# Inequalities

1. Statement: A ≥ B < C ≥ D > E ≥ F = G ≤ H

Conclusions: i) C > F ii) E ≥ G

A) Only i follows    B) Only ii follows    C) Either i or ii follow   D) Neither i nor ii follows   E) Both i and ii follows

Sol: From the given statement

A ≥ B < C ≥ D > E ≥ F = G ≤ H

For conclusion (i) C > F

Here, the sign between (C ≥ D > E ≥ F) ≥, > , ≥ → give priority to > then final conclusion is C > F

∴ Conclusion i follows

For conclusion (ii) E ≥ G (E ≥ F = G) E ≥ G

the final conclusion is E ≥ G

Conclusion ii also follow

∴ Both (i) and (ii) follows.

Ans: E

2. Statement: P > Q ≥ R ≤ S ≥ T < U ≥ V > W

Conclusions: i) P < S ii) U > W

A) Only i follows    B) Only ii follows    C) Either i or ii follows    D) Neither i nor ii follows    E) Both i and ii follows

Sol: For conclusion (i) P < S

In the above statement (P > Q ≥ R ≤ S) in between P and S opposite signs are there, when ever opposite signs there is no relation between subject and predicate

∴ Conclusion i not satisfied

For conclusion (ii) U > W

(U ≥ V > W)

Symbol Priority to " > " U > W The conclusion ii follows Only (ii) follows

Ans: B

3. Statement: 1 > 2 ≤ 3 > 4 ≥ 6 > 8 ≤ 9

Conclusions: i) 3 > 6 ii) 1 < 6

A) Only i follows    B) Only ii follows    C) Either i or ii follows    D) Both i and ii follows   E) Neither i nor ii follows

Sol: For conclusion (i) 3 > 6 Here, in between 3 and 6 same signs are there.

3 > 6 is satisfied For conclusion (ii) 1 < 6 Here, in between 1 and 6 opposite signs are there.

1 < 6 is not satisfied Only (i) follows

Ans: A

4. Statement: P > Q ≥ R < S ≤ W ≥ T ≥ U > X ≥ Y Conclusions: i) S ≥ U ii) Q > Y

A) Only i follows    B) Only ii follows    C) Either i or ii follows    D) Neither i nor ii follows   E) Both i and ii follows

Sol: For conclusion (i) S ≥ U (S ≤ W ≥ T ≥ U)

In between S and U opposite signs are there. Thus no relationship can be formed.

For conclusion (ii) Q > Y (Q ≥ R < S ≤ W ≥ T ≥ U > X ≥ Y)

In between Q and Y opposite sings are there. Thus no relationship can be formed Neither (i) nor (ii) follows.

Ans: D

5. Statements: P < Q, Q ≤ R , R = S, S > T

Conclusions: i) P < S ii) Q > T

A) Only i follows    B) Only ii follows    C) Either i or ii follows    D) Neither i nor ii follows   E) Both i and ii follows

Sol: By combining all statements, we get following equation

P < Q ≤ R = S > T

For conclusion (i) P < S

Here, the common sign between P and S is “<”. thus P < S “

conclusion (i) follows.

For conclusion (ii) Q > TT Here, we can see the opposite signs between Q and T.

Thus no relationship can be established between them. Hence, only (i) follows.

Ans: A

6. Statements: x > y ≤ z, w > z, w ≤ t

Conclusions: i) x < w ii) y < t

A) Only i follows    B) Only ii follows    C) Either i or ii follows    D) Neither i nor ii follows    E) Both i and ii follows

Sol: x > y ≤ z, w > z, w ≤ t

By combining the all statements, we get following equation.

x > y ≤ z < w ≤ t

For conclusion (i) x < w

Here, opposite signs between X and W.

Thus no relationship can be established between them.

For conclusion (ii) y < t

In the above equation, there is common sign between Y and T.

Hence conclusion (ii) follows.

Ans: B

7. Statements: m > n, n ≤ t, t = q, q > r

Conclusions: i) n < q ii) n = q

A) Only i follows    B) Only ii follows    C) Either i or ii follows    D) Neither i nor ii follows     E) Both i and ii follows

Sol: By combining the all statements, we get following equation.

m > n ≤ t = q > r

For conclusion (i) n < q

For conclusion (ii) n = q

from the above statements, we get n ≤ q.

n ≤ q consisting of n < q and n = q

Either (i) or (ii) follows

Ans: C

8. Statements: 1 > 2 ≤ 4, 4 < 5 > 6, 6 > 8, 8 ≤ 9

Conclusions : i) 1 < 5 ii) 1 ≥ 9

A) Only i follows     B) Only ii follows     C) Either i or ii follows    D) Neither i nor ii follows   E) Both i and ii follows

Sol: By combining all the statements

1 > 2 ≤ 4 < 5 > 6 > 8 ≤ 9

For conclusion (i) 1 < 5

Here, opposite signs between 1 and 5. Thus no relationship can be established between them

