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What is the least number of cuts required to cut a cube into 84 identical pieces, assuming all cuts are made parallel to the faces of the cube?

  1. 11
  2. 12
  3. 13
  4. 10
asked in Quantitative Aptitude by (1.3k points)   | 1.7k views

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according to question , its asking about least number of cuts , which give 84 identical pieces ...

lets consider the case , in which its not least (for maximum ) then simply ...83 cuts ...which all are in same direction...

but you cut in (X,Y,Z) directions ...you will get minimum no of cuts ....

for eg we want 8 identical pieces ... if i cut in single direction then i have to cut it in 7 times , if i cut in X,Y direction , then 3 cut in one direction and 1 in other direction so total 4 cuts required , now if i cut in X,Y,Z directions then , 1 cut in X, 1 cut in Y, 1 Cut in Z , so total required cuts only 3 which is least ...(8= 2*2*2= (1+1)(1+1)(1+1) ) at each direction 1 cut , 2 pieces so total 8 picese using only 3 cuts .

 

Now come to the question .. 84identical pieces = 3*4*7=  here 3 using 2 cuts in X, 4 using 3cuts in Y, 7 using 6cuts in Z , 

 so totals cuts = 2+3+6= 11(least cuts) hence answer is option 1)11.

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