# 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