Aptitude Questions: Quadratic Equations Set 23

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1. (x – 2)(x + 1) = 0
   2y² – y + 1/8 = 0
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   E. X = Y or relation cannot be established
   Explanation:
   (x – 2) (x + 1) = 0
   x = -1, 2
   2y² – y + 1/8 = 0
   1/8(16y² – 8y + 1) = 0
   16y² – 8y + 1 = 0
   y = 0.25, 0.25
   
   
2. x² – 27x + 182 = 0
   y² + (y + 1)² = 365
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   C. X ≥ Y
   Explanation:
   x² – 27x + 182 = 0
   x = 13, 14
   y² + (y + 1)² = 365
   y² + y² + 1 + 2y = 365
   y² + y – 182 = 0
   y = -14, 13
   
   
3. x² + (x – 7)² = 13²
   y(2y + 3) = 90
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   E. X = Y or relation cannot be established
   Explanation:
   x² + (x – 7)² = 13²
   x² – 7x – 60 = 0
   x = 12, -5
   y(2y + 3) = 90
   2y² + 3y – 90 = 0
   y = – 7.5, 6
   
   
4. 1/(x – 3) + 1/(x + 5) = 1/3
   (y + 2)(27 – y) = 210
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   B. X < Y
   Explanation:
   1/(x – 3) + 1/(x + 5) = 1/3
   x² – 4x -21 = 0
   x = 7, -3
   (y + 2)(27 – y) = 210
   y² – 25x + 156 = 0  => y = 12, 13
   
   
5. √(x² + (x + 30)²)= x + 60
   (y + 5) (360/y – 1)= 0
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   E. X = Y or relation cannot be established
   Explanation:
   √(x² + (x + 30)²)= x + 60
   x² – 60x – 2700 = 0
   x = 90, – 30
   y² – 355y – 1800 = 0
   y = 360, -5
   
   
6. (3x – 2)/y = (3x + 6)/(y + 16)
   (x + 2)/(y + 4) = (x + 5)/(y + 10)
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   B. X < Y
   Explanation:
   (3x – 2)/y = (3x + 6)/(y + 16)
   y + 16(3x – 2) = y (3x + 16)
   48x – 8y = 32 —(a)
   (x + 2)/(y + 4) = (x + 5)/(y + 10)
   (x + 2)(y + 10) = (x + 5)(y + 4)
   2x = y —(b)
   From (a) and (b) x = 1, y = 2
   
   
7. 1/x  + 1/(x-10) = 8/75
   132/y – 132/(y + 11) = 1
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   E. X = Y or relation cannot be established
   Explanation:
   1/x  + 1/x-10 = 8/75
   8x² – 230x + 750 = 0
   x = 25, 3.75
   132/y – 132/(y + 11) = 1
   y² + 11y – 1452 = 0
   y = -44, 33
   
   
8. x² – 4x – 21 = 0
   y² – 35y + 306 = 0
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   B. X < Y
   Explanation:
   x² – 4x – 21 = 0
   x = 7, -3
   y² – 35y + 306 = 0
   y = 18, 17
   
   
9. (x – 2)(x + 1) = (x – 1)(x + 3)
   (y + 3)(y – 2) = (y + 1)(y + 2)
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   A. X > Y
   Explanation:
   (x – 2)(x + 1) = (x – 1)(x + 3)
   x = 1/3
   (y + 3)(y – 2) = (y +1)(y + 2)
   y = – 4
   
   
10. (x – 4)(x – 3) = (x – 6)(x – 5)
    (y – 9)(y – 3) = (y – 4)(y – 3)
    A. X > Y
    B. X < Y
    C. X ≥ Y
    D. X ≤ Y
    E. X = Y or relation cannot be established
    
    Answer & Explanation

    A. X > Y
    Explanation:
    (x – 4)(x – 3) = (x – 6)(x – 5)
    4x = 18
    x = 4.5
    (y – 9)(y – 3) = (y – 4)(y – 3)
    y = 3