1) (1000 1111)2=( ? )10

2) A cube is coloured orange on one face , pink on the opposite face, brown on one face and silver on a face adjacent to the brown face. The other two faces are left uncoloured. It is then cut into 125 smaller cubes of equal size. Now, answer the following questions based on the above statements:
(i) How many cubes have at least one face coloured pink?
option
A.6 B. 9
C.16 D. 25

(ii) How many cubes have all the faces uncoloured?
option
A.24 B.36
C.48 D. 64

(iii) How many cubes have at least two faces coloured ?
option
A.19 B.20
C.21 D. 23

(iv) How many cubes are coloured orange on one face and have the remaining faces uncoloured ?
option
A.19 B. 12
C.14 D. 16

(v) How many cubes one coloured pink ?
A.8 B.10
C.12 D.16

• First lets understand, what are the faces uncoloured. Two of the opposite faces are painted orange and pink, so we are left with four faces, the middle four faces. Of these four, two adjacent are painted brown and silver, so the remaining two adjacent are left uncolored.
  
  There can be some direct quesstions, where we can count easily. Lets solve them first.
  
  So, in that order, lets look at the fist question, which is asking for the total number of cubes painted pink. Here, we have to count one entire face of the bigger cube. the entire face will be a square of 5*5, so it makes up of 25 cubes.
  
  In the same vein, lets look at the last two questions,
  
  Of the 25 cubes on each face of the bigger cube, if we leave out the edges, we are left out with a 4*4 square, these are the cubes that are painted on only one face. So answers for both the last two questions is 16.
  
  Lets move to the next level, the cubes that are painted on atleast two faces. these are the cubes on the edges. Of the total 12 edges, only 5 edges are painted on both the sides.Of the five edges, one edge we have to count all the five cubes, and as there are some common cubes, we have to count only 4 cubes on each of the remaining edges. so a total of 5+4+4+4+4= 21cubes.
  
  To find the cubes that are not painted on any face, we have to peel of the faces that are painted. So, two opposite faces and two adjacent faces are to be peeled off. So, if the remaining cube is considered it is a 4*4*3 solid, so total 48 cubes are uncolored.
  
  Final key
  (1)D
  (2)C
  (3)C
  (4)D
  (5)D
• 11 years agoHelpfull: Yes(27) No(13)
• binary to desimal answer is 143
• 11 years agoHelpfull: Yes(13) No(3)
• 1000 1111=(143)10=2^7*1+2^6*0+2^5*0+2^4*0+2^3*1+2^2*1+2^1*1+2^0*1
• 11 years agoHelpfull: Yes(6) No(1)
• decimal number is 143.
• 11 years agoHelpfull: Yes(3) No(0)
• 1-D
  2-A
  3-C
  4-D
  5-D
• 11 years agoHelpfull: Yes(3) No(1)
• b-24,.because there are 2 faces and in each face there is 12 cubes.
• 11 years agoHelpfull: Yes(2) No(1)
• 1) I guess its making the number from binary to decimal so its 815
• 11 years agoHelpfull: Yes(1) No(18)
• 1. So if only one face is painted pink, how many cubes have at least 1 face colored in pink ? Isn't it the number of cubes with only one side colored in pink because pink is only colored on one face ?
  
  So the answer would be : 5∗5=25
  2. Now we know that 2 adjacent faces are not painted. We know for sure that all the cubes which are present in the center of the bigger cube, i.e., all the cubes that are not visible to human eye are not colored. Number of such cubes are : 3∗3∗3=27. But there are also some cubes which are visible to us on the sides which are left uncolored. Number of such cubes are : 4∗3+3∗3=21. Please do not count the cubes on the uncolored edges twice while doing this calculation.
  
  So total uncolored cubes : 27+21=48
  21 cubes, depending on how you coloured: one row of 5 from both the pink and Orange, that adjoin with silver say, two rows of 4 from pink and orange that connect with brown,
  then 3 further cubes on the silver brown border. That is 21 cubes.
  That is a 4x4 section so 16
  Same reasoning as 4, so 16
  
• 10 years agoHelpfull: Yes(1) No(0)
• D
  A
  B
  D
  D
  
• 10 years agoHelpfull: Yes(0) No(0)
• 1:D-25
  2:C-48
  3:B-20
  4:D-16
  5:B-10
• 10 years agoHelpfull: Yes(0) No(0)
• 1000 1111=(143)10
  =2^7*1+2^6*0+2^5*0+2^4*0+2^3*1+2^2*1+2^1*1+2^0*1
  =128+0+0+16+8+4+2+1
  =159
• 10 years agoHelpfull: Yes(0) No(2)
• 1000 1111=(149)10
  =2^7*1+2^6*0+2^5*0+2^4*0+2^3*1+2^2*1+2^1*1+2^0*1
  =128+0+0+16+8+4+2+1
  =159
• 10 years agoHelpfull: Yes(0) No(5)
• i)48
  ii)19
  iii)16
  iv)16
• 6 years agoHelpfull: Yes(0) No(0)