# IBPS > Algebraic Expressions and Inequalities

Explore popular questions from Algebraic Expressions and Inequalities for IBPS. This collection covers Algebraic Expressions and Inequalities previous year IBPS questions hand picked by experienced teachers.

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Q 1.

Correct4

Incorrect-1

Two-fifths of one-fourth of three-sevenths of a number is {tex}15{/tex}. What is half of that number?

A

96

B

196

C

94

D

188

None of these

##### Explanation

Q 2.

Correct4

Incorrect-1

{tex}\mathrm{I.}{/tex} {tex} 20 \mathrm { P } ^ { 2 } + 31 \mathrm { P } + 12 = 0 \quad {/tex} {tex}\mathrm {II.}{/tex} {tex} 21 \mathrm { Q } ^ { 2 } + 23 \mathrm { Q } + 6 = 0 {/tex}

If {tex} \mathrm { P } < \mathrm { Q } {/tex}

B

If {tex} \mathrm { P } > \mathrm { Q } {/tex}

C

If {tex} \mathrm { P } \leq \mathrm { Q } {/tex}

D

If {tex} \mathrm { P } \geq \mathrm { Q } {/tex}

E

If {tex}\mathrm P = \mathrm Q {/tex}

##### Explanation

Q 3.

Correct4

Incorrect-1

In each of these questions two equations
are given. You have to solve these equations and Give answer
I. {tex} \quad x ^ { 2 } - 6 x = 7 {/tex}
II. {tex} 2 y ^ { 2 } + 13 y + 15 = 0 {/tex}

A

if {tex} x < y {/tex}

if {tex} x > y {/tex}

C

if {tex} x = y {/tex}

D

if {tex} x \geq y {/tex}

E

if {tex} x \leq y {/tex}

##### Explanation

Q 4.

Correct4

Incorrect-1

The difference between the digits of a two-digit number is one-ninth of the difference between the original number and the number obtained by interchanging positions of the digits. What definitely is the sum of digits of that number?

A

5

B

14

C

12

Data inadequate

E

None of these

##### Explanation

Q 5.

Correct4

Incorrect-1

(i) {tex} 4 p ^ { 2 } - 5 p + 1 = 0 \quad {/tex} (ii) {tex} \quad q ^ { 2 } - 2 q + 1 = 0 {/tex}

A

(a) if {tex} p = q {/tex}

B

if {tex} p > q {/tex}

C

if {tex} q > p {/tex}

D

if {tex} p \geq q {/tex} and

if {tex} q \geq p {/tex}

##### Explanation

Q 6.

Correct4

Incorrect-1

In each of the following questions two equations are given. You have to solve them and Give answer
I. {tex} \quad p ^ { 2 } - 7 p = - 12 {/tex}
II. {tex} \quad q ^ { 2 } - 3 q + 2 = 0 {/tex}

A

if {tex} p < q {/tex}

if {tex} p > q {/tex}

C

if {tex} p \leq q {/tex}

D

if {tex} p \geq q {/tex}

E

if {tex} p = q {/tex}

##### Explanation

Q 7.

Correct4

Incorrect-1

In each question one or more equation(s) is (are) provided. On the basis of these you have
(i) {tex} \quad \frac { 5 } { 28 } \times \frac { 9 } { 8 } p = \frac { 15 } { 14 } \times \frac { 13 } { 16 } q {/tex}

A

(a) if {tex} p = q {/tex}

if {tex} p > q {/tex}

C

if {tex} q > p {/tex}

D

if {tex} p \geq q {/tex}

E

if {tex} q \geq p {/tex}

##### Explanation

Q 8.

Correct4

Incorrect-1

Out of total number {tex} { 3 } {/tex} of students in a college {tex} 12 \% {/tex} are interested in sports. {tex} \frac { 3 } { 4 } {/tex} th of the total number of students are interested in dancing. {tex} 10 \% {/tex} of the total number of students are interested in singing and the remaining {tex}15{/tex} students are not interested in any of the activities. What is the total number of students in the college?

A

450

500

C

600

D

Cannot be determined

E

None of these

##### Explanation

Q 9.

