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Home Non Verbal Reasoning Cubes and Dice See What Others Are Saying!
  • Question
  • Of all the removed cubes which one of the following could be the number of cubes with exactly 2 face painted after 3 steps?


  • Options
  • A. 112
  • B. 114
  • C. 116
  • D. 118

  • Correct Answer
  • 114 

    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.
    After step 1 number of cubes with exactly 2 face painted is 4(N - 1) + (N - 2) = 5N - 6
    Similarly after 2nd step number of cubes with exactly 2 face painted is 5(N - 2) - 6 = 5N - 11
    And after 3rd step number of cubes with exactly 2 face painted is 5(N - 2) - 6 = 5N - 16
    So total number of such cubes is 15N - 33 out of the given options only option B satisfy the given condition.


  • More questions

    • 1. Select the one which is different from the other three responses

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 2. Select the figure which satisfies the same conditions of placement of the dots as in Figure-X.


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

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

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 5. 
      A piece of paper is folded and cut as shown below. From the responses indicate how it will appear when opened:

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 6. Select the one which is different from the other three responses

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 7. In each of the following questions which of the answer figures is exactly the mirror image of the question figure when the mirror is held at the given point

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 8. 
      Which answer figure will complete the pattern in the question figure?

    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • Discuss
    • 9. Choose the figure which is different from the rest.

         (1)     (2)     (3)     (4)     (5)


    • Options
    • A. 1
    • B. 2
    • C. 3
    • D. 4
    • E. 5
    • Discuss
    • 10. 
      Select a suitable figure from the answer figures that would replace the question mark (?) from question figure.

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


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