Mathematics · Quantitative Aptitude

Algebraic Equations and Expressions

152 Questions

Algebraic equations and expressions test mathematical skills in solving for unknown variables. Questions involve linear equations, ratios, and evaluating complex expressions. This topic forms a core component of quantitative aptitude sections in various competitive exams.

Linear equationsEvaluating expressionsRatio proportionsExponential equationsHypergeometric functions

Algebraic Equations and Expressions Questions

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $a\neq 0$ and $\dfrac{5}{x}=\dfrac{5+a}{x+a}$, what is the value of $x$?

  1. $-5$
  2. $-1$
  3. $5$
  4. $2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given:

$a$ $\neq$ $0$ and $\dfrac {5}{x}$ $=$ $\dfrac {5 \space + \space a}{x \space + \space a}$
To find the value of $x$,
$\Rightarrow \dfrac {5}{x}$ $=$ $\dfrac {5 \space + \space a}{x \space + \space a}$
$\Rightarrow 5$ $\times$ $(x$ $+$ $a)$ $=$ $x$ $\times$ $(5$ $+$ $a)$
$\Rightarrow 5x$ $+$ $5a$ $=$ $5x$ $+$ $xa$
Get the co-efficients of $'x'$ on one-side,
$\Rightarrow 5x$ $+$ $xa$ $-$ $5x$ $=$ $5a$
$\Rightarrow xa$ $=$ $5a$
As $(a$ $\neq$ $0)$,    $x$ $=$ $5$
Therefore, the value of $'x'$ is $'5'$.

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

Which of the following is the solution of the equation $\displaystyle \frac{7y+4}{y+2}=\frac{-4}{3}$ ?

  1. $\displaystyle y = -\frac{4}{5}$
  2. $\displaystyle y = \frac{4}{5}$
  3. $\displaystyle y = -\frac{5}{4}$
  4. $\displaystyle y = \frac{5}{4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$\dfrac{7y+4}{y+2}=\dfrac{-4}{3}$
$21y+12=-4y-8$
$25y=-20$
$y=\dfrac{-20}{25} = \dfrac{-4}{5}$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $t = x+2$, find the value of x .If $2t-7 +\dfrac{3(t-1)}{2}=3$

  1. $\frac{23}{7}$
  2. $\frac{3}{7}$
  3. $\frac{9}{7}$
  4. $\frac{37}{7}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$(2t-7)+(\frac{3t-3}{2})=3\\(\frac{4t-14+3t-3}{2})=3\\7t-17=6\\\therefore 7t=6+17\\t=(\frac{23}{7})\\then x+2=(\frac{23}{7})\\\therefore x=(\frac{23}{7})-2\\=(\frac{23-14}{7})\\=(\frac{9}{7})$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

Find the value of $a$, if $x = 0.5$ is a solution of equation $ax^{2}\, +\, (a\, -\, 1)\,
x\, +\, 3\, =\, a$.

  1. $24$
  2. $15$
  3. $10$
  4. $8$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given equation is $ax^2+(a-1)x+3=a$
The equation can be written as
$ax^2+(a-1)x+3-a=0$
Since $x=0.5$ is a solution of the equation, 
$a(0.5)^2 + (a-1)(0.5) + 3 - a = 0$
$\Rightarrow 0.25a + 0.5a - 0.5 + 3 - a = 0$
$\Rightarrow   (0.25 + 0.5 -1)a - 0.5+3 = 0$
$\Rightarrow  -0.25a + 2.5 = 0$
$\Rightarrow  0.25a = 2.5$
$\Rightarrow  a = \dfrac{2.5}{0.25}$
$\Rightarrow a = 10$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

If $2^{x} + 2^{x + 2} = 40$, then the value of $x$ is

  1. $1$
  2. $2$
  3. $3$
  4. $4$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given, ${ 2 }^{ x }+{ 2 }^{ x+2 }=40\ \Rightarrow { 2 }^{ x }+{ 2 }^{ 2 }{ 2 }^{ x }=40\ \Rightarrow { 2 }^{ x }+(4){ 2 }^{ x }=40\ \Rightarrow (5){ 2 }^{ x }=40\ \Rightarrow { 2 }^{ x }=8\ \Rightarrow { 2 }^{ x }={ 2 }^{ 3 }$

So, $ x=3$

Multiple choice maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

Find the value of $x: \dfrac {1}{x} + \dfrac {4}{5x} = \dfrac {2}{x + 5}$

  1. $0.71$
  2. $3.57$
  3. $5.8$
  4. $45$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation
Given  $\dfrac { 2 }{ x+5 } =\dfrac { 1 }{ x } +\dfrac { 4 }{ 5x } $
Taking RHS:

$\dfrac { 1 }{ x } +\dfrac { 4 }{ 5x } $

LCM is $5x$
$\Rightarrow \dfrac { 5 }{ 5x } +\dfrac { 4 }{ 5x } \\ \Rightarrow \dfrac { 9 }{ 5x } $
Now taking LHS:
$\dfrac { 2 }{ x+5 } $
LHS $=$ RHS
$\dfrac { 2 }{ x+5 } =\dfrac { 9 }{ 5x } $
$\Rightarrow 5x\times 2=9(x+5)\\ \Rightarrow 10x=9x+45\\ \Rightarrow x=45$
Multiple choice maths calculations and mental strategies 1 equations from statements forming equations from statements writing mathematical statements

If  $2x  + 2(4 + 3x) < 2 + 3x > 2x + \dfrac{x}{2}$ then $x$ can take which of the following values. 

  1. $-3$
  2. $1$
  3. $0$
  4. $-1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given,
$2x+2(4+3x) < 2+3x > 2x+\dfrac{x}{2}$

Solving $1^{st}$ inequality

$2x+8+6x < 2+3x$

$5x < -6$

$x < \dfrac{-6}{5}$

Solving $2^{nd}$ inequality

$2+3x > 2x+\dfrac{x}{2}$

$\dfrac{x}{2} > -2$

$x > -4$

$x\in \left (-4, \dfrac{-6}5\right )$

$x$ can take values $-3$

$A$ is correct.