Inequality Questions PDF Download: -Inequality is a topic asked in almost every competitive exam. In every competitive exam, at least 5-6 questions can be expected from this topic. If you are slightly comfortable with elementary mathematics, this topic is an easy task for you. Practice with the Inequality Questions to get familiar with different question types.

#### Symbols and Meanings in Inequalities

 Symbol What does it mean? Example > Greater than A > B → A is greater than B < Less than A < B → A is less than B ≥ Greater than or equal to A ≥ B → A is greater than or equal to B ≤ Less than or equal to A ≤ B → A is greater than or equal to B = Equal to A = B → A is equal to B

1. A relationship can be easily established between two elements if they have similar signs.

For e.g.

> B > C > D

Here we can draw a conclusion – A > D, B > D, A > C or D < A, D < B or C < A, C < B

2. A relationship cannot be easily established between two elements if they don’t have similar signs. In these cases, you have to put extra care seeking either-or cases type conclusions.

For e.g.

> B < C > D

Here relationship cannot be established between – A & C, A & D, B & D.

Few of the questions related to Inequality are given below:-

Directions (1-5): In the following questions, the symbols >, <, %, = and ≥ are used with the following meaning as illustrated below-

P>Q’ means ‘P is neither greater than nor equal to Q’

P<Q’ means ‘P is neither equal to nor smaller than Q’

P%Q’ means ‘P is neither smaller than nor greater than Q’

P=Q’ means ‘P is not smaller than Q’

P≥Q’ means ‘P is not greater than Q’

Now in each of the following questions assuming the given statement to be true, find which of the conclusions  given below them is/are definitely true and give your answer accordingly.

Q1. Statements: P > X = B < I ≥ O

Conclusions:

I. P>B II. B=O

(a) None is true

(b) Only I is true

(c) Only II is true

(d) Either I or II is true

(e) Both are true

Q2. Statements: A = B, B % M, K < M

Conclusions:

I. A<M  II. B % A

(a) Only I true

(b) Only II true

(c) Only I and II are true

(d) Either I or II is true

(e) None of these

Q3. Statements: R = M, M ≥ Z, Z % A, Y > Z

Conclusions:

I. Y > A  II. M ≥ A

(a) None is true

(b) Only I is true

(c) Both I and II are true

(d) Only II is true

(e) None of these

Q4. Statements: A = B, B % M, K < M

Conclusions:

I. K < B II. A % M

(a) None follows

(b) Only I is true

(c) Only II is true

(d) Either I or II is true

(e) None of these

Q5. Statements P > X = B < I ≥ O>K

Conclusions:

I. I > K II. X = I

(a) None follows

(b) Only I is true

(c) Only I and II are true

(d) Only II is true

(e) None of these

Solutions (1-5):

S1. Ans.(a)

I. P>B (false) II. B=O (false)

S2. Ans.(d)

I. A<M(false) II. B % A(false)

S3. Ans.(c)

I. Y > A(true)  II. M ≥ A(true)

S4. Ans.(b)

I. K < B(true) II. A % M(false)

S5. Ans.(b)

I. I > K(true) II. X = I(False)

Directions (6-10): In the following questions, the symbols @, #, %, \$ and © are used with the following meaning as illustrated below-

P#Q’ means ‘P is neither greater than nor equal to Q’

P©Q’ means ‘P is neither equal to nor smaller than Q’

P%Q’ means ‘P is neither smaller than nor greater than Q’

‘P\$Q’ means ‘P is not smaller than Q’

’ means ‘P is not greater than Q’

Now in each of the following questions assuming the given statement to be true, find which of the three conclusions I, II and III given below them is/are definitely true and give your answer accordingly.

