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Home Non Verbal Reasoning Cubes and Dice See What Others Are Saying!
  • Question
  • If after 7 th step number of cubes painted in exactly 2 faces with colour 7 is 21, then what is the number of cubes removed in 3 rd step.


  • Options
  • A. 469
  • B. 455
  • C. 433
  • D. None of these

  • Correct Answer
  • 469 

    Explanation

    Consider the 1st step, initial number of cubes N3 after removal of 1st set of coloured cubes number of cubes left out is (N - 1)3 hence number of cubes removed in 1st step (i.e with colour 1) is
    N3 - (N - 1)3 = 3N2 - 3N + 1
    Similarly number of cubes removed in 2nd step (i.e with colour 2) is
    Similarly number of cubes removed in 3rd step is (i.e with colour 3) and so on.
    = 3(N - 1)2 - 3(N - 1) + 1
    Number of cubes remaining after 1st step is (N - 1)3
    Number of cubes remaining after 2nd step is (N - 2)3 and so on.
    Total number of Cubes left after 7thstep in (N - 7)3 in the form of (N - 7) x (N - 7) x (N - 7) cubes.
    And out of these number of cubes whose two sides are painted is given by three edges with each edge has (N - 8) so total number of cubes is 3 x (N - 8)
    From the given information 3(N - 8) = 21 or N = 15
    Number of cubes removed in 3rd step (i.e with colour 3) is = 3(N - 2)2 - 3(N - 2) + 1 = 469


  • More questions

    • 1. 
      Find the question mark ? figure from answer figure.

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 2. 
      Which one of the answer figures shall complete the given question figure?

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 3. 
      Which answer figure will complete the question figure?

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 4. Find the question mark ? figure from answer figure:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 5. 
      Which of the four cubes pictured below are correct view when the six squares are folded (in clockwise direction) into a cube?

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 6. 
      Among the four answer figures which figure can be formed from the cut- pieces given below in the question figure?

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 7. Find the missing figure of the series from the given answer figures:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 8. Find out the answer for the question mark that completes the series from the Answer Figures:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 9. Choose the correct alternative from the given ones that will complete the series:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 10. What will come in place of?:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss


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