# Aptitude Questions: Quadratic Equations Set 19

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

Bank PO Level Questions :-

1. x2 – 1 = 0, y2 + 4y + 3 = 0
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 = 1
x = ± 1
y2 + 4y + 3 = 0
y2 + y + 3y + 3 = 0
y = -1, -3
Put on number line
-3 -1 -1 1

2. x2 – 10x + 24 = 0, y2 – 14y + 48 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
D. X ≤ Y
Explanation:

x2 – 10x + 24 = 0
x2 – 6x – 4x + 24 = 0
x = 4, 6
y2 – 14y + 48 = 0
y2 – 6y – 8y + 48 = 0
y = 6, 8
Put on number line
4 6 6 8

3. 2x2 – 13x + 20 = 0, 2y2 – 7y + 6 = 0
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
A. X > Y
Explanation:

2x2 – 13x + 20 = 0
2x2 – 8x – 5x + 20 = 0
x = 2.5, 4
2y2 – 7y + 6 = 0
2y2 – 3y – 4y + 6 = 0
y = 1.5, 2
Put on number line
1.5 2 2.5 4

4. (15/√x) + (9/√x) = 11√x, (√y/4) + (5√y/12)= (1/√y)
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
A. X > Y
Explanation:

(15/√x) + (9/√x) = 11√x
24/√x = 11√x
x = 24/11 = 2.18
(√y/4) + (5√y/12)= (1/√y)
(8√y/12) = (1/√y)
y = 1.5

5. x4 – 227 = 398, y2 + 321 = 346
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:

x4 – 227 = 398
x4 = 625
Take square root on both sides
x2 = 25
x = 5, -5
y2 + 321 = 346
y2 = 25
y2 = 25
y = ±5

6. x2 + x – 20 = 0, y2 + y – 30 = 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 – 20 = 0
x2 + 5x – 4x + 20 = 0
x = -5, 4
y2 + y – 30 = 0
y2 +6y -5y – 30 = 0
y = -6, 5
Put on number line
-6 -5 4 5

7. x2 – 365 = 364, y – √324 = √81
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
D. X ≤ Y
Explanation:

x2 – 365 = 364
x2 = 729
x = ± 27
y – √324 = √81
y – 18 = 9
y = 27
Put on number line
-27 27 27

8. 9x – 15.45 = 54.55 + 4x, √(y+155) – 6 = 7
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:

9x – 15.45 = 54.55 + 4x
9x – 4x = 54.55 + 15.45
5x = 70 => x= 14
√(y+155) – 6 = 7
√(y+155) = 13
Squaring on both sides
y + 155 = 169
y = 14

9. x2 + 11x + 30 = 0, y2 + 7y + 12 = 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 + 11x + 30 = 0
x2 + 6x + 5x + 30 = 0
x = -6, -5
y2 + 7y + 12 = 0
y2 + 4y + 3y + 12 = 0
y = -4, -3
Put on number line
-6 -5 -4 -3

10. y2 – x2 = 32, y – x = 2
A. X > Y
B. X < Y
C. X ≥ Y
D. X ≤ Y
E. X = Y or relation cannot be established
B. X < Y
Explanation:

y2 – x2 = 32
(y + x)(y – x) = 32
From equation(2) y – x = 2
(y + x)2 = 32
y + x = 16 –(a)
y – x = 2 —(b)
2y = 18 => y = 9
9 – x = 2
x = 7

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