Quantitative Aptitude: Quadratic Equations Questions Set 51

Directions(1-10): Comparing the values of x and y and then choose a required option.

  1. I.x^2 + 40x + 399 = 0
    II.y^2 + 43y + 462 = 0

    x >= y
    No relation
    y >= x
    x >= y
    y > x
    Option D
    From I: x^2 + 40x + 399 = 0
    => x^2 + 21x + 19x + 399 = 0
    =>(x+21)(x+19) = 0
    => x = – 21, – 19
    From II: y^2 + 43y + 462 = 0
    =>y^2 + 22y + 21y + 462 = 0
    => (y+22)(y+21) = 0
    => y = – 22, – 21
    x >= y

     

  2. I.19x + 14y = 80
    II.12x – 7y = 3

    y > x
    x >= y
    x >= y
    No relation
    y >= x
    Option A
    On solving both the equations, we get the values
    x = 2
    y = 3
    y > x

     

  3. I.2x^2 – 12x + 16 = 0
    II.2y^2 = 5y + 12

    x >= y
    y > x
    y >= x
    No relation
    x >= y
    Option D
    From I: 2x^2 – 12x + 16 = 0
    => 2x^2 – 8x – 4x + 16 = 0
    => (2x-4)(x-4) = 0
    => x = 2,4
    From II: 2y^2 = 5y + 12
    => 2y^2 – 8y + 3y + 12 = 0
    => (2y+3)(y-4) = 0
    => y = 4,-3/2
    No relation

     

  4. I.x^2 + [12+5(5)^1/2]x + 60(5)^1/2 = 0
    II.y^2 + 9(5)^1/2y + 100 = 0

    y >= x
    x >= y
    y > x
    x >= y
    No relation
    Option A
    From I: x^2 + [12+5(5)^1/2]x + 60(5)^1/2 = 0
    => x^2 + 12x + 5(5)^1/2x + 60(5)^1/2 = 0
    => (x+12)[x+5(5)^1/2] = 0
    => x = -12, -5(5)^1/2
    From II: y^2 + 9(5)^1/2y + 100 = 0
    => y^2 + 5(5)^1/2y + 4(5)^1/2y + 100 = 0
    => [y+5(5)^1/2][y+4(5)^1/2] = 0
    => y = -5(5)^1/2, -4(5)^1/2
    y >= x

     

  5. I.2x^2 – 11x + 15 = 0
    II.4y^2 = 2y + 20

    y >= x
    x >= y
    x >= y
    No relation
    y > x
    Option C
    From I: 2x^2 – 11x + 15 = 0
    => 2x^2 – 6x – 5x + 15 = 0
    => (2x-3)(x-3) = 0
    => x = 3,5/2
    From II: 4y^2 = 2y + 20
    => 2y^2 – y – 10 = 0
    => (y+2)(2y – 5) = 0
    => y = -2,5/2
    x >= y

     

  6. I.x^2 + 33x + 272 = 0
    II.y^2 + y – 306 = 0

    No relation
    x >= y
    y > x
    x >= y
    y >= x
    Option A
    From I: x^2 + 33x + 272 = 0
    => x^2 + 17x + 16x + 272 = 0
    => (x+17)(x+16) = 0
    => x = -17,-16
    From II: y^2 + y – 306 = 0
    => y^2 + 18y – 17y -306 = 0
    => (y+18)(y-17) = 0
    => y = -18,17
    No relation

     

  7. I.12x + 7y = 133
    II.17x – 9y = 56

    y > x
    No relation
    x >= y
    x >= y
    y >= x
    Option B
    On solving both the equations, we get the same values of x and y.
    x = y = 7
    No relation

     

  8. I.x^2 + 15x + 56 = 0
    II.y^2 + 17y + 72 = 0

    y >= x
    y > x
    No relation
    x >= y
    x >= y
    Option D
    From I: x^2 + 15x + 56 = 0
    => x^2 + 8x + 7x + 56 = 0
    => (x+8)(x+7) = 0
    => x = -8,-7
    From II: y^2 + 17y + 72 = 0
    => y^2 + 9y + 8y + 72 = 0
    => (y+9)(y+8) = 0
    => y = -9,-8
    x >= y

     

  9. I.x^2 + 31x + 238 = 0
    II.y^2 + 35y + 306 = 0

    No relation
    x >= y
    y >= x
    x >= y
    y > x
    Option D
    From I: x^2 + 31x + 238 = 0
    => x^2 + 17x + 14x + 238 = 0
    => (x+14)(x+17) = 0
    => x = -14, -17
    From II: y^2 + 35y + 306 = 0
    =>y^2 + 17y + 18y + 306 = 0
    => (y+17)(y+18) = 0
    => y = -17, -18
    x >= y

     

  10. I.3x^2 – 14x + 16 = 0
    II.2y^2 = 5y + 18

    y >= x
    No relation
    y > x
    x >= y
    x >= y
    Option B
    From I: 3x^2 – 14x + 16 = 0
    =>3x^2 – 8x – 6x + 16 = 0
    => (3x-8)(x-2) = 0
    => x = 2,8/3
    From II: 2y^2 = 5y + 18
    => 2y^2 – 9y + 4y – 18 = 0
    => (y+2)(2y – 9) = 0
    => y = -2,9/2
    No relation

     


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