Mathematics · Quantitative Aptitude

Algebraic Equations and Expressions

142 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

√(18*14*x) = 84then the value of x is ?

  1. 30

  2. 28

  3. 35

  4. 40

  5. none of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

since x is under square root, so squaring both sides we get18*14*x=84*84x= (84 * 84) / (18 * 14)therefore, x=28hence, Correct answer

Multiple choice

(43)4 ÷ (42)3 * (45)0 = 2xFind the value of x

  1. 12

  2. 6

  3. 3

  4. 9

  5. none of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

(43)4 ÷ (42)3 * (45)0 = 2x4(12-6) = 2x      [ when bases are same powers are added in multiplication and subtract in division]46   =  2x212 = 2xtherefore x = 12Correct Answer

Multiple choice

In the given figure, DE || BC. If AD = x, DB = x - 2, AE = x+ 2 and EC = x - 1, find the value of x.

  1. 2

  2. -2

  3. 4

  4. -4
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Since DE || BC,     AE/ EC  =    AD/ DB$\Rightarrow$                x + 2 / x - 1  =     x / x - 2$\Rightarrow$               x2 - 4     =    x (x - 1)                                                   $\Rightarrow$              x2 - 4     =     x2 - x $\Rightarrow$ x  =  4.

Multiple choice

Find the value of x in $\frac{2x + 4}{x+ 5} = 7$.
  1. x = $\frac{-39}{9}$
  2. x = $\frac{-1}{2}$
  3. x = $\frac{-31}{5}$
  4. x = $\frac{39}{9}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

$\frac{2x + 4}{x+ 5} = 7$             2x + 4 = 7 (x + 5)             2x + 4 = 7x + 35             2x – 7x = 35 – 4             – 5x = 31 $\therefore$        x =$\frac{-31}{5}$

Multiple choice

What is the value of x, in linear equation 11 (x + 7) = 2x + 13?
  1. x = - $\frac{6.4}{9}$
  2. x = $\frac{2}{3}$
  3. x = $\frac{90}{13}$
  4. $x=\frac{22}{4}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

11(x + 7) = 2x + 13             11x + 77 = 2x + 13             11x – 2x = 13 – 77             9x = – 64             x =$\frac{-64}{9}$.