Quantitative Aptitude: Quadratic Equations Questions Set 55

Directions(1-5): What will be the values of x and y and chose a correct option.

1. I.63x - 94√x +35=0
   II. 32y - 52√y + 21=0
   
   y>=x
   x>y
   x>=y
   y>x
   No Relation
   Option E
   I.63x - 94√x +35=0
   II. 32y - 52√y + 21=0
   √x = 7/9 , 5/7
   x = 49/ 81 , 25/ 49
   √y = 3 /4 , 7 /8
   y = 9 /16 , 49 /64
   No Relation
   
   
    



2. I. 2x² + 17x + 35 = 0
   II. 3y² + 17y + 24 = 0
   
   x>y
   y>=x
   x>=y
   No Relation
   y>x
   Option E
   I. 2x² + 17x + 35 = 0
   2x² + 10x+ 7x + 35 = 0
   2x (x+ 5) +7 (x+ 5) = 0
   (2x+ 7) (x+ 5) =0
   x = (-7)/2, -5
   II. 3y² + 17y + 24 = 0
   3y² + 9y + 8y + 24 = 0
   3y (y + 3) + 8 (y+ 3) = 0
   (y+ 3) (3y + 8) = 0
   y= -3, -8/3
   y > x
   
   
    



3. I.x² – 17x + 72 = 0
   II.y² – 27y + 180 = 0
   
   x>y
   No Relation
   x>=y
   y>x
   y>=x
   Option D
   I.x² – 17x + 72 = 0
   x² - 9x – 8x + 72 = 0
   x(x – 9) – 8 (x – 9) = 0
   (x – 8) (x – 9) = 0
   x = 8, 9
   II. y² – 27y + 180 = 0
   y² – 12y – 15y + 180 = 0
   y(y – 12) – 15 (y – 12) = 0
   (y – 15) (y – 12) = 0
   y = 15, 12
   y > x
   
   
    



4. I. 2x² – 5x + 3 = 0
   II. 3y² – 4y + 1 = 0
   
   y>=x
   x>y
   No Relation
   x>=y
   y>x
   Option D
   I.2x² – 5x + 3 = 0
   2x² – 2x – 3x + 3 = 0
   2x (x – 1) – 3(x – 1) = 0
   (x – 1) (2x – 3) = 0
   x = 1, 3 /2
   II. 3y² – 4y + 1 = 0
   3y² – 3y – y + 1 = 0
   3y(y – 1) –1 (y – 1) = 0
   (3y – 1) (y – 1) = 0
   𝑦 = 1/3 , 1
   x≥y
   
   
   
    



5. I. x² + 2x – 35 = 0
   II. y² + 15y + 56 = 0
   
   y>=x
   x>=y
   x>y
   y>x
   No Relation
   Option B
   I.x² + 2x – 35 = 0
   x² + 7x – 5x – 35 = 0
   x (x + 7) – 5 (x + 7) = 0
   (x – 5) (x + 7) = 0
   x = 5, –7
   II. y² + 15y + 56 = 0
   y² + 7y + 8y + 56 = 0
   y (y + 7) + 6 (y + 7) = 0
   (y + 8) (y + 7) = 0
   y = – 8, – 7
   x ≥ y
   
   
    



6. I. 2x² + 7x + 5 = 0
   II.3y² + 12y + 9 = 0
   
   y>=x
   x>y
   y>x
   x>=y
   No Relation
   Option E
   I.2x² + 7x + 5 = 0
   2x² + 2x + 5x + 5 = 0
   2x (x + 1) + 5 (x + 1) = 0
   (2x + 5) (x + 1) = 0
   𝑥 = – 5/2 , – 1
   II.3y² + 12y + 9 = 0
   3y² + 9y + 3y + 9 = 0
   3y (y + 3) +3 (y + 3) = 0
   (3y + 3) (y + 3) = 0
   y = –1, – 3
   No relation
   
   
    



7. I. (x – 12)² = 0
   II.y² – 21y + 108 = 0
   
   x>y
   y>=x
   x>=y
   No Relation
   y>x
   Option C
   I.(x – 12)² = 0
   x – 12 = 0
   x = 12
   II. y² – 21y + 108 = 0
   y² – 12y – 9y + 108 = 0
   y (y – 12) – 9 (y – 12) = 0
   (y – 9) (y – 12) = 0
   y = 9, 12
   x ≥ y
   
   
    



8. I. x² + 72 = 108
   II. y³ + 581 = 365
   
   x>=y
   y>=x
   x>y
   y>x
   No Relation
   Option A
   I. x² + 72 = 108
   x² =108 – 72 = 36
   x = ±6
   II. y³ + 581 = 365
   y³ = –216
   y = –6
   x ≥ y
   
   
    



9. I. 8x² + 26x + 15 = 0
   II. 4y² + 24y + 35 = 0
   
   y>=x
   y>x
   x>y
   x>=y
   No Relation
   Option D
   I. 8x² + 26x + 15 = 0
   8x^2 + 20x +6x + 15 = 0
   4(2x+5)+3(2x+5) = 0
   x = -5/2,-3/4
   II. 4y² + 24y + 35 = 0
   4y^2 + 10y + 14 y + 35 = 0
   y = -5/2,-7/2
   x >= y
   
    



10. I. 15x^2 - 46x+35
    II. 4y^2 - 15y+14=0
    
    x>y
    y>=x
    x>=y
    y>x
    No Relation
    Option D
    x = 7/5, 5/3
    Y = 2, 7/4
    x < y