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

     


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