Q6. Statements: M © S @ Z % R \$ N

Conclusions:

(a) None is true

(b) Only I is true

(c) Only III is true

(d) Either I or II is true

(e) All are true

Q7. Statements: A \$ B, B % M, K © M

Conclusions:

I. K © B    II. M @ A III. A © K

(a) Only I and III are true

(b) Only II and III are true

(c) Only I and II are true

(d) All are true

(e) None of these

Q8. Statements: R \$ M, M © Z, Z @ A, Y © Z

Conclusions:

(a) None is true

(b) Only II is true

(c) Only I and II are true

(d) Only II and III are true

(e) All are true

Q9. Statements: M © S @ Z % R \$ N

Conclusions:

I. N # Z    II. R # M III. S % N

(a) None follows

(b) Only I is true

(c) Only III is true

(d) Either I or II is true

(e) All are true

Q10. Statements: R \$ M, M © Z, Z @ A, Y © Z

Conclusions:

I. R © Z    II. Z # A III.R % A

(a) Only I is true

(b) Only II is true

(c) Only I and II are true

(d) Only II and III are true

(e) All are true

Solutions (6-10):

S6. Ans.(d)

I. M © Z (false) II. R \$ M(false) III.S © N(false)

S7. Ans.(c)

I. K © B(true)   II. M @ A(true) III. A © K(false)

S8. Ans.(b)

S9. Ans.(a)

I. N # Z(false)  II. R # M(false) III. S % N(false)

S10. Ans.(a)

I. R © Z(true)  II. Z # A(false) III.R % A(false)

Directions (11-15): In the following questions, the symbols @, ^, *, # and ! used with the following meaning as illustrated below:

‘P ^ Q’ means ‘P is not smaller than Q’

means ‘P is neither smaller than nor equal to Q’

‘P # Q’ means ‘P is neither greater than nor equal to Q’

P % Q means “P is neither greater than nor smaller than Q’

‘P !Q’ means ‘P is not greater than Q’

Now, in each of the following questions assuming the given statements to be true, find which of the four conclusions I, II, III and IV is/are definitely true and give your answer accordingly.

Q11. Statements: A ! B ^ C @ D # M

Conclusions:      I. B @ D    II. [email protected] M

III. A ! M     IV. C # B

(a) Only I is true

(b) Only III is true

(c) Only IV is true

(d) Only either III or IV is true

(e) Only either III or II and I are true

Q12. Statements:  A ! Z, Z ^ J, J # X, X @ L

Conclusions:       I. L # J       II. Z @ X

III. A # X    IV. [email protected] L

(a) None is true

(b) Only I is true

(c) Only II is true

(d) Only III is true

(e) Only IV is true

Q13. Statements: A ! B ^ C @ D # M

Conclusions:      I. C ! B    II. D # C

III. C @ M    IV. B @ A

(a) Only I and II are true

(b) Only I, II and IV are true

(c) Only II, III and IV are true

(d) Only I, III and IV are true

(e) All I, II, III and IV are true

Q14. Statements:  A ! Z, Z ^ J, J # X, X @ L

Conclusions:       I. A @ X     II. X ^ A

III. J ! L     IV. Z % X

(a) None is true

(b) Either I or II is true

(c) Only II is true

(d) Only III is true

(e) Only IV is true

Q15. Statements:   H ^ G, G @ I, I ! J, J # K

Conclusions:        I. I # K   II. H ^ J

III. G @ K           IV. H @ I

(a) Only I and II are true

(b) Only I is true

(c) Only III and IV are true

(d) Only III is true

(e) Only I and IV is true

Solutions (11-15):

S11. Ans.(e)

Sol. :   I. B @ D(true)       II. [email protected] M (false)

III. A ! M(false)    IV. C # B(false)

S12. Ans.(a)

Sol.  I. L # J(false)         II. Z @ X(false)

III. A # X(false)    IV. [email protected] L(false)

S13. Ans.(a)

Sol. : I. C ! B(true)          II. D # C(true)

III. C @ M(false)   IV. B @ A(false)

S14. Ans.(b)

Sol. : I. A @ X(false)     II. X ^ A(false)

III. J ! L(false)     IV. Z % X(false)

S15. Ans.(e)

Sol.  I.    I # K(true)         II. H ^ J(false)

III. G @ K(false)    IV. H @ I(true)

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