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

What is the value of the Hypergeometric function (_2F_1(3, 4; 5; x)) at x = 0?

  1. 0

  2. 1

  3. 2

  4. 3
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The Hypergeometric function (_2F_1(3, 4; 5; x)) at x = 0 is equal to 1.

Multiple choice

Find the value of $x$ in the equation $x^2 - 4x + 3 = 0$.

  1. 1

  2. 2

  3. 3

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

Using the quadratic formula, $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$, where $a = 1$, $b = -4$, and $c = 3$, we get $x = \frac{4 \pm \sqrt{(-4)^2 - 4(1)(3)}}{2(1)} = \frac{4 \pm \sqrt{16 - 12}}{2} = \frac{4 \pm \sqrt{4}}{2} = \frac{4 \pm 2}{2} = 1$ or $3$. Therefore, the value of $x$ is $1$.

Multiple choice

In the 2021 China Girls' Mathematical Olympiad, what was the value of x in the equation x^2 - 4x + 3 = 0?

  1. 1

  2. 2

  3. 3

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

To solve the equation x^2 - 4x + 3 = 0, we can use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a. Plugging in the values a = 1, b = -4, and c = 3, we get x = (4 ± √(16 - 12)) / 2 = (4 ± 2) / 2. Therefore, x = 1 or x = 3.

Multiple choice

In the 2015 China Girls' Mathematical Olympiad, what was the value of x in the equation x^3 - 2x^2 + x - 2 = 0?

  1. 1

  2. 2

  3. 3

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

To solve the equation x^3 - 2x^2 + x - 2 = 0, we can use the Rational Root Theorem to find the possible rational roots. The possible rational roots are ±1, ±2, and ±1/2. Plugging in these values, we find that x = 2 is a root of the equation. Therefore, x = 2 is the correct answer.

Multiple choice

In the 2012 China Girls' Mathematical Olympiad, what was the value of x in the equation 3x + 5 = 17?

  1. 2

  2. 3

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To solve the equation 3x + 5 = 17, we can subtract 5 from both sides to get 3x = 12. Then, we can divide both sides by 3 to get x = 4.

Multiple choice

In the 2009 China Girls' Mathematical Olympiad, what was the value of x in the equation 2x - 3 = 5?

  1. 2

  2. 3

  3. 4

  4. 5
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To solve the equation 2x - 3 = 5, we can add 3 to both sides to get 2x = 8. Then, we can divide both sides by 2 to get x = 4.

Multiple choice

Find the value of x in the following proportion: $$\frac{x}{3} = \frac{4}{6}$$

  1. 2

  2. 3

  3. 4

  4. 6
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

To solve the proportion, we can cross-multiply: $$x \times 6 = 3 \times 4$$ $$6x = 12$$ Dividing both sides by 6, we get: $$x = \frac{12}{6}$$ $$x = 2$$