 # Quantitative Aptitude: Quadratic Equations Questions Set 66

1. 102-x-2=0
6y2+33y+15=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option E
10x2-x-2=0
10x2 – 5x+ 4x-2=0
5x(2x -1) + 2(2x -1)=0
(2x-1) ( 5x+2)=0
x= 1/2 , -2/5
6y2+33y+15=0
6y2 +30y+ 3y +15=0
6y( y+5) + 3(y+5)=0
(y+5) ( 6y+3)=0
y= -5, -3/6
Hence the relation cannot be determined

2. 35x2-13x-4=0
9y2 +9y-2=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option C
35x2-13x-4=0
35x2 – 20x+ 7x-4=0
5x(7x -4) + 1(7x -4)=0
(7x-4) ( 5x-1)=0
x= 4/7 , 1/5
9y2 +9y-2=0
9y2 +6y+ 3y -2=0
3y( 3y+2) + 1(3y+2)=0
(3y+2) ( 3y+1)=0
y= -2/3,- 1/3
Hence x>y

3. 35x2-46x+15=0
10y2+131y+13=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option C
35x2-46x+15=0
35x2 – 25x- 21x+15=0
5x(7x -5) – 3(7x -5)=0
(7x-5) ( 5x-3)=0
x= 5/7 , 3/5
10y2+131y+13=0
10y2 +y+ 130y +13=0
y( 10y+1) + 13(10y+1)=0
(10y+1) ( y+13)=0
y= -1/10,- 13
Hence x>y

4. 10x2+59x+45=0
20y2-13y+2=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option A
10x2+59x+45=0
10x2 +50x+9x+45=0
10x(x +5) + 9(x +5)=0
(x+5) ( 10x+9)=0
x= -5 , -9/10
20y2-13y+2=0
20y2 -5y- 8y +2=0
5y( 4y-1) – 2(4y-1)=0
(4y-1) ( 5y-2)=0
y= 1/4, 2/5
Hence y>x

5. 2x2-31x= -120
8y2-74y=-143
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option C
2x2-31x= -120
2x2 -16x-15x+120=0
2x(x -8) -15(x -8)=0
(x-8) ( 2x-15)=0
x= 8 , 15/2
8y2-74y=-143
8y2 -22y-52y+143 =
2y( 4y-11) -13(4y-11)=0
(4y-11) ( 2y-13)=0
y= 11/4, 13/2
Hence x>y

6. 8x2-41x-5=0
49y2-49y-18=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option C
8x2-41x-5=0
8x2 -40x-x-5=0
8x(x -5) – 1(x -5)=0
(x-5) ( 8x-1)=0
x= 5 , 1/8
49y2-49y-18=0
49y2 -63y+ 14y -18=0
7y( 7y-9) + 2(7y-9)=0
(7y-9) ( 7y+2)=0
y= 9/7, -2/7
Hence x>y

7. 40x2-59x+21=0
14y2+53y+14=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option C
40x2-59x+21=0
40x2 -24x-35x+21=0
8x(5x -3) -7(5x -3)=0
(5x-3) ( 8x-7)=0
x= 3/5 , 7/8
14y2+53y+14=0
14y2 +49y+4y +14=0
7y( 2y+7) + 2(2y+7)=0
(2y+7) ( 7y+2)=0
y= -7/2, -2/7
Hence x>y

8. 40x2-13x+1=0
10y2+19y+6=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option C
40x2-13x+1=0
40x2 -8x-5x+1=0
8x(5x -1) -1(5x -1)=0
(5x-1) ( 8x-1)=0
x= 1/5 , 1/8
10y2+19y+6=0
10y2 +15y+4y -6=0
5y( 2y+3) +2(2y+3)=0
(2y=3) ( 5y+2)=0
y= -3/2, -2/5
x>y

9. 10x2-9x+2=0
6y2+ 27y-15=0
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option D
10x2-9x+2=0
10x2 – 5x- 4x+2=0
5x(2x -1) – 2(2x -1)=0
(2x-1) ( 5x-2)=0
x= 1/2 , 2/5
6y2+ 27y-15=0
6y2 +30y-3y -15=0
6y( y+5) – 3(y+5)=0
(y+5) ( 6y-3)=0
y= -5, +3/6
Hence x≥y

10. 35x2+51x+18=0
16y2 =1
x<y
x<=y
x>y
x>=y
the relation cannot be determined
Option A
35x2+51x+18=0
35x2 + 30x+ 21x+18=0
5x(7x +6) + 3(7x +6)=0
(7x+6) ( 5x+3)=0
x= -6/7 , -3/5
16y2 =1
16y2-1=0
(4y-1) ( 4y+1)=0
y= 1/4,- 1/4
Hence y>x

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