Aptitude Questions: Quadratic Equations Set 27

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1. For which of the following equations the value of X is less than Y(X<Y)
   I.5x + 2y = 31; 3x + 7y = 36
   II.2x² -15x + 27 = 0; 5y² – 26y + 33 = 0
   III.25/√x + 9/√x = 17√x; √y/3 + 5√y/6 = 3/√y
   1.Only I
   2.Only II
   3.Only III
   4.Both II and III
   5.None
   
   Answer & Explanation

   Answer – 3.Only III
   Explanation :
   25/√x + 9/√x = 17√x
   34 = 17x
   x = 2
   21√y/18 = 3/√y
   y = 18/7 = 2.57
   
   
   
2. For which of the following equations the value of X is less than or equal to Y (X≤ Y)
   I.X²– 4X + 3= 0; Y² – 8Y + 15 = 0
   II. 3X² – 19X + 28= 0; 4Y² – 29Y + 45 = 0
   III.x² – (16)² = (23)² – 56; y^1/3 – 55 + 376 = (18)²
   1.Only I
   2.Only II
   3.Both I and III
   4.Both II and III
   5.All follow
   
   Answer & Explanation

   Answer – 3.Both I and III
   Explanation :
   From I, (x-3)(x-1) = 0 X=1,3
   (y-5)(y-3) = 0 Y = 5,3
   From III, x² – (16)² = (23)² – 56
   x² = 729
   x = ± 27
   y^1/3 – 55 + 376 = (18)²
   y = 3³ = 27
   
   
   
3. For which of the following equations the value of X is greater than or equal to Y (X ≥ Y)
   I.X² -3X – 4 = 0; 3Y² – 10Y+8 = 0
   II.√(x + 6) = √121 – √36; y² + 112 = 473
   III.5x²– 7x – 6 = 0; 5y² + 23y + 12 = 0
   1.Only I
   2.Only II
   3.Both I and III
   4.Both II and III
   5.None follow
   
   Answer & Explanation

   Answer – 4.Both II and III
   Explanation :
   From II, √(x + 6) = √121 – √36
   x + 6 = 25; x = 19
   y² + 112 = 473
   y² = 361; y = ± 19
   From III, 5x² – 7x – 6 = 0; x = -3/5, 2
   5y² + 23y + 12 = 0; y = -4, -3/5
   
   
   
4. For which of the following equations the value of X is greater than Y(X>Y)
   I.3X²+23X + 44 = 0; 3Y² + 20Y +33 = 0
   II.3X²+29 X +56 = 0; 2Y² + 15Y + 25 = 0
   III.3X²– 16X + 21 = 0; 3Y² – 28Y + 65 = 0
   1.Only I
   2.Only II
   3.Both I and III
   4.Both II and III
   5.None follow
   
   Answer & Explanation

   Answer – 5.None follow
   Explanation :
   From I, X = -4, -11/3; Y = -3, -11/3
   From II, X=-7, -8/3; Y = -5, -5/2
   From III,X= 3,7/3; Y = 5,13/3
   
   
   
5. For which of the following equations the value of X=Y or relationship cannot be established.
   I.1/x + 1/(x-10) = 8/75; 132/y – 132/(y + 11) = 1
   II.(3x – 2)/y = (3x + 6)/(y + 16); (x + 2)/(y + 4) = (x + 5)/(y + 10)
   III. x² – 4x – 21 = 0; y² – 35y + 306 = 0
   1.Only I
   2.Only II
   3.Both I and III
   4.Both II and III
   5.All follow
   
   Answer & Explanation

   Answer – 1.Only I
   Explanation :
   From I, x = 25, 3.75; y = -44, 33
   
   
   
6. For which of the following equations the value of Y is greater than X(Y>X)
   I.7x + 6y + 4z = 122; 4x + 5y + 3z = 88; 9x + 2y + z = 78
   II.7x + 6y = 110; 4x + 3y = 59
   III.2x + 5y = 23.5, 5x+ 2y = 22
   1.Only I
   2.Only II
   3.Both I and II
   4.Both II and III
   5.All follow
   
   Answer & Explanation

   Answer – 5.All follow
   Explanation :
   From I, x = 6, y = 8
   From II, x = 8; y = 9
   From III, x = 3, y = 3.5
   
   
   
7. For which of the following equations the value of X is less than or equal to Y (X≤ Y)
   I.[48 / x^4/7] – [12 / x^4/7] = x^10/7; y³ + 783 = 999
   II.9/√x + 19/√x = √x; y⁵ – [(28)11/2 /√y] = 0
   III.6X² – 7X + 2 = 0; 12Y² – 7Y+1 = 0
   1.Only I
   2.Only II
   3.Both I and II
   4.Both I and III
   5.All follow
   
   Answer & Explanation

   Answer – 1.Only I
   Explanation :
   From I, x = ± 6; y = 6
   
   
   
8. For which of the following equations the value of X is greater than or equal to Y (X ≥ Y)
   I.3X² +17X + 10=0; 10Y² + 9Y+2 = 0
   II.X² +X – 56 = 0; Y² – 17Y+72 = 0
   III.X²– 12X + 35= 0; Y² + Y – 30 = 0
   1.Only I
   2.Only II
   3.Both I and II
   4.Both I and III
   5.None of these
   
   Answer & Explanation

   Answer – 5.None of these
   Explanation :
   Only III follows, From III, X = 7,5; Y = 5, -6
   
   
   
9. For which of the following equations the value of X is greater than Y(X>Y)
   I.2X² + 15X + 25= 0; 3Y² + 29Y + 56 = 0
   II.3X² – 19X + 28= 0; 4Y² – 29Y + 45 = 0
   III.X² – 13X + 42= 0; Y² – 9Y + 20 = 0
   1.Only I
   2.Only II
   3.Only III
   4.Both II and III
   5.None of these
   
   Answer & Explanation

   Answer – 3.Only III
   Explanation :
   From III, X=7,6; Y =5,4
   
   
   
10. For which of the following equations the value of X=Y or relationship cannot be established.
    I.x² – 18x + 72= 0; 3y² + 7y + 4 = 0
    II.2x² + x – 36 = 0; 2y² – 13y + 20 = 0
    III.4X² – 19X + 12= 0; 3Y² + 8Y + 4 = 0
    1.Only I
    2.Only II
    3.Both I and II
    4.Both II and III
    5.None of these
    
    Answer & Explanation

    Answer – 2.Only II
    Explanation :
    From II, x = 4 , -9/2; y = 4, 5/2