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Quant - Quadratic Test 516
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Quant - Quadratic Test 516

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  • Question 1/5
    1 / -0.25

    Directions For Questions

    Direction: In the following question two equations are given in variables Xand Y. You have to solve these equations and determine relation between X and Y.

    ...view full instructions

    I. 96x2 – 24x − 12 = 0

    II. 48y2 + 154y − 124 = 0

    Solutions

    I. 96x2 – 24x -12 = 0

    96x2 –(48 – 24)x -12 = 0

    96x2 – 48x + 24x – 12 = 0

    48x( 2x – 1) + 12(2x – 1) = 0

    ( 48x + 12) ( 2x – 1) = 0

    X =

    II. 48y2 + 154y -124 = 0

    48y2 + (186 – 32 )y – 124 = 0

    48y2 + 186y – 32y – 124 = 0

    6y ( 8y – 31 ) – 4(8y + 31)= 0

    (6y – 4) (8y + 31) = 0

    Y

    On comparing the roots of x and y , No relation can be established.

  • Question 2/5
    1 / -0.25

    Directions For Questions

    Direction: In the following question two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

    ...view full instructions

    I. X2− ( +)X +  = 0

    II. Y2− ( + )Y +  = 0

    Solutions
    I. X2 − ( +)X +  = 0

    ⇒ X2 −  X −  X + = 0

    ⇒ X(X − ) − (X −) = 0

    ⇒ (X − )(X −  ) = 0

    ⇒ X = ,

    II. Y2 − ( +)Y +  = 0

    ⇒ Y2 −  Y − Y + = 0

    ⇒ Y(Y − ) −  (Y − ) = 0

    ⇒ (Y − )(Y − ) = 0

    ⇒ Y = ,

    Hence, Y > X.

  • Question 3/5
    1 / -0.25

    Directions For Questions

    Direction: In the following question two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

    ...view full instructions

    I. x2 – 18.5x + 75 = 0

    II. 2y2 + 40y + 175.5 = 0

    Solutions

    I. x2 – 18.5x + 75 = 0

    ⇒ 2x2 – 37x + 150 = 0 ….Multiplied by 2

    ⇒ 2x2 – 25x – 12x + 150 = 0

    ⇒ x(2x – 25) – 6(2x – 25) = 0

    ⇒ (x – 6)(2x – 25) = 0

    ⇒ x = 6 or 

    II. 2y² + 40y + 175.5 = 0

    ⇒ 4y² + 80y + 351 = 0 ….Multiplied by 2

    ⇒ 4y² + 54y + 26y + 351 = 0

    ⇒ 2y(2y + 27) + 13(2y + 27) = 0

    ⇒ (2y + 13)(2y + 27) = 0

    ⇒ y = 

    Hence, option A is correct.

  • Question 4/5
    1 / -0.25

    Directions For Questions

    Direction: In the following question two equations are given in variables X and Y. You have to solve these equations and determine relation between X and Y.

    ...view full instructions

    I. 18X² + 12X – 126 = 0

    II. 24Y² + 11Y – 200 = 0

    Solutions

    I. 18X² + 12X – 126 = 0

    ⇒ 18X² + 54X – 42X – 126 = 0

    ⇒ (18X – 42)(X + 3) = 0

    ∴ X =  = 2.33, –3

    II. 24Y² + 11Y – 200 = 0

    ⇒ 24Y² + 75Y – 64Y – 200 = 0

    ⇒ (3Y – 8)(8Y + 25) = 0

    ∴ Y =  = 2.66, – = –3.125

    Hence, option E is correct.

  • Question 5/5
    1 / -0.25

    Directions For Questions

    Direction: In the following question two equations are given in variables X and Y. You have to solve these equations and determine the relation between X and Y.

    ...view full instructions

    I. X2 –  X + 44 = 0

    II. Y2 – 29Y + 210 = 0

    Solutions

    I. X2 –  X + 44 = 0

    ⇒ X2 – X –X + 44 = 0

    ⇒ X(X – ) – (X – ) = 0

    ⇒ (X – )(X – ) = 0

    ⇒ X = ,

    II. Y2– 29Y + 210 = 0

    ⇒ Y2– 14Y – 15Y + 210 = 0

    ⇒ Y(Y – 14) –15(Y – 14) = 0

    ⇒ (Y – 14)(Y – 15) = 0

    ⇒ Y = 14, 15

    Hence, Y > X.

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