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Quantitative Ability Test - 4

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Quantitative Ability Test - 4
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Weekly Quiz Competition
  • Question 1
    1 / -0

    tan 54° can be expressed as

    Solution

  • Question 2
    1 / -0

    A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is:

    Solution

  • Question 3
    1 / -0

    The length of the base of a triangle is 5/7 of the base of a parallelogram. The area of the triangle and the parallelogram is the same. Find the ratio of the respective heights of the triangle and the parallelogram.

    Solution

    ∴ The required ratio of the respective heights of the triangle and the parallelogram is 14 ∶ 5.

  • Question 4
    1 / -0

    Find the mean of the given data:

    3, 5, 8, 6, 9, 4, 5, 2, 7, 1, 5

    Solution

  • Question 5
    1 / -0

    The mean deviation from the median is:

    Solution

    Case 1:

    It is a fundamental property.

    Example

    Consider a set of 5 data points

    {1, 2, 3, 4, 5}

    median = 3

    Deviation from mean:

    1 - 3 = -2

    2 - 3 = -1

    3 - 3 = 0

    4 - 3 = 1

    5 - 3 = 2

    Mean of deviations (about mean) = 0/5 = 0

    Case 2:

    Consider data point 2

    Deviations of data about 2

    1 - 2 = - 1

    2 - 2 = 0

    3 - 2 = 1

    4 - 2 = 2

    5 - 2 = 3

    Mean of deviation of data about median is minimum and this is true for all data.

  • Question 6
    1 / -0

    Solution

  • Question 7
    1 / -0

    Which one of the following represents the number 'eleven thousand eleven hundred eleven'?

    Solution

    As we know,

    Thousand → 1000

    Hundred → 100

    Tens → 10

    Ones → 1

    Eleven thousand eleven hundred eleven = 11 × 1000 + 11 × 100 + 11

    = 11000 + 1100 + 11

    = 12111

  • Question 8
    1 / -0

    How many kilogram of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per kg?

    Solution

  • Question 9
    1 / -0

    If sin α + cos α = p, then what is cos2 (2α) equal to?

    Solution

    Given: sin α + cos α = p

    By squaring both the sides, we get

    ⇒ sin2 α + cos2 α + 2 sin α cos α = p2

    As we know that, sin2 x + cos2 x = 1 and sin 2x = 2 sin x cos x

    ⇒ 1 + sin 2α = p2 ⇒ sin 2α = p2 – 1

    ⇒ cos2 2α = 1 – sin2 2α = 1 – (p2 – 1)2

    ⇒ cos2 2α = p2 (2 – p2)

  • Question 10
    1 / -0

    40% of the employees in a factory are workers. All the remaining employees are executives. The annual income of each worker is Rs. 390. The annual income of each executive is Rs. 420. What is the average annual income of all the employees in the factory together?

    Solution

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