Quadratic equations

1. 1

   Solve both equations and compare x and y.
   I. x² + 12x + 27 = 0
   II. y² − 2y − 24 = 0

   Question 1

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer EE

   I gives x = −9 or −3. II gives y = −4 or 6. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

2. 2

   Solve both equations and compare x and y.
   I. x² − 3x − 10 = 0
   II. y² + y − 6 = 0

   Question 2

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer EE

   I gives x = −2 or 5. II gives y = −3 or 2. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

3. 3

   Solve both equations and compare x and y.
   I. x² + 13x + 40 = 0
   II. y² + 3y − 10 = 0

   Question 3

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer DD

   I gives x = −8 or −5. II gives y = −5 or 2. No x is greater than any y, and one value of each is equal: x ≤ y.

4. 4

   Solve both equations and compare x and y.
   I. x² − 5x − 84 = 0
   II. y² − 25 = 0

   Question 4

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer EE

   I gives x = −7 or 12. II gives y = −5 or 5. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

5. 5

   Solve both equations and compare x and y.
   I. x² − 8x − 48 = 0
   II. y² + 4y = 0

   Question 5

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer EE

   I gives x = −4 or 12. II gives y = −4 or 0. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

6. 6

   Solve both equations and compare x and y.
   I. x² − 9x + 20 = 0
   II. y² − 2y − 63 = 0

   Question 6

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer EE

   I gives x = 4 or 5. II gives y = −7 or 9. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

7. 7

   Solve both equations and compare x and y.
   I. x² − 18x + 72 = 0
   II. y² − 2y = 0

   Question 7

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer AA

   I gives x = 6 or 12. II gives y = 0 or 2. Every x is greater than every y: x > y.

8. 8

   Solve both equations and compare x and y.
   I. x² − 15x + 44 = 0
   II. y² − 17y + 66 = 0

   Question 8

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer EE

   I gives x = 4 or 11. II gives y = 6 or 11. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

9. 9

   Solve both equations and compare x and y.
   I. x² − 2x − 15 = 0
   II. y² − 8y = 0

   Question 9

   Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

   Answer and working

   Answer EE

   I gives x = −3 or 5. II gives y = 0 or 8. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

10. 10

    Solve both equations and compare x and y.
    I. x² + 7x − 8 = 0
    II. y² + 3y = 0

    Question 10

    Ax > y Bx ≥ y Cx < y Dx ≤ y Ex = y or no relation can be established

    Answer and working

    Answer EE

    I gives x = −8 or 1. II gives y = −3 or 0. Some x are bigger and some smaller than some y, so no single relation holds: x = y or no relation can be established.

More quantitative aptitude: Percentages, Profit, loss and discount, Simple interest, Compound interest, Ratio and proportion, Averages.