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Problem of Inequalities

Example 1

C < D < R = K, A = G ≥ C; L ≤ N < A

(I) N > C

(II) G > N

(a) Only (I) follow

(b) Only (II) follow

(c) Both (I) or (II) follow

(d) Either (I) nor (II) follow

(e) None follow

Solution:

By combining this

L ≤ N < A = G ≥ C < D < R = K

We can see N < A = G ≥ C Direction changes

So, no relation between N and C

N < A = G which means G > N

So, only (II) follows.

So, option (b) is correct.

Example 2

A = B < C < D = E, B > G, C < H

(I) G < H

(II) E > H

(a) Only (I) follow

(b) Only (II) follow

(c) Both (I) or (II) follow

(d) Either (I) nor (II) follow

(e) None follow

Solution:

So, G < B < C < H. So, from this, we can conclude G < H

Now, E = D > C < H. So, between E and H direction changes. So, between E and H no relation can be established.

So, only (I) follows.

So, option (a) is correct.

Example 3

What will come in place of question mark (?) so that in the given expression B >G and B ≥  F is definitely true?

A > B = C ? D = E ≥ F > G

(a) =                                         

(b) <                                         

(c) ≤

(d) ≥                                         

(e) Either (a) or (d)

Solution:

A > B = C ? D = E ≥ F > G

To make B > G and B ≥ F definitely true.

We need = or ≥ in place of the question mark.

A > B = C = D = E ≥ F > G

From this we can conclude B > G and B ≥ F

When we put ≥ then

A > B = C ≥ D = E ≥ F > G from these we can also conclude B > G and B ≥ F

So, option (d) is correct.

Example 4

Which of the following expression will be true?

If A > B ≤ C > D = E ≥ F is definitely true

(a) A < C

(b) C > F

(c) B < D

(d) D > F

(e) None of these

Solution:

(a) A < C not true as A > B ≤ C, So, no relation between A and C

(b) C > F true as C > D = E ≥ F. So, C > F

(c) B < D not true as B ≤ C > D, So no relation between B and D

(d) D > F not true as D = E ≥ F which implies D ≥ F

So, option (b) is correct.