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Quant - Quadratic Equation Test 346
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Quant - Quadratic Equation Test 346

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  • Question 1/5
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    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. X2 – 5X – 84 = 0

    II. Y2 – 4Y – 60 = 0

    Solutions

    I. X2 – 5X – 84 = 0
    X2 + 7X – 12X – 84 = 0
    X(X + 7) – 12(X + 7) = 0
    (X – 12) (X + 7) = 0
    X = 12 and –7

    II. Y2 – 4Y – 60 = 0
    Y2 – 10Y + 6Y – 60 = 0
    Y(Y – 10) + 6(Y – 10) = 0
    (X + 6) (Y – 10) = 0
    Y = 10 and –6

    Hence, we cannot establish relation between X and Y.

  • 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 – 15X + 56 = 0

    II. Y2 – 6Y – 72 = 0

    Solutions

    I. X2 – 15X + 56 = 0

    ⇒ X2 – 8X – 7X + 56 = 0

    ⇒ X(X – 8) – 7(X – 8) = 0

    ⇒ (X – 8)(X – 7) = 0

    ⇒ X = 8, 7

    II. Y2 – 6Y – 72 = 0

    ⇒ Y2 – 12Y + 6Y – 72 = 0

    ⇒ Y(Y – 12) + 6(Y – 12) = 0

    ⇒ (Y – 12)(Y + 6) = 0

    ⇒ Y = 12, –6

    Hence, no relation can be established between X and Y.

  • Question 3/5
    1 / -0.25
    In the following question, two equations are given. You have to solve both the equations and find the relation between ‘a’ and ‘b’ and mark correct answer.
    I. a2 – 19a + 84 = 0
    II. b2 – 25b + 156 = 0
    Solutions
    We will solve both the equations separately
    Equation 1:
    a2 – 19a + 84 = 0
    ⇒ a2–12a – 7a + 84 = 0
    ⇒ a (a –12) – 7 (a – 12) = 0
    ⇒ (a –7) (a – 12) = 0
    ⇒ a = 7 or 12
    Equation 2:
    b2 - 25b + 156 = 0
    ⇒ b2 – 12y – 13y + 156 = 0
    ⇒ b (b –12) – 13 (b –12) = 0
    ⇒ (b –13)(b – 12) = 0
    ⇒ b = 13 or 12
    ∴ b ≥a
  • 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. 3x2  – 24x + 48 = 0
    II. 4y2 – 4y – 48 = 0
    Solutions
    I. 3x2  – 24x + 48 = 0
    x2 – 8x + 16 = 0
    x2 – 4x – 4x + 16 = 0
    x(x – 4) – 4(x – 4) = 0
    (x – 4)(x – 4) = 0
    x = 4, 4

    II. 4y2 – 4y – 48 = 0
    y2 – y – 12 = 0
    y2 – 4y + 3y – 12 = 0
    y(y – 4) + 3(y – 4) = 0
    (y + 3)(y – 4) = 0
    y = –3, 4

    Hence, x ≥ y
  • Question 5/5
    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 answer the question.

    ...view full instructions

    I. 8x – 7y = 18
    II. 3y + 2x = 33
    Solutions
    Given equations are
    8x – 7y = 18  .... (i)
    2x + 3y = 33  .... (ii)
    Multiply (ii) by 4 and subtract (i) from it.
    8x + 12y – 8x + 7y = 132 – 18
    ⇒ 19y = 114
    ⇒ y = 6
    Put this in (ii), we get
    x = 7.5 
    Hence, x > y.
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