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Quant - Quadratic Equation Test 331
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Quant - Quadratic Equation Test 331

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  • Question 1/5
    1 / -0.25

    Directions For Questions

    Direction: In the following question, there are two equations. Solve the equations and answer accordingly:

    ...view full instructions

    I. 12p2 – 32p – 240 = 0
    II. 4q2 + 32q + 64 = 0
    Solutions
    I. 12p2 – 32p – 240 = 0
        3p2 – 8p – 60 = 0    
        3p2 – 18p + 10p – 60 = 0    
        3p(p – 6) + 10(p – 6) = 0  
        (3p + 10)(p – 6) = 0
    ∴ p =
    II. 4q2 + 32q + 64 = 0 
        q2 + 8q + 16 = 0
        q2 + 4q + 4q + 16 = 0
        q(q + 4) + 4(q + 4) = 0 
    ∴ q = – 4, – 4

    p > q
  • 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. 2X2 + 10X – 12 = 0
    II. 4Y2 – 12Y – 16 = 0
    Solutions
    I. 2X2 + 10X – 12 = 0
    X2 + 5X – 6 = 0
    X2 + 6X – X – 6 = 0
    X(X + 6) – 1(X + 6) = 0
    (X + 6)(X – 1) = 0
    X = 1, –6

    II. 4Y2 – 12Y – 16 = 0
    Y2 – 3Y – 4 = 0
    Y2 – 4Y + Y – 4 = 0
    Y(Y – 4) + 1(Y – 4) = 0
    (Y – 4)(Y + 1) = 0
    Y = –1, 4

    Relationship cannot be established.
  • 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 relation between X and Y.

    ...view full instructions

    I. 2x2 − 11x + 15 = 0
    II. 5y2 − 3y − 2 = 0
    Solutions
    I. 2x2 − 6x − 5x + 15 = 0
    ⇒ 2x(x − 3) − 5(x− 3) = 0
    ⇒ (2x − 5) (x − 3) = 0
    ⇒ x = 3, 5/2

    II. 5y2 − 5y + 2y − 2 = 0
    ⇒ 5y (y − 1) + 2(y − 1) = 0
    ⇒ (5y + 2)(y − 1) = 0
    ⇒ y = 1, −2/5
    So, x > y.
  • 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 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 5/5
    1 / -0.25

    Directions For Questions

    Direction: In the following question, there are two equations. Solve the equations and answer accordingly.

    ...view full instructions

    I. X2 − 29X + 208 = 0

    II. Y2 − 15Y + 56 = 0

    Solutions

    I. X2 − 29 X + 208 = 0

    X2 − 13X − 16X + 208 = 0

    X(X − 13) − 16(X − 13) = 0

    (X − 13)(X − 16) = 0

    X = 13, 16

    II. Y2 − 15 Y + 56 = 0

    Y2 − 7Y − 8Y + 56= 0

    Y(Y − 7) − 8(Y − 7) = 0

    (Y − 7)(Y − 8) = 0

    Y = 8, 7

    Hence, X > Y

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