Mixed Quantitative Aptitude Questions Set 90

Directions(1-5) : Find the relation between x and y and choose the correct options.

  1. I. 2x² + 11x + 15 = 0
    II. 4y² + 22y + 24 = 0

    x=y or no relation cannot be established.
    y>x
    x>=y
    y>=x
    x>y
    Option A
    I. 2x² + 11x + 15 = 0
    ⇒ 2x² + 6x + 5x + 15 = 0
    ⇒ (x + 3) (2x + 5) = 0
    ⇒ x = – 3, –5/2
    II. 4y² + 22y + 24 = 0
    ⇒ 2y² + 11y + 12 = 0
    ⇒ 2y² + 8y + 3y + 12 = 0
    ⇒ (y + 4) (2y + 3) = 0
    ⇒ y = –4, –3/2
    No relation.

     

  2. I. 5x² + 29x + 20 = 0
    II. 25y² + 25y + 6 = 0

    y>=x
    x>y
    x>=y
    y>x
    x=y or no relation cannot be established.
    Option D
    I. 5x² + 29 + 20 = 0
    ⇒ 5x² + 25x + 4x + 20 = 0
    ⇒ (x + 5) (5x + 4) = 0
    ⇒ x = –5, –4/5
    II. 25y² + 25y + 6 = 0
    ⇒ 25y² + 15y + 10y + 6 = 0
    ⇒ (5y + 3) (5y + 2) = 0
    ⇒ y = – 3/5, –2/5
    y > x

     

  3. I. 2x^2 − (4 + √13) x + 2√13 = 0 II. 10y^2 − (18 + 5√13)y + 9√13 = 0
    y>x
    x>=y
    x>y
    x=y or no relation cannot be established.
    y>=x
    Option B
    I.2𝑥^2 − 4𝑥 − √13𝑥 + 2√13 = 0
    =>2𝑥(𝑥 − 2) − √13(𝑥 − 2) = 0
    =>𝑥 = √13/ 2 , 2
    II. 10𝑦^2 − 18𝑦 − 5√13𝑦 + 9√13 = 0
    =>2𝑦(5𝑦 − 9) − √13(5𝑦 − 9) = 0
    => 𝑦 = √13/2 , 9/5
    𝑥 ≥ y

     

  4. I. 16x² + 20x + 6 = 0
    II. 10y² + 38y + 24 = 0

    y>=x
    x=y or no relation cannot be established.
    x>=y
    y>x
    x>y
    Option E
    I. 16x² + 20x + 6 = 0
    ⇒ 8x² + 10x + 3 = 0
    ⇒ 8x² + 4x + 6x + 3 = 0
    ⇒ (2x + 1) (4x + 3) = 0
    ⇒ x = –1/2, –3/4
    II. 10y² + 38y + 24 = 0
    ⇒ 5y² + 19y + 12 = 0
    ⇒ 5y² + 15y + 4y + 12 = 0
    ⇒ (y + 3) (5y + 4) = 0
    y = –3, –4/5
    x > y

     

  5. I. 2𝑥^2 + 11𝑥 + 14 = 0
    II.4𝑦^2 + 12𝑦 + 9 = 0

    y>=x
    x>y
    x=y or no relation cannot be established.
    x>=y
    y>x
    Option E
    I. 2𝑥^2 + 4𝑥 + 7𝑥 + 14 = 0
    =>2𝑥(𝑥 + 2) + 7(𝑥 + 2) = 0
    𝑥 = −2, −3.5
    II. (2𝑦 + 3)^2 = 0
    𝑦 = −1.5, −1.5
    x < y

     

  6. Directions(6-10) : Given below is a pie chart. This pie chart shows the percentage efficiency (out of 100) of different people named A, B, C, D and E.

  7. E can finish a piece of work in 45 days. If E, D and B work alternatively starting from E on day 1, D on day 2 and B on day 3 then, in how many days will they complete work working alternatively.
    28
    30
    34
    26
    22
    Option C
    Work efficiency ratio of E, D and B
    = 15 : 20 : 25
    = 3 : 4 : 5
    Let, E completes 3x units in one day.
    In 45 days, he completes 45 × 3x = 135x units
    In every three days, [3x + 4x + 5x] units are being completed.
    In 33 days, 12x × 11 units will be completed.
    On 34th day the remaining 3x units will be completed by E.

     

  8. If C can finish a work in 8 days, what is the average of the no. of days that A, B, C, D & E take individually to finish the work?
    6
    5
    7
    9
    10
    Option B
    Ratio of efficiency of A, B, C, D and E = 6:5:2:4:3
    Ratio of number of days taken by A, B, C, D and E to complete the work
    = 1/6 ∶ 1/ 5 ∶ 1/ 2 : 1/ 4 ∶ 1/ 3
    = 10 : 12 : 30 : 15 : 20
    C finishes the work in 8 days. A, B, D and E complete the work individually in 8/ 3 , 16/ 5 , 4 and 16/ 3 days respectively.
    The required average = (8 + 16 /5 + 8 /3 + 16/ 3 + 4 )/5
    = 4.64 day == 5 days

     

  9. If A, D and C can finish a piece of work in 10 days. What is the ratio of the no. of days that A takes to complete the work alone to the no. of days that D takes to complete it alone?
    7:3
    5:2
    8:5
    1:3
    5:4
    Option D
    Ratio of efficiency of A, D and C
    = 3 : 2 : 1
    Ratio of number of days taken by A, D and C to complete the work
    = 1 /3 : 1/ 2 : 1 = 2 : 3 : 6
    Required ratio = 2 : 6 = 1 : 3

     

  10. A can finish a piece of work in 48 days less than C. The number of days in which they finish the work together is what percent of the number of days that C takes to do it alone?
    40%
    32%
    25%
    20%
    22%
    Option C
    Work efficiency ratio of A and C = 3 : 1
    Ratio of time taken by A and C to complete the work = 1 : 3
    Time taken by A to complete the work = x days
    Time taken by C to complete the work = 3x days
    Now, 3x – x = 48 days
    ⇒ 2x = 48 days
    ⇒ x = 24 & 3x = 72 days
    C can do it alone in 72 days (A + C)’s 1 day work
    = 1 /24 + 1 /72
    = (3 + 1)/ 72
    = 4 /72
    = 1/ 18
    They together can complete the work in 18 days
    Therefore, required percent = 18 /72 × 100 = 25%

     

  11. E can do 6/7th of a job in 24 days. Time taken by A is what percent more or less by E?
    25%
    50%
    30%
    15%
    20%
    Option B
    Ratio of efficiency of A and E is 30 : 15 = 2 : 1
    Ratio of number of days taken by A and E to complete the work
    = 1/2 : 1
    = 1 : 2
    Required % = 1 2 × 100 = 50%

     


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