For conclusion (ii) 1 ≥ 9 Here, opposite signs between 1 and 9. there is no relation between them.

conclusions (i) and (ii) are not satisfied. Neither (i) nor (ii) follows

Ans: D

9. Statements: Cat > Dog, Dog ≥ Lion = Pet, Pet ≥ Pen ≥ Tiger

Conclusions: i) Cat > Tiger

ii) Dog ≥ Pen

A) Only i follows     B) Only ii follows     C) Either i or ii follows    D) Neither i nor ii follows     E) Both i and ii follows

Sol: By combining all the statement Cat > Dog ≥ Lion = Pet ≥ Pen ≥ Tiger

For conclusion (i) Cat > Tiger

Here, common sign between Cat and Tiger. conclusion (i) follows

For conclusion (ii) Dog ≥ Pen conclusion (ii) also follows Hence, Both (i) and (ii) follows

Ans: E

Directions (Q.10-13): Study the given information carefully and answer the questions given below.

A \$ B means A either smaller than or equal to B.

A # B means A either greater than or equal to B.

A@B means A greater than B.

A ! B means A less than B.

A ∗ B means A equals to B.

10. Statement: P # Q @ R ∗ S \$ T

Conclusions: i) P @ S ii) Q ! T

A) Only i follows    B) Only ii follows    C) Either i or ii follows    D) Neither i nor ii follows   E) Both i and ii follows

Sol: P # Q @ R ∗ S \$ T

Symbols are substituted with signs.

\$      #    @     !     ∗

≤      ≥      >    <     =

P ≥ Q > R = S ≤ T

For Conclusion (i): P@S P > S

Here, P and S same sign are there The conclusion (i) follows.

For conclusion (ii) Q ! T (Q < T)

Here, Q and T opposite signs are there.

conclusion (ii) does not follows

Ans: A

11. Statement: U @ W \$ X ! Y # Z

Conclusions: i) U @ Z ii) X @ Y

A) Only i follows    B) Only ii follows   C) Either i or ii follows      D) Neither i nor ii follows    E) Both i and ii follows

Sol:       \$    #   @    !    ∗

≤    ≥    >   <   =

U > W ≤ X < Y ≥ Z

For conclusion (i): U @ Z (U > Z) (ii) X @ Y (X > Y)

In between U and Z: Opposite signs between U and Z.

X and Y opposite signs between x and y.

Both Conclusion (i) & (ii) does not follows

Ans: D

12. Statement: M ! N ∗ O \$ P # Q

Conclusions: i) M ! P ii) O ∗ Q

A) Only i follows     B) Only ii follows   C) Either i or ii follows     D) Neither i nor ii follows     E) Both i and ii follows

Sol: \$ # @ ! ∗ ≤ ≥ > < =

M < N = O ≤ P ≥ Q

For conclusion (i): M ! P (M < P)

In between M and P same signs are there. the conclusion (i) follows,

For conclusion (ii) O ∗ Q (O = Q)

In between O and Q Opposite signs are there. There in no relation between O and Q. Hence, conclusion (i) follows.

Ans: A

13. Statement: M \$ N @ O ! Q ∗ R

Conclusions: i) M \$ Q ii) N ! O

A) Only i follows   B) Only ii follows   C) Either i or ii follows   D) Neither i nor ii follows  E) Both i and ii follows

Sol:   \$    #    @    !    ∗

≤    ≥    >    <   =

M ≤ N > O < Q = R

For conclusion (i) M \$ Q (M ≤ Q]

(ii) N ! O (N < O]

In the above two conclusions opposite signs are between subject and predicate. Thus no relationship can be formed. So that both conclusions are not satisfied. Neither (i) nor (ii) follows.

Ans: D

Posted Date : 18-04-2023

గమనిక : ప్రతిభ.ఈనాడు.నెట్‌లో కనిపించే వ్యాపార ప్రకటనలు వివిధ దేశాల్లోని వ్యాపారులు, సంస్థల నుంచి వస్తాయి. మరి కొన్ని ప్రకటనలు పాఠకుల అభిరుచి మేరకు కృత్రిమ మేధస్సు సాంకేతికత సాయంతో ప్రదర్శితమవుతుంటాయి. ఆ ప్రకటనల్లోని ఉత్పత్తులను లేదా సేవలను పాఠకులు స్వయంగా విచారించుకొని, జాగ్రత్తగా పరిశీలించి కొనుక్కోవాలి లేదా వినియోగించుకోవాలి. వాటి నాణ్యత లేదా లోపాలతో ఈనాడు యాజమాన్యానికి ఎలాంటి సంబంధం లేదు. ఈ విషయంలో ఉత్తర ప్రత్యుత్తరాలకు, ఈ-మెయిల్స్ కి, ఇంకా ఇతర రూపాల్లో సమాచార మార్పిడికి తావు లేదు. ఫిర్యాదులు స్వీకరించడం కుదరదు. పాఠకులు గమనించి, సహకరించాలని మనవి.