Quantitative Aptitude

Algebra

3,715 Questions
All Polynomial Roots and Coefficients 2451 Zero-Product Root Finding 667 Linear System Manipulation 162 Polynomial Theorems and Reduction 85 Algebraic Identity Simplification 82 Surds and Indices 70 Modulus and Absolute Value 54 Algebraic Expression Substitution 46 Algebraic Fraction Simplification 33 Logarithmic Equations 25 Repeated Series Sum 12 Linear Equation Word Problems 9

Algebra Questions

Multiple choice

Directions: The following question consists of two quantities, Quantity I and Quantity II. You are to compare the two quantities and find the correct relationship between both the quantities. Quantity 1 Quantity 2 Sum of squares of roots of quadratic equation x2 – 2x – 3 = 0 12

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II, or No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Roots of x^2 - 2x - 3 = 0 are (x-3)(x+1) = 0, so roots are 3 and -1. Sum of squares = 3^2 + (-1)^2 = 9 + 1 = 10. Quantity I = 10, Quantity II = 12. Thus, 10 < 12.

Multiple choice

Directions: You are given two quantities, Quantity I and Quantity II. Compare the two quantities and choose the correct option accordingly. One of the roots of the equation 78y2 - ay + 78 = 0 is 13/6, and a is a constant. Quantity I: a Quantity II: 169

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I = Quantity II

  4. No relation
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Substitute y = 13/6 into 78y^2 - ay + 78 = 0: 78*(169/36) - a*(13/6) + 78 = 0. Divide by 6: 13*(169/6) - a*(13/6) + 78 = 0. Multiply by 6/13: 169 - a + 36 = 0 => a = 205. Quantity I (205) > Quantity II (169).

Multiple choice

Directions: In the given question, two equations (I) and (II) are given. You have to solve both the equations and select answer from the given options. I. 2x2 + 11x - 40 = 0 II. 4y2 - 27y + 44 = 0

  1. If x < y

  2. If x ≥ y

  3. If x > y

  4. If x ≤ y

  5. x = y, or the relationship cannot be established.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

I: 2x^2 + 11x - 40 = 0. Roots: x = (-11 +/- sqrt(121 + 320))/4 = (-11 +/- 21)/4. x = 2.5 or -8. II: 4y^2 - 27y + 44 = 0. Roots: y = (27 +/- sqrt(729 - 704))/8 = (27 +/- 5)/8. y = 4 or 2.75. Comparing values, x < y.

Multiple choice

Directions: In the following question, equations numbered I and II are given. You have to solve both the equations and choose the correct option. I. 35p2 - 29p + 6 = 0 II. 20q2 + q - 1 = 0

  1. p > q

  2. p ≥ q

  3. p < q

  4. p ≤ q

  5. p = q or no relation can be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Solving I: 35p^2 - 29p + 6 = 0 gives (5p-2)(7p-3)=0, so p = 0.4 or 0.428. Solving II: 20q^2 + q - 1 = 0 gives (4q-1)(5q+1)=0, so q = 0.25 or -0.2. Comparing values, p > q.

Multiple choice

Directions: In the following question, equations numbered I and II are given. You have to solve both the equations and choose the correct option. I. 22p2 + 5p - 3 = 0 II. 6q2 - 43q + 77 = 0

  1. p > q

  2. p ≥ q

  3. p < q

  4. p ≤ q

  5. p = q or no relation can be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: 22p^2 + 5p - 3 = 0. Roots are p = [-5 +/- sqrt(25 - 4*22*-3)] / 44 = [-5 +/- sqrt(289)] / 44 = [-5 +/- 17] / 44. p = 12/44 = 3/11 or p = -22/44 = -0.5. II: 6q^2 - 43q + 77 = 0. Roots are q = [43 +/- sqrt(1849 - 4*6*77)] / 12 = [43 +/- sqrt(1849 - 1848)] / 12 = [43 +/- 1] / 12. q = 44/12 = 11/3 or q = 42/12 = 3.5. Since both values of p are less than both values of q, p < q.

Multiple choice

Directions: In the given question, two equations (I) and (II) are given. You have to solve both the equations and select answer from the given options. I. 6x2 - 5x + 1 = 0 II. 4y2 - 7y + 3 = 0

  1. If x > y

  2. If x ≥ y

  3. If x < y

  4. If x ≤ y

  5. x = y, or no relation cannot be established.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

For 6x^2 - 5x + 1 = 0, roots are x = 1/2, 1/3. For 4y^2 - 7y + 3 = 0, roots are y = 1, 3/4. Comparing values: 1/2 < 3/4 and 1/3 < 1, so x < y.