# Quantitative Aptitude: Quadratic Equations Questions Set 62

1. I. 10x2+9x+2=0
II. 6y2– 27y-15=0
x > y
x ≥ y
x < y
x ≤ y
x = y or 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 y≥x

2. I. 35x2+27x+4=0
II. 9y2– 3y-2=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option E
35x2+27x+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– 3y-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 the relation cannot be determined

3. I. 35x2-4x-15=0
II. 10y2+129y-13=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option A
35x2-4x-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+129y-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. I. 10x2 +79x+63=0
II. 20y2+3y-2=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option C
10x2+79x+63=0
10x2 +70x+9x+63=0
10x(x +7) + 9(x +7)=0
(x+7) ( 10x+9)=0
x= -7 , -9/10
20y2+3y-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. I. 2x2-31x= -120
II. 8y2-74y=-143
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option A
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. I. 8x2+41x+5=0
II. 49y2-49y-18=0
x > y
x ≥ y
x < y
x ≤ y
x = y or 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 y>x ( 9/7> -1/8) and( -2/7 > -5)

7. I. 40x2-59x+21=0
II. 14y2+45y-14=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option A
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+45y-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. I. 40x2-13x+1=0
II. 10y2-11y-6=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option E
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
10y2-11y-6=0
10y2 -15y+4y -6=0
5y( 2y-3) +2(2y-3)=0
(2y-3) ( 5y+2)=0
y= 3/2, -2/5
Hence the relation cannot be determined

9. I. 10x2-9x+2=0
II. 6y2+ 27y-15=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option B
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. I. 35x2+51x+18=0
II. 9y2 =1
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option C
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
9y2 =1
9y2-1=0
(3y-1) ( 3y+1)=0
y= 1/3,- 1/3
Hence y>x

11. I. 35x2+16x-3=0
II. 10y2+136y-56=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option E
35x2+16x-3=0
35x2 -5x+ 21x-3=0
5x(7x -1) + 3(7x -1)=0
(7x-1) ( 5x+3)=0
x= 1/7 , -3/5
10y2+136y-56=0
10y2 -4y+ 140y -56=0
y( 10y-4) + 14(10y-4)=0
(10y-4) ( y+14)=0
y= 4/10,- 14
Hence the relation cannot be determined

12. I. 10x2-136x-14=0
II. 25y2-10y-8=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option A
10x2-136x-14=0
10x2 -140x+x-14=0
10x(x -14) + 1(x -14)=0
(x-14) ( 10x+1)=0
x= +14 , -1/10
25y2-10y-8=0
25y2 -20y+ 10y -8=0
5y( 5y-4) + 2(5y-4)=0
(5y-4) ( 5y+2)=0
y= 5/4, -2/5
Hence x>y

13. I. 11x2+120x= 11
II. 8y2+74y+143=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option E
11x2+120x= 11
11x2 +121x-x-11=0
11x(x +11) -1(x +11)=0
(x+11) ( 11x-1)=0
x=- 11 , 1/11
8y2+74y+143=0
8y2 +22y+52y+143 =
2y( 4y+11) +13(4y+11)=0
(4y+11) ( 2y+13)=0
y= -11/4, -13/2
Hence the relation cannot be determined

14. I. 8x2+51x +18=0
II. 49y2-1=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option C
8x2+51x+18=0
8x2 +48x+3x+18=0
8x(x +6) + 3(x +6)=0
(x+6) ( 8x+3)=0
x= -6 , -3/8
49y2-1=0
(7y-1) ( 7y+1)=0
y= 1/7, -1/7
Hence y>x

15. 40x2-13x+1=0
18y2+77y-18=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option B
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
18y2+77y-18=0
18y2 +81y- 4y -18=0
9y( 2y+9) – 2(2y+9)=0
(2y+9) ( 9y-2)=0
y= -9/2, 2/9
Hence x ≥ y

16. I. 16x2+60x+14=0
II. 8y2– 77y-30=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option C
16x2+60x+14=0
16x2 + 56x+ 4x+14=0
8x(2x +7) + 2(2x +7)=0
(2x+7) ( 8x+2)=0
x= -7/2 , -2/8
8y2– 77y-30=0
8y2 -80y+ 3y -30=0
8y( y-10) + 3(y-10)=0
(y-10) ( 8y+3)=0
y= 10, -3/8
Hence y>x

17. I. 35x2+32x+5=0
II. 9y2– 20y+24=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option C
35x2+32x+5=0
35x2 + 25x+ 7x+5=0
5x(7x +5) + 1(7x +5)=0
(7x+5) ( 5x+1)=0
x= -5/7 , -1/5
9y2– 36y+32=0
9y2 -12y-24y +32=0
3y( 3y-4) -8(3y-4)=0
(3y-4) ( 3y-8)=0
y= 4/3, 8/3
Hence y>x

18. I. 35x2-18x-81=0
II. 10y2+184y-114=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option A
35x2-18x-81=0
35x2 – 45x+ 63x-81=0
5x(7x -9) + 9(7x -9)=0
(7x-9) ( 5x+9)=0
x= 9/7 , -9/5
10y2+184y-114=0
10y2 -6y+ 190y -114=0
y( 10y-6) + 19(10y-6)=0
(10y-6) ( y+19)=0
y= 6/10,- 19
Hence x>y

19. I. 10x2+79x+63=0
II.2+10y-2=0
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option C
10x2+79x+63=0
10x2 +70x+9x+63=0
10x(x +7) + 9(x +7)=0
(x+7) ( 10x+9)=0
x= -7 , -9/10
48y2+10y-2=0
48y2 -6y+ 16y -2=0
6y( 8y-1) + 2(8y-1)=0
(8y-1) ( 6y+2)=0
y= 1/8, -2/6
Hence y>x

20. I. 2x2-18x= -17
II. 2-97y=-117
x > y
x ≥ y
x < y
x ≤ y
x = y or Cannot be determined.
Option E
2x2-35x= -17
2x2 -34x-1x+17=0
2x(x -17) -1(x -17)=0
(x-17) ( 2x-1)=0
x= 17 , 1/2
20y2-97y=-117
20y2 -45y-52y+117 =
5y( 4y-9) -13(4y-9)=0
(4y-9) ( 5y-13)=0
y= 9/4, 13/5
Hence the relation cannot be determined

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