# Quantitative Aptitude: Quadratic Equations Questions Set 65

1. I) m2 – 3m – 28 = 0
II) n2 – n – 72 = 0
m
m<=n
m>n
m>=n
Can’t be determined
Option E
I) m2 – 3m – 28 = 0
(m + 4) (m – 7) = 0
M = -4, 7
II) n2 – n – 72 = 0
(n + 8) (n – 9) = 0
N = -8, 9
Can’t be determined

2. I) 3m2 + 19m + 28 = 0
II) 2n2 + 13n + 21 = 0
m
m<=n
m>n
m>=n
Can’t be determined
Option E
I) 3m2 + 19m + 28 = 0
3m2 + 12m + 7m + 28 = 0
3m (m + 4) + 7 (m + 4) = 0
(3m + 7) (m + 4) = 0
m = -7/3, -4 = -2.33, – 4
II) 2n2 + 13n + 21 = 0
2n2 + 6n + 7n + 21 = 0
2n (n + 3) + 7 (n + 3) = 0
(2n + 7) (n + 3) = 0
n = -7/2, -3 = -3.5, -3
I) 3m2 + 19m + 28 = 0
3m2 + 12m + 7m + 28 = 0
3m (m + 4) + 7 (m + 4) = 0
(3m + 7) (m + 4) = 0
m = -7/3, -4 = -2.33, – 4
II) 2n2 + 13n + 21 = 0
2n2 + 6n + 7n + 21 = 0
2n (n + 3) + 7 (n + 3) = 0
(2n + 7) (n + 3) = 0
n = -7/2, -3 = -3.5, -3
Can’t be determined

3. I) 2m – 3n = -6
II) 3m + 4n = 25
m < n
m<=n
m>n
m>=n
can’t be determined
Option A
2m-3n = -6 –> (1)
3m + 4n = 25 –> (2)
Bn solving the equation (1) and (2),
m = 3, n = 4
m < n

4. I) 12m2– 37m + 21 = 0
II) 15n2 + 54n + 27 = 0
m < n
m<=n
m > n
m>=n
can’t be determined
Option C
I) 12m2 – 37m + 21 = 0
12m2 – 28m – 9m + 21 = 0
4m (3m – 7) – 3 (3m – 7) = 0
(4m – 3) (3m – 7) = 0
m = ¾, 7/3 = 0.75, 2.33
II) 15n2 + 54n + 27 = 0
15n2 + 45n+ 9n + 27 = 0
15n (n + 3) + 9 (n + 3) = 0
(15n + 9) (n + 3) = 0
n = -9/15, -3 = -3/5, -3

5. I) m2 + 3√7 m – 70 = 0
II) n2 + 2√3 n – 105 = 0
m < n
m<=n
m>n
m>=n
Can’t be determined
Option E
I) m2 + 3√7 m – 70 = 0
m2 + 5√7 m – 2√7 m – 70 = 0
(m + 5√7) (m – 2√7) = 0
m = 2√7, – 5√7
II) n2 + 2√3 n – 105 = 0
n2 + 7√3 n – 5√3 n – 105 = 0
(n + 7√3) (n – 5√3) = 0
n = 5√3, – 7√3
Can’t be determined

6. I) 14x² – 5√15 x – 90 = 0

II) 6y² + √21 y – 21 = 0

x < y
x<=y
x>y
x>=y
relationship between x and y cannot be determined
Option E
I) 14x²-5√15 x-90=0

14x²-12√15 x+7√15 x – 90 = 0

2x(7x – 6√15)+ √15(7x – 6√15) = 0

(2x + √15)(7x – 6√15) = 0

x = -√15/2, (6√15)/7

II) 6y²+√21 y-21=0

6y²+3√21 y-2√21 y -21=0

3y(2y+√21)- √21(2y+√21)=0

(3y- √21)(2y+√21)=0

y =√21/3 ,-√21/2

Hence, relationship between x and y cannot be determined

7. I) 3×2– 13√2x + 24 = 0

II) y2– 4√2y + 6 = 0

x < y
x<=y
x>y
x>=y
relationship between x and y cannot be determined
Option E
I) 3×2– 13√2x + 24 = 0

3x2 – 9√2x – 4√2x + 24 = 0

3x(x – 3√2) – 4√2 (x – 3√2) = 0

(3x – 4√2)(x – 3√2) = 0

x = 4√2/3, 3√2

II)y2– 4√2y + 6 = 0

y2 – √2y – 3√2y + 6 = 0

y(y – √2) – 3√2 (y – √2) = 0

(y – √2) (y – 3√2) = 0

y = √2, 3√2

Hence, relationship between x and y cannot be determined

8. I) 3×2– (6 + √5)x + 2√5 = 0

II) 8y2– (16 + 3√5)y + 6√5 = 0

x < y
x<=y
x>y
x>=y
relationship between x and y cannot be determined
Option E
I) 3×2– (6 + √5)x + 2√5 = 0

3x2 – 6x – √5x + 2√5 = 0

3x (x – 2) – √5 (x – 2) = 0

(3x – √5) (x – 2) = 0

x = √5/3,2

II) 8y2– (16 + 3√5)y + 6√5 = 0

8y2 – 16y – 3√5y + 6√5 = 0

8y (y – 2) – 3√5 (y – 2) = 0

(8y – 3√5) (y – 2) = 0

y = (3√5)/8, 2

Hence, relationship between x and y cannot be determined

9. I) 18x² – 63x + 40 = 0

II) 12y² + 47y + 45 = 0

x < y
x<=y
x>y
x>=y
relationship between x and y cannot be determined
Option C
I) 18x² – 63x + 40 = 0

18x²-15x-48x+40=0

3x(6x-5)-8(6x-5)=0

(3x-8)(6x-5)=0

x=8/3,5/6

II) 12y²+47y+45=0

12y²+27y+20y+45=0

3y(4y+9)+5(4y+9)=0

(3y+5)(4y+9)=0

Y =-5/3,-9/4

Hence, x > y

10. I) 20x²-119x+176=0

II) 45y²+200y+155=0

x < y
x<=y
x>y
x>=y
relationship between x and y cannot be determined
Option C
I) 20x²-119x+176=0

20x²-64x-55x+176=0

4x(5x-16)-11(5x-16)=0

(4x-11)(5x-16)=0

x=11/4,16/5

II)

45y²+200y+155=0

45y²+45y+155y+155=0

45y(y+1)+155(y+1)=0

(45y+155)(y+1)=0

y=-155/45,-1

Hence, x > y