### IAS Preparation – CSAT: Data Interpretation and Logical Reasoning (DI and LR)

if you look at the front face, how many exactly 2 side cubes you have? you have two here, two here, two here, two here, 8. Similarly in the back side you have 8 again. 8 in front, 8 behind. Now have you missed any in the two side or something? Yes. You have missed these two exactly 2 sides. get my point? So there 4 that are here. 4 here, there are 8 behind, 8 ahead, 4 here, and 4 here also. In total, 8+8=16, 16+4=20, 20+4=24 cubes in two sides. You can continue this. Take out all outer cubes, look inside. You will find that inside there is a segment, inside there is segment which will only be this much that is which has no color at all. You will calculate that and you will find a particular number to that also. Okay? By removing all the outer cubes. question here is there is a definite pattern for 2 cuts, 3 cuts, 4 cuts, 5 cuts. 3 cuts give you 4/4 parts, 2 cuts give you 3/3 that is 27 parts. 4 cuts will give you 5/5. 125 equal parts. Right? It will go on. These are basically the n+1 numbers right? If ask me how exactly to solve it not by drawing the cube, not by visualizing anything, but by just this 4 lines. Okay? Any cube, number of 3 side color please write this down, and verify is 8. Number of 2 side color in this case it is 24, please verify it is 12(n-2)^{1}. Number of one side color is 6(n-2)^{2}. No side color, inner ones, is nothing, (n-2)^{3}. What is n? n is number of equal cubes, in a side. When you have 3 cuts you are making how many cubes? 4. When you are making 2 cuts, how many equal cubes are you making? 3. So it is not number of cuts. It is number of equal cubes okay, that you are getting in one side. So this one, this one here, what did you get? We had a cube here, imagine the cube is going back like this, one, two cuts how many equal? 1, 2, 3. If you are having 3 cuts what happens is, one two three here, you are having 1,2,3,4. Obviously you will do 3 cuts like this also, right? But you are getting 4 equal. Everywhere you look you will getting 4 equal. So n here is 4. When you are giving 3 cuts, you are getting 4 equal parts, n is 4. When you having 2 cuts, you are getting 3 equal parts and n is 3, in this question, substitute n=4, you will get all the answers. Very fine. So what I told you in terms of imagining, visualizing, getting, counting through it off. Not required. So if you want quickly get 2 side color, 3 side color, one side color this is the way to go about. This is the way to go about. Okay.