Directions (Qs. 1 - 18): In this question two equations numbered I & II are given. You have to solve both the equations and mark the appropriate option:
1. I. x2 − 10x + 21 = 0 II. y2 − 16y + 63 = 0
A) x ≥ y B) Relationship between x and y cannot be established. C) x < y D) x ≤ y E) x > y
Explanation:
x2 − 10x + 21 = 0 y2 − 16y + 63 = 0
−7x −3 = + 21 −9x − 7 = +63
−7 − 3 = −10 −9 − 7 = −16
x = 7, 3 y = 9, 7
∴ x ≤ y
Ans: D
2. I. 6x2 + 17x + 12 = 0 II. 6y2 + 11y + 4 = 0
A) x > y
B) Relationship between x and y cannot be established. C) x ≥ y D) x ≤ y E) x < y
Explanation:
6x2 + 17x + 12 = 0 6y2 + 11y + 4 = 0
12 × 6 = 72 6 × 4 = 24
9 × 8 = 72 8 × 3 = 24
9 + 8 = 17 8 + 3 = 24
x ≤ y
Ans: D
3. I. 25x2 + 25x + 4 = 0 II. 5y2 + 11y + 6 = 0
A) x > y B) x < y C) x ≤ y D) x ≥ y E) Relationship between x and y cannot be established.
Explanation:
25x2 + 25x + 4 = 0 5y2 + 11y + 6 = 0
25 × 4 = 100 5 × 6 = 30
20 × 5 = 100 5 + 6 = 11
20 + 5 = 25
∴ x > y
Ans: A
4. I. 2x2 + 11x + 15 = 0 II. 5y2 + 22y + 24 = 0
A) Relationship between x and y cannot be established. B) x < y C) x ≥ y D) x ≤ y E) x > y
Explanation: 2x2 + 11x + 15 = 0 5y2 + 22y + 24 = 0
2 × 15 = 30 5 × 24 = 120
6 × 5 = 30 10 × 12 = 120
6 + 5 = 11 10 + 12 = 22
∴ x < y
Ans: B
5. I. 2x2 + x − 1 = 0 II. 2y2 + y − 6 = 0
A) x ≥ y B) x > y C) x ≤ y D) x < y E) Relationship cannot be decided.
Explanation:
2x2 + x − 1 = 0 2y2 + y − 6 = 0
2 × − 1 = −2 2 × − 6 = −12
2 − 1 = +1 4 × − 3 = −12
4 − 3 = +1
∴ x ≠ y
Relationship b/w x & y can not be estimated
Ans: E
6. I. 6x2 + 31x + 35 = 0 II. 6y2 + 31y + 40 = 0
A) x < y B) x ≥ y C) x ≤ y D) Relationship cannot be decided (or) x = y E) x > y
Explanation:
6x2 + 31x + 35 = 0 6y2 + 31y + 40 = 0
6 × 35 = 210 6 × 40 = 240
21 × 10 = 210 16 × 15 = 240
21 + 10 = 31 16 + 15 = 31
Relationship cannot be established b/w x & y
Ans: D
7. I. 4x2 + 21x + 27 = 0 II. 3y2 + 17y + 20 = 0
A) x ≤ y B) x ≥ y C) x < y D) x > y E) Relationship cannot be decided (or) x = y
Explanation:
4x2 + 21x + 27 = 0 3y2 + 17y + 20 = 0
4 × 27 = 108 3 × 20 = 60
12 × 9 = 108 12 × 5 = 60
12 + 9 = 21 12 + 5 = 17
Ans: E
8. I. 2x2 + 5x + 3 = 0 II. 4y2 + 14y + 12 = 0
A) Relationship cannot be decided (or) x = y B) x < y C) x ≤ y D) x ≥ y E) x > y
Explanation:
2x2 + 5x + 3 = 0 4y2 + 14y + 12 = 0
2 × 3 = 6 4 × 12 = 48
2 + 3 = 5 8 × 6 = 48
8 + 6 = 14
∴ x ≥ y
Ans: D
9. I. 3x2 − 9x + 6 = 0 II. 2y2 − 9y + 10 = 0
A) x > y B) Relationship can't be decided (or) x = y C) x ≥ y D) x ≤ y E) x < y
Explanation:
3x2 − 9x + 6 = 0 2y2 − 9y + 10 = 0
2 × + 10 = 20
−3 × −6 = +18 −4 × − 5 = 20
−3 − 6 = −9 −4 − 5 = −9
∴ x ≤ y
Ans: D
10. I. 2x2 + 29x + 99 = 0 II. 3y2 + 17y + 24 = 0
A) x ≥ y B) x > y C) Relationship cannot be decided (or) x = y D) x < y E) x ≤ y
Explanation:
2x2 + 29x + 99 = 0 3y2 + 17y + 24 = 0
2 × 99 = 198 3 × 24 = 72
18 × 11 = 198 9 × 8 = 72
18 + 11 = 29 9 + 8 = 17
∴ x < y
Ans: D
11. I. x2 − 18x + 81 = 0 II. y2 = 81
A) x ≥ y B) x > y C) x = y or relationship cannot be decided D) x < y E) x ≤ y
Explanation:
x2 − 18x + 81 = 0 y2 = 81
1 × 81 = 81 y = +9, −9
−9 × −9 = 81
−9 −9 = −18
x = 9, 9
∴ x ≥ y
Ans: A
12. I. 15x2 − 19x + 6 = 0 II. 21y2 − 46y + 24 = 0
A) x = y or relationship cannot be decided B) x < y C) x > y D) x ≥ y E) x ≤ y
Explanation:
15x2 − 19x + 6 = 0 21y2 − 46y + 24 = 0
15 × 6 = 90 21 × 24 = 50y
−10 × −9 = 90 −18 × −28 = 50y
−10 −9 = −19 −18 −28 = − 46
∴ x < y
Ans: B
13. I. 2x2 + 21x + 55 = 0 II. 2y2 + 13y + 15 = 0
A) x = y or relationship cannot be decided B) x ≥ y C) x > y D) x ≤ y E) x < y
Explanation:
2x2 + 21x + 55 = 0 2y2 + 13y + 15 = 0
2 × 55 = 110 2 × 15 = 30
10 × 11 + 110 10 × 3 = 30
10 + 11 = 21 10 + 3 = 13
∴ x ≤ y
Ans: D
14. I. 5x2 + 14x + 8 = 0 II. 3y2 + 16y + 21 = 0
A) x ≤ y B) x < y C) x ≥ y D) x > y E) x = y or relationship cannot be decided
Explanation:
5x2 + 14x + 8 = 0 3y2 + 16y + 21 = 0
5 × 8 = 40 3 × 21 = 63
10 × 4 = 40 9 × 7 = 63
10 + 4 = 14 9 + 7 = 63
∴ x > y
Ans: D
15. I. x2 + 19x + 60 = 0 II. 5y2 + 10y + 5 = 0
A) x > y B) x ≥ y C) x < y D) x ≤ y E) x = y or relation cannot be established
Explanation:
x2 + 19x + 60 = 0 5y2 + 10y + 5 = 0
1 × 60 = 60 5 × 5 = 25
15 × 4 = 60 5 + 5 = 10
15 + 4 = 19
x = − 15, − 4 
∴ x < y
Ans: C
16. I. 3p2 − 7p + 2 = 0 II. 2q2 − 11q + 15 = 0
A) p > q B) p < q C) p ≥ q D) p ≤ q E) p = q or relation cannot be established
Explanation:
3p2 − 7p + 2 = 0 2q2 − 11q + 15 = 0
3 × 2 = 6 2 × 15 = 30
−6 × −1 = 6 −6 × −5 = 30
−6 − 1 = − 7 −6 − 5 = −11
∴ x < y
Ans:B
17. I. x2 − 57x + 506 = 0 II. y2 − 20y + 99 = 0
A) x > y B) x ≥ y C) x < y D) x ≤ y E) x = y or relation cannot be established
Explanation:
x2 − 57x + 506 = 0 y2 − 20y + 99 =0
1 × 506 = 506 1 × 99 = 99
46 × 11 = 506 −9 × −11 = 99
− 46 −11 = −57 − 9 − 11 = −20
x = 46, 11 y = 9, 11
∴ x ≥ y
Ans: B
18. I. 5p2 − 18x + 9 = 0 II. 3q2 + 5q − 2 = 0
A) p > q B) p < q C) p ≥ q D) p ≤ q E) p = q or Can't be determined
Explanation:
5p2 − 18p + 9 = 0 3q2 + 5q − 2 = 0
5 × 9 = 45 3 × −2 = − 6
−15 × −3 = 45 6 × −1 = − 6
−15 − 3 = − 18 6 −1 = + 5
∴ p > q
Ans: A