Correct4

Incorrect-1

If the ages of {tex} P {/tex} and {tex} R {/tex} are added to twice the age of {tex} Q {/tex}, the total becomes {tex} 59 . {/tex} If the ages of {tex} Q {/tex} and {tex} R {/tex} are added to thrice the age of {tex} P , {/tex} the total becomes {tex}68{/tex} . And if the age of {tex} P {/tex} is added to thrice the age of {tex} Q {/tex} and thrice the age of {tex} R , {/tex} the total becomes {tex}108{/tex} . What is the age of {tex} P ? {/tex}

A

{tex}15{/tex} years

B

{tex}19{/tex} years

C

{tex}17{/tex} years

{tex}12{/tex} years

E

None of these

##### Explanation

Q 10.

Correct4

Incorrect-1

In each of the following questions, oneor two equation(s) is/are given. On their basis you have to determine the relation between {tex} x {/tex} and {tex} y {/tex} and then give answer
{tex} \begin{array} { c c c c } { \mathbf { I } } & { x ^ { 2 } + 3 x + 2 = 0 } & { \mathbf { } } & { \mathbf { II.}\quad 2y ^ { 2 } = 5 y } \end{array} {/tex}

if {tex} x < y {/tex}

B

if {tex} x > y {/tex}

C

if {tex} x \leq y {/tex}

D

if {tex} x \geq y {/tex}

E

if {tex} x = y {/tex}

##### Explanation

Q 11.

Correct4

Incorrect-1

The sum of the digits of a two-digit number is {tex} 1 / 11 {/tex} of the sum of the number and the number obtained by interchanging the position of the'digits. What is the difference between the digits of that number?

A

3

B

2

C

6

Data inadequate

E

None of these

##### Explanation

Q 12.

Correct4

Incorrect-1

A

if {tex} p = q {/tex}

B

if {tex} p > q {/tex}

if {tex} q > p {/tex}

D

if {tex} p \geq q , {/tex} and

E

if {tex} q \geq p {/tex}

##### Explanation

Q 13.

Correct4

Incorrect-1

A classroom has equal number of boys and girls. Eight girls left to play Kho-kho, leaving twice as many boy as girls in the classroom. What was the total number of girls and boys present initially?

A

Cannot be determined

B

16

C

24

32

E

None of these

##### Explanation

Q 14.

Correct4

Incorrect-1

The denominator of a fraction is {tex}2{/tex} more than thrice its numerator. If the numerator as well as denominator is increased by one, the fraction becomes {tex} 1 / 3 . {/tex} What was the original fraction?

A

{tex} \frac { 4 } { 13 } {/tex}

{tex} \frac { 3 } { 11 } {/tex}

C

{tex} \frac { 5 } { 13 } {/tex}

D

{tex} \frac { 5 } { 11 } {/tex}

E

None of these

##### Explanation

Q 15.

Correct4

Incorrect-1

If the numerator of a fraction is increased by {tex} 2{/tex} and denominator is increased by {tex} 3 , {/tex} the fraction becomes {tex} 7 / 9 {/tex}; and if numerator as well as denominator are decreased by {tex}1{/tex} the fraction becomes {tex} 4 / 5 . {/tex} What is the original fraction?

A

{tex} \frac { 13 } { 16 } {/tex}

B

{tex} \frac { 9 } { 11 } {/tex}

{tex} \frac { 5 } { 6 } {/tex}

D

{tex} \frac { 17 } { 21 } {/tex}

E

None of these

##### Explanation

Q 16.

Correct4

Incorrect-1

{tex} \begin{array} { l l } { \text { I. }\quad x ^ { 2 } - 5 x + 6 = 0 } & { \text { II. }\quad y ^ { 2 } + y - 6 = 0 } \end{array} {/tex}

A

if {tex} x < y {/tex}

B

if {tex} x > y {/tex}

C

if {tex} x \leq y {/tex}

if {tex} x \geq y {/tex}

E

if {tex} x = y {/tex}

##### Explanation

Q 17.

Correct4

Incorrect-1

{tex}\mathrm{I.}{/tex} {tex}4 a ^ { 2 } = 1 {/tex}
{tex}\mathrm{II.}{/tex} {tex} 4 b ^ { 2 } - 12 b + 5 = 0 {/tex}

A

if {tex} a < b {/tex}

if {tex} a \leq b {/tex}

C

if {tex} a \geq b {/tex}

D

if {tex} a = b {/tex}

E

if {tex} a > b {/tex}

##### Explanation

Q 18.

