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Quant - Quadratic Equation Test 579
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Quant - Quadratic Equation Test 579
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  • Question 1/5
    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 + 3X – 88 = 0

    II. Y2 – 23Y + 126 = 0

    Solutions

    I. X2 + 3X – 88 = 0

    ⇒ X2 + 11X – 8X – 88 = 0

    ⇒ X(X + 11) – 8(X + 11) = 0

    ⇒ (X + 11)(X – 8) = 0

    ⇒ X = –11 & 8

    II. Y2 – 23Y + 126 = 0

    ⇒ Y2 – 14Y – 9Y + 126 = 0

    ⇒ Y(Y – 14) – 9(Y – 14) = 0

    ⇒ (Y – 14)(Y – 9) = 0

    ⇒ Y = 14 & 9

    Hence, Y > X.

  • Question 2/5
    1 / -0.25

    Directions For Questions

    Directions: In the following question, two equations numbered I and II are given. You have to solve both the equations and establish the relationship between the given variables:

    ...view full instructions


    I. x2 - 208 = 233
    II. y2 + 47 - 371 = 0
    Solutions
    From I, 
    x2 - 208 = 233 
    x2 = 233 + 208 
    x = 
    From II, 
    y2 + 47 - 371 = 0 
    y2 = 324 
    y =+18 or -18
    So, Relationship cannot be established.
  • Question 3/5
    1 / -0.25

    Directions For Questions

    Direction: In the following questions 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 – 30 = 0

    II. Y2 + 13Y + 42 = 0

    Solutions

    I. X2 – X – 30 = 0

    X2 – 6X + 5X – 30 = 0

    X(X – 6) + 5(X – 6) = 0

    (X + 5)(X – 6) = 0

    X = –5, 6

    II. Y2 + 13Y + 42 = 0

    Y2 + 6Y + 7Y + 42 = 0

    Y(Y + 6) + 7(Y + 6) = 0

    (Y + 6)(Y + 7) = 0

    Y = –6, –7

    Here, X > Y. Hence, the answer is option B.

  • 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 – 16 = 0

    II. Y2 + 9Y + 20 = 0

    Solutions

    I. X2 – 16 = 0

    (X + 4)(X – 4) = 0

    X = +4 & –4

    II. Y2 + 9Y + 20 = 0

    Y2 + 5Y + 4Y + 20 = 0

    Y(Y + 5) + 4(Y + 5) = 0

    (Y + 5)(Y + 4) = 0

    Y = –5 & –4

    Hence, X ≥ Y

  • 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 – 12 = 0

    II. Y2 – 17Y + 72 = 0

    Solutions

    I. X2 + X – 12 = 0

    ⇒ X2 + 4X – 3X – 12 = 0

    ⇒ X(X + 4) – 3(X + 4) = 0

    ⇒ (X + 4) (X – 3) = 0

    ⇒ X = –4 & 3

    II. Y2 – 17Y + 72 = 0

    ⇒ Y2 – 8Y – 9Y + 72 = 0

    ⇒ Y(Y – 8) – 9(Y – 8) = 0

    ⇒ (Y – 8) (Y – 9) = 0

    ⇒ Y = 8 & 9

    Hence, Y > X.

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