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