Correct4

Incorrect-1

The price of four tables and seven chairs is {tex} \mathrm {Rs. } 12,090 {/tex}. Approximately, what will be the price of twelve tables and twenty-one chairs?

A

{tex} 32,000 {/tex}

B

{tex} \mathrm{Rs.} 46,000 {/tex}

C

{tex}\mathrm{Rs.} 38,000 {/tex}

{tex}\mathrm{Rs.}36,000{/tex}

E

{tex} \mathrm{Rs.} 39,000 {/tex}

##### Explanation

Q 19.

Correct4

Incorrect-1

{tex}\mathrm{I.}{/tex} {tex} 20 \mathrm { P } ^ { 2 } - 17 \mathrm { P } + 3 = 0 \quad {/tex} {tex}\mathrm{II.}{/tex} {tex} 20 \mathrm { Q } ^ { 2 } - 9 \mathrm { Q } + 1 = 0 {/tex}

A

If {tex} \mathrm { P } < \mathrm { Q } {/tex}

B

If {tex} \mathrm { P } > \mathrm { Q } {/tex}

C

If {tex} \mathrm { P } \leq \mathrm { Q } {/tex}

If {tex} \mathrm { P } \geq \mathrm { Q } {/tex}

E

If {tex}\mathrm P={/tex} {tex}\mathrm Q {/tex}

##### Explanation

Q 20.

Correct4

Incorrect-1

(i) {tex} 4 p ^ { 2 } = 16 \quad {/tex} (ii) {tex} q ^ { 2 } - 10 q + 25 = 0 {/tex}

A

if {tex} p = q {/tex}

B

if {tex} p > q {/tex}

if {tex} q > p {/tex}

D

if {tex} p \geq q {/tex} and

E

if {tex} q \geq p {/tex}

##### Explanation

(i). {tex}4p^2=16 \implies p=\pm2{/tex}. (ii). {tex}q^2-10q+25=0 \implies (q-5)^2=0 \implies q=5.{/tex} Hence, {tex}q>p{/tex}.

Q 21.

Correct4

Incorrect-1

By the how much is two-fifth of {tex}200{/tex} greater than three fifths of {tex} 125 ? {/tex}

A

15

B

3

5

D

30

E

None of these

##### Explanation

Q 22.

Correct4

Incorrect-1

Which of the following values of {tex} \mathrm { P } {/tex} satisfy the inequality {tex} P ( P - 3 ) < 4 P - 12 ? {/tex}

A

{tex} P > 4 {/tex} or {tex} P \leq 3 {/tex}

B

{tex} 24 \leq P < 71 {/tex}

C

{tex} P > 13 ; P < 51 {/tex}

{tex} 3 < P < 4 {/tex}

E

{tex} P = 4 , P = + 3 {/tex}

##### Explanation

Q 23.

Correct4

Incorrect-1

If the digit in the unit's place of a two-digit number is halved and the digit in the ten's place is doubled, the number thus, obtained is equal to the number obtained by interchanging the digits. Which of the following is definitely true ?

A

Digits in the unit's place and the ten'splace are equal.

B

Sum of the digits is a two-digit number.

C

Digit in the unit's place is half of the digit in the ten's place.

Digit in the unit's place is twice the digit in the ten's place.

E

None of these

##### Explanation

Q 24.

Correct4

Incorrect-1

In each question below one or more equation(s) is/are provided. On the basis of these, you have to find out relation between {tex} \mathrm { p } {/tex} and {tex} \mathrm { q } {/tex}.
{tex}\mathrm {I.}{/tex} {tex} \quad 4 q ^ { 2 } + 8 q = 4 q + 8 {/tex}
{tex}\mathrm{II.}{/tex} {tex} \quad p ^ { 2 } + 9 p = 2 p - 12 {/tex}

A

if {tex} p = q , {/tex}

B

if {tex} p > q , {/tex}

if {tex} q > p , {/tex}

D

if {tex} p \geq q {/tex}

E

if {tex} q \geq p {/tex}