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Theory of Numbers Test - 5

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Theory of Numbers Test - 5
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  • Question 1
    1 / -0

    Which of the following will be the smallest number to be multiplied with 134456 to make it a perfect cube?

    Solution

    134456 = 2 x 2 x 2 x 7 x 7 x 7 x 7 x 7
    So, we will multiply it by 7 to make a perfect cube.

     

  • Question 2
    1 / -0

    If 3x + 1 . 2n = 1728, then n/x is equal to

    Solution

    3x + 1 . 2n = 1728
    3x + 1 2n = 33 (26)
    So, n = 6 and x = 2, hence n/x = 3

     

  • Question 3
    1 / -0

    If a = - 30, b = - 20 and c = 50, then find a3 + b3 +c3.

    Solution

    Now, a + b + c = 3abc, when a + b + c = 0
    Thus, the required answer is 3(- 30)(- 20)(50) = 90,000

     

  • Question 4
    1 / -0

    If 4- 4n -1 = 48, then nn is equal to

    Solution

    4- 4n -1 = 48 or 22n - 22n-2 = 48 or y - y/4 = 48 (where 22n = y)
    Or y = 64

    Now, 22n = 64 or 2n = 6 or n = 3
    Thus, nn = 33 = 27

     

  • Question 5
    1 / -0

    If x < y < z but x2 > y2 > z2 > 0, which of the following must be positive?

    Solution

    If x < y < z, then two cases arise.
    Case I: x = - 3, y = - 2, z = - 1
    Case II: x = - 3, y = - 2, z = 1

    From the above two cases, we conclude that for the expression to be positive, z must be raised
    to some even power.

    On checking the options, we find that option (2) has x and y raised to odd power, resulting in a positive expression.

     

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