common sign between D and M is of '>'. Thus, the given conclusion D ≥ M is not valid.

Now, common sign between N and D (moving from N to D) is '<' and the given conclusion is N < D. Hence Conclustion II follows.

Option C is hence the correct answer.