Quantitative Aptitude: Quadratic Equations Questions Set 60

Directions(1-10): Find the values of x and y, compare their values and choose a correct option.

1. (i) x² = 81
   (ii) y² – 18y + 81 = 0
   
   y > x
   y > x
   x >= y
   y >= x
   No relation exists
   Option D
   (i)x² = 81
   x = ± 9
   (ii)Y² – 18y + 81 = 0
   (y – 9)² = 0
   y = 9, 9
   x ≤ y
   
   
    



2. (i) 4x² – 24x + 32 = 0
   (ii) y² – 8y + 15 = 0
   
   y > x
   y >= x
   x >= y
   No relation exists
   y > x
   Option D
   (i)4x² – 24x + 30 = 0
   4x² – 16x – 8x + 32 = 0
   4x (x – 4) –8 (x–4) = 0
   x = 4, 2
   (ii) y² – 8y + 15 = 0
   y² – 5y – 3y + 15 = 0
   y(y – 5)–3 (y – 5) = 0
   y = 5, 3
   No relation exists
   
   
    



3. (i) x² – 21x + 108 = 0
   (ii) y² – 17y + 72 = 0
   
   y > x
   y > x
   x >= y
   No relation exists
   y >= x
   Option C
   (i)x² – 21x + 108 = 0
   x² – 9x – 12x + 108 = 0
   x(x – 9) – 12 (x – 9) = 0
   x = 9, 12
   (ii) y² – 17y + 72 = 0
   y² – 8y – 9y + 72 = 0
   y (y – 8) – 9 (y – 8) = 0
   y = 8,9
   x ≥ y
   
   
    



4. (i) x² – 11x + 30 = 0
   (ii) y² – 15y + 56 = 0
   
   y > x
   x >= y
   y > x
   y >= x
   No relation exists
   Option C
   (i)x² – 11x + 30 = 0
   x² – 6x – 5x + 30 = 0
   x(x – 6) – 5(x – 6) = 0
   x = 6, 5
   (ii)y² – 15y + 56 = 0
   y² – 7y – 8y + 56 = 0
   y (y – 7) – 8 (y – 7) = 0
   y = 7, 8
   x < y
   
   
    



5. (i) x^2 + 12x + 35 =0
   (ii) 5y^2 + 33y + 40 =0
   
   y >= x
   y > x
   x >= y
   y > x
   No relation exists
   Option A
   (i) 𝑥^2 + 12𝑥 + 35 = 0
   𝑥^2 + 7𝑥 + 5𝑥 + 35 = 0
   𝑥(𝑥 + 7) + 5(𝑥 + 7) = 0
   (𝑥 + 7)(𝑥 + 5) = 0
   𝑥 = −7 , −5
   (ii) 5𝑦 2 + 33y + 40 = 0
   5𝑦 2 + 25𝑦 + 8𝑦 + 40 = 0
   5𝑦(𝑦 + 5) + 8(𝑦 + 5) = 0
   (𝑦 + 5)(5𝑦 + 8) = 0
   𝑦 = − 8/5 , −5
   𝑦 ≥ x
   
   
    



6. (i) 4x^2 + 9x + 5 =0
   (ii) 3y^2 + 5y + 2 =0
   
   y > x
   y >= x
   No relation exists
   x >= y
   y > x
   Option B
   (i) 4𝑥^2 + 9𝑥 + 5 = 0
   4𝑥^2 + 4𝑥 + 5𝑥 + 5 = 0
   4𝑥(𝑥 + 1) + 5(𝑥 + 1) = 0
   (4𝑥 + 5)(𝑥 + 1) = 0
   𝑥 = −1 , − 5/4
   (ii) 3𝑦^2 + 5y + 2 = 0
   3𝑦^2 + 3y + 2y + 2 = 0
   3𝑦(𝑦 + 1) + 2(𝑦 + 1) = 0
   (3𝑦 + 2)(𝑦 + 1) = 0
   𝑦 = − 2/3 , −1
   𝑦 ≥ x
   
   
    



7. (i) x^2 − 11x + 24 = 0
   (ii) y^2 − 12y + 27 = 0
   
   y > x
   y > x
   x >= y
   y >= x
   No relation exists
   Option E
   (i) 𝑥^2 − 11𝑥 + 24 = 0
   𝑥^2 − 8𝑥 − 3𝑥 + 24 = 0
   𝑥(𝑥 − 8) − 3(𝑥 − 8) = 0
   (𝑥 − 3)(𝑥 − 8) = 0
   𝑥 = 3 , 8
   (ii) 𝑦^2 − 12y + 27 = 0
   𝑦^2 – 9𝑦 − 3𝑦 + 27 = 0
   𝑦(𝑦 − 9) − 3(𝑦 − 9) = 0
   (𝑦 − 9)(𝑦 − 3) = 0
   𝑦 = 9 , 3
   No relation exists
   
   
    



8. (i) 4𝑥^2 − 21𝑥 + 20 = 0
   (ii) 3y^2 − 19y + 30 = 0
   
   y > x
   y >= x
   y > x
   No relation exists
   x >= y
   Option D
   (i) 4𝑥^2 − 21𝑥 + 20 = 0
   4𝑥^2 − 16𝑥 − 5𝑥 + 20 = 0
   4𝑥(𝑥 − 4) − 5(𝑥 − 4) = 0
   (4𝑥 − 5)(𝑥 − 4) = 0
   𝑥 = 5/4 , 4
   (ii) 3𝑦^2 − 19𝑦 + 30 = 0
   3𝑦^2 – 9𝑦 − 10𝑦 + 30 = 0
   3𝑦(𝑦 − 3) − 10(𝑦 − 3) = 0
   (3𝑦 − 10)(𝑦 − 3) = 0
   𝑦 = 10/3 , 3
   No relation exists
   
   
    



9. (i) 𝑥^2 − 20𝑥 + 96 = 0
   (ii) 𝑦^2 = 64
   
   y > x
   No relation exists
   x >= y
   y >= x
   y > x
   Option C
   (i) 𝑥^2 − 20𝑥 + 96 = 0
   𝑥^2 − 12𝑥 − 8𝑥 + 96 = 0
   (𝑥 − 12) − 8(𝑥 − 12) = 0
   (𝑥 − 12)(𝑥 − 8) = 0
   𝑥 = 12,8
   (ii) 𝑦^2 = 64
   𝑦 = ±8
   𝑥 ≥ 𝑦
   
   
    



10. (i) x³ = 512
    (ii) y² = 64
    
    x >= y
    y >= x
    y > x
    No relation exists
    y > x
    Option A
    (i) x³ = 512
    x = 8
    (ii) y² = 64
    y = √64 = ± 8
    x ≥ y