Aptitude Questions: Quadratic Equations Set 21

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Follow the link To solve Quadratic Equations with the help of Number Line

1. 5x + 2y = 31
   3x + 7y = 36
   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:
   5x + 2y = 31 —-(1)
   3x + 7y = 36 —-(2)
   By solving eqn(1) and (2)
   x = 5 ; y = 3
   
   
2. x² – x – √3x + √3= 0
   y² – 3y + 2 = 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 – √3x + √3= 0
   x (x-1) – √3(x -1) = 0
   (x-1) (x-√3) = 0
   x = 1, 1.732
   y² – 3y + 2 = 0
   y² – y – 2y + 2 = 0
   y = 1, 2
   Put on number line
   1, 1, 1.732, 2
   
   
3. [48 / x^4/7] – [12 / x^4/7] = x^10/7
   y³ + 783 = 999
   A. X > Y
   B. X < Y
   C. X ≥ Y
   D. X ≤ Y
   E. X = Y or relation cannot be established
   
   Answer & Explanation

   D. X ≤ Y
   Explanation:
   (48 – 12) / x^4/7 = x^10/7
   36 = x^{(10/7 + 4/7)}
   36 = x²
   x =  ± 6
   y³ + 783 = 999
   y³ = 999 – 783
   y³ = 216
   y = 6
   Put on number line
   -6, 6, 6
   
   
4. 17² + 144 ÷ 18 = x
   26² – 18 * 21 = y
   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:
   17² + 144 ÷ 18 = x
   x = 297
   26² – 18 * 21 = y
   y = 676 – 378 = 29
   
   
5. 5/7 – 5/21 = √x/42
   √y/4 + √y/16 = 250/√y
   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:
   5/7 – 5/21 = √x/42
   10/21 = √x/42
   √x = 20
   x = 400
   √y/4 + √y/16 = 250/√y
   5√y/16 = 250/√y
   y = 800
   
   
6. 9/√x + 19/√x = √x
   y5 – [(28)^11/2 /√y] = 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:
   9/√x + 19/√x = √x
   x = 28
   y5 – [(28)^11/2 /√y] = 0
   y^11/2 = (28)^11/2
   y = 28
   
   
7. 12/√x – 23/√x = 5√x
   √y/12 – 5√y/12 = 1/√y
   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:
   12/√x – 23/√x = 5√x
   -11 = 5x
   x = -2.2
   √y/12 – 5√y/12 = 1/√y
   √y[1/12 – 5/12]= 1/√y
   y = -3
   
   
8. 7x + 6y + 4z = 122
   4x + 5y + 3z = 88
   9x + 2y + z = 78
   A. X < Y = Z
   B. X ≤ Y < Z
   C. X < Y > Z
   D. X = Y > Z
   E. X = Y = Z or relation cannot be established
   
   Answer & Explanation

   A. X < Y = Z
   Explanation:
   7x + 6y + 4z = 122 —(1)
   4x + 5y + 3z = 88 —(2)
   9x + 2y + z = 78 —(3)
   From (1) and (2) => 5x – 2y =4 —(a)
   From (2) and (3) => 23x + y = 146 —(b)
   From (a) and (b) => x = 6, y = 8. Put values in eqn (3) => z = 8
   
   
9. (x+y)³ = 1331
   x – y + z = 0
   xy = 28
   A. X < Y = Z
   B. X ≤ Y < Z
   C. X < Y > Z
   D. X = Y > Z
   E. X = Y = Z or relation cannot be established
   
   Answer & Explanation

   E. X = Y or relation cannot be established
   Explanation:
   (x + y)³ = 1331
   x + y = 11 —(a)
   (x + y)2 = 121
   (a + b)2 – (a – b)2 = 4ab
   (x – y)2 + 4xy = 121
   x – y = 3 —(b)
   From eqn (a) and (b)
   x = 7; y = 4 Put values in eqn (2) => z = -3
   
   
   
10. 7x + 6y = 110
    4x + 3y = 59
    x + z = 15
    A. X < Y = Z
    B. X ≤ Y < Z
    C. X < Y > Z
    D. X = Y > Z
    E. X = Y = Z or relation cannot be established
    
    Answer & Explanation

    C. X < Y > Z
    Explanation:
    7x + 6y = 110 —(1)
    4x + 3y = 59 —(2)
    x + z = 15 —(3)
    From eqn(1) and (2)
    x = 8; y = 9 Put values in eqn (3) => z = 7