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) 3x2– 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) 3x2– 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) 3x2– (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) 3x2– (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