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

Solve the following pair of equations: $7x+6y= 71$ $5x-8y= -23$
  1. $x= -5;y= 4$
  2. $x= 3,y= -2$
  3. $x= 5,y= 6$
  4. $x= 1,y= 3$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Solving 7x + 6y = 71 and 5x - 8y = -23. Multiply first by 4 and second by 3: 28x + 24y = 284 and 15x - 24y = -69. Adding them gives 43x = 215, so x = 5. Substituting x=5 into the first equation: 35 + 6y = 71, 6y = 36, y = 6.

Multiple choice

Solve the following pair of equations: $13+2y= 9x$, $3y= 7x$
  1. $x= 8;y= 3$
  2. $x= 0;y= 5$
  3. $x= 3;y= 7$
  4. $x= 1;y= 9$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Substitute 3y = 7x into the first equation. From 3y = 7x, y = 7x/3. Substitute into 13 + 2y = 9x: 13 + 2(7x/3) = 9x. Multiply by 3: 39 + 14x = 27x. 39 = 13x, so x = 3. Then y = 7(3)/3 = 7.

Multiple choice

Solve the following pair of equations : $\displaystyle \frac{3}{5}x-\displaystyle \frac{2}{3}y+1= 0$ $\displaystyle \frac{1}{3}y+\displaystyle \frac{2}{5}x= 4$
  1. $x= 2;y= -1$
  2. $x= 5;y= 6$
  3. $x= 7;y= -4$
  4. $x= 0;y= 5$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The equations are (3/5)x - (2/3)y = -1 and (2/5)x + (1/3)y = 4. Multiplying the second by 2 gives (4/5)x + (2/3)y = 8. Adding this to the first gives (7/5)x = 7, so x = 5. Substituting x=5 into the second equation: 2 + (1/3)y = 4, so (1/3)y = 2, y = 6.

Multiple choice

Solve the following pair of equations: $6x+5y=7x+3y+1=2x+12y-2$
  1. $x=3, \, y=2$
  2. $x=1, \, y=0$
  3. $x=5, \, y=3$
  4. $x=7, \, y=1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

6x + 5y = 7x + 3y + 1 => x - 2y = -1. 7x + 3y + 1 = 2x + 12y - 2 => 5x - 9y = -3. From first, x = 2y - 1. Substitute: 5(2y - 1) - 9y = -3 => 10y - 5 - 9y = -3 => y = 2. Then x = 2(2) - 1 = 3.