# Aptitude Questions: Quadratic Equations Set 23

Hello Aspirants. Welcome to Online Quantitative Aptitude Section in AffairsCloud.com. Here we are creating sample questions in Quadratic Equations which is common for all the competitive exams. We have included Some questions that are repeatedly asked in bank exams !!!

Follow the link To solve Quadratic Equations with the help of Number Line

1. (x – 2)(x + 1) = 0
2y² – y + 1/8 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
E. X = Y or relation cannot be established
Explanation:

(x – 2) (x + 1) = 0
x = -1, 2
2y² – y + 1/8 = 0
1/8(16y² – 8y + 1) = 0
16y² – 8y + 1 = 0
y = 0.25, 0.25

2. x2 – 27x + 182 = 0
y2 + (y + 1)2 = 365
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
C. X ≥ Y
Explanation:

x2 – 27x + 182 = 0
x = 13, 14
y2 + (y + 1)2 = 365
y2 + y² + 1 + 2y = 365
y2 + y – 182 = 0
y = -14, 13

3. x2 + (x – 7)² = 13²
y(2y + 3) = 90
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
E. X = Y or relation cannot be established
Explanation:

x2 + (x – 7)² = 13²
x2 – 7x – 60 = 0
x = 12, -5
y(2y + 3) = 90
2y² + 3y – 90 = 0
y = – 7.5, 6

4. 1/(x – 3) + 1/(x + 5) = 1/3
(y + 2)(27 – y) = 210
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
B. X < Y
Explanation:

1/(x – 3) + 1/(x + 5) = 1/3
x2 – 4x -21 = 0
x = 7, -3
(y + 2)(27 – y) = 210
– 25x + 156 = 0  => y = 12, 13

5. √(x² + (x + 30)²)= x + 60
(y + 5) (360/y – 1)= 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
E. X = Y or relation cannot be established
Explanation:

√(x² + (x + 30)²)= x + 60
x² – 60x – 2700 = 0
x = 90, – 30
y2 – 355y – 1800 = 0
y = 360, -5

6. (3x – 2)/y = (3x + 6)/(y + 16)
(x + 2)/(y + 4) = (x + 5)/(y + 10)
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
B. X < Y
Explanation:

(3x – 2)/y = (3x + 6)/(y + 16)
y + 16(3x – 2) = y (3x + 16)
48x – 8y = 32 —(a)
(x + 2)/(y + 4) = (x + 5)/(y + 10)
(x + 2)(y + 10) = (x + 5)(y + 4)
2x = y —(b)
From (a) and (b) x = 1, y = 2

7. 1/x  + 1/(x-10) = 8/75
132/y – 132/(y + 11) = 1
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
E. X = Y or relation cannot be established
Explanation:

1/x  + 1/x-10 = 8/75
8x² – 230x + 750 = 0
x = 25, 3.75
132/y – 132/(y + 11) = 1
y² + 11y – 1452 = 0
y = -44, 33

8. x² – 4x – 21 = 0
y² – 35y + 306 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
B. X < Y
Explanation:

x² – 4x – 21 = 0
x = 7, -3
y² – 35y + 306 = 0
y = 18, 17

9. (x – 2)(x + 1) = (x – 1)(x + 3)
(y + 3)(y – 2) = (y + 1)(y + 2)
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
A. X > Y
Explanation:

(x – 2)(x + 1) = (x – 1)(x + 3)
x = 1/3
(y + 3)(y – 2) = (y +1)(y + 2)
y = – 4

10. (x – 4)(x – 3) = (x – 6)(x – 5)
(y – 9)(y – 3) = (y – 4)(y – 3)
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
A. X > Y
Explanation:

(x – 4)(x – 3) = (x – 6)(x – 5)
4x = 18
x = 4.5
(y – 9)(y – 3) = (y – 4)(y – 3)
y = 3

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