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SBI PO Quadratic Equation Questions and Answers set – 5

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    1 . Directions (Q. 1-10): In each of these questions, two equations (I) and (II) are given. You have to solve both the equations and give answer
    (1) if x > y
    (2) if x $\geq$y
    (3) if x < y
    (4) if x $\leq$y
    (5) if x = y or relationship between x and y cannot be established
    $Q.$
    I. $7x^ 2 $ - 9x + 2 = 0
    II. $y^ 2 $ - 4y + 3 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    2 . I.$ x^ 2$ = 64
    II. $2y^ 2$ + 25y + 72 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x \leq y$
    D.   x = y or no relation can be established between ‘x’ and ‘y’.
    3 . I. $x^ 2$ + x - 20 = 0
    II. $2y^ 2 $ - 19y + 45 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    4 . I. 7x + 3y = 26
    II. 2x + 17y = -41

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    5 . I. $3x^ 2 $ - 20x + 33 = 0
    II. $2y^ 2 $ - 11y + 15 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    6 . I. $4x^ 2 $ - 43x + 105 = 0
    II. $7y^ 2 $ - 29y + 30 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    7 . I. $x^ 2$ + 13x + 40 = 0
    II. $y^ 2$ + 7y + 10 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    8 . I . x = $\sqrt[3]{2197}$
    II. $2y^ 2 $ - 54y + 364 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    9 . I.$5x^ 2 $ - 27x + 36 = 0
    II. $y^ 2 $ - 2y + 2 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
    10 . I. 13x - 8y + 81 = 0
    II. 15x + 5y + 65 = 0

    A.   $ x > y$
    B.   $ x \geq y $
    C.   $ x < y$
    D.   $ x \leq y$
      Answers & Solutions
       
      1 .    
      Answer : Option D
      Explanation :
      I. $7x^ 2$ - 7x - 2x + 2 = 0
      or, 7x(x - 1) - 2(x - 1) = 0
      (7x - 2) (x - 1) = 0
      or, x = $2\over 7$ , 1

      II. $y^ 2$ - y - 3y + 3 = 0
      or, y(y - 1) - 3(y - 1) = 0
      or, (y - 3) (y - 1) = 0
      y = 1, 3

      $x \leq y$
      2 .    
      Answer : Option D
      Explanation :
      I. $x^ 2$ = 64
      x = ±8

      II. $2y^ 2$ + 9y + 16y + 72 = 0
      or, y(2y + 9) + 8(2y + 9) = 0
      or, (y + 8) (2y + 9) = 0
      y = -8 , - $9\over 2$

      ie,. no relation between x and y
      3 .    
      Answer : Option C
      Explanation :
      I. $ x^ 2$ + x - 20 = 0
      or, $x^ 2$ + 5x - 4x - 20 = 0
      or, x(x + 5) - 4(x + 5) = 0
      or, (x - 4) (x + 5) = 0
      x = 4, - 5

      II. $2y^ 2$ - 10y - 9y + 45 = 0
      or, 2y(y - 5) - 9(y - 5) = 0
      or, (y - 5) (2y - 9) = 0
      y = 5 , $9\over 2$

      X < y
      4 .    
      Answer : Option A
      Explanation :
      Eqn (I) × 2
      Eqn (II) × 7
      14x + 6y = 52
      14x + 119y = - 287
      -----------------------
      - 113y = 339
      y = - 3 and x = 5,

      ie x > y
      5 .    
      Answer : Option B
      Explanation :
      I. $ 3x^ 2$ - 9x - 11x + 33 = 0
      or, 3x(x - 3) - 11(x - 3) = 0
      or, (3x - 11) (x - 3) = 0
      x = 3 , $11\over 3$
      II. $2y^ 2$ - 6y - 5y + 15 = 0
      or, 2y(y - 3) - 5(y - 3) = 0
      or, (y - 3) (2y - 5) = 0
      y = 3 , $5\over 2$

      x$\geq y$
      6 .    
      Answer : Option A
      Explanation :
      I. $ 4x^ 2$ - 28x - 15x + 105 = 0
      or, 4x(x - 7) - 15(x - 7) = 0
      or, (x - 7) (4x - 15) = 0
      x = 7, $15\over 4$

      II. $7y^ 2$ - 14y - 15y + 30 = 0
      or, 7y(y - 2) - 15(y - 2) = 0
      or, (y - 2)(7y - 15) = 0
      y = 2 , $15\over 7$

      x > y
      7 .    
      Answer : Option D
      Explanation :
      I. $x^ 2$ + 8x + 5x + 40 = 0
      or, x(x + 8) + 5(x + 8) = 0
      or, (x + 5) (x + 8) = 0
      x = - 5, - 8

      II. $y^ 2$ + 2y + 5y + 10 = 0
      or, y(y + 2) + 5(y + 2) = 0
      or, (y + 2)(y + 5) = 0
      y = - 2, - 5

      $x \leq y$
      8 .    
      Answer : Option D
      Explanation :
      I . x = $\sqrt[3]{2197}$
      x = 13
      II. $2y^ 2$ - 28y - 26y + 364 = 0
      or, 2y(y - 14) - 26(y - 14) = 0
      or, (2y - 26) (y - 14) = 0
      y = 14, 13

      $x \leq y$
      9 .    
      Answer : Option A
      Explanation :
      I.$ 5x^ 2$ - 15x - 12x + 36 = 0
      or, 5x(x - 3) - 12(x - 3) = 0
      or, (5x - 12) (x - 3) = 0
      x = $12\over 8$ , 3

      II. $y^ 2$ - y - 2y + 2 = 0
      or, y(y - 1) - 2(y - 1) = 0
      or, (y - 1)(y - 2) = 0
      y = 1, 2

      x > y
      10 .    
      Answer : Option C
      Explanation :
      eqn (I) × 5 + eqn (II) × 8

      65x - 40y + 405 = 0
      120x + 40y + 520 = 0
      ------------------------------ 185x + 0 + 925 = 0
      x = -$925\over 185$ = - 5
      y = $13x + 81\over 8$ = $-65 + 81\over 8$ = $16 \over 8$ = 2
      X < y

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