### Logical Puzzles-1

1)What is the least number of cuts required to cut a cube into 504 identical pieces?
1)24 2)20 3)21 4)22

2)What is the maximum number of identical pieces obtained when a cube is cut by 15 cuts?
1)125 2)216 3)210 4)64

3)What is the maximum number of identical pieces a cube can produce when cut into by 20 cuts?
1)441 2)343 3)512 4)448

4)What is the least number of cuts required to cut a cube into 343 identical pieces?
1)18 2)21 3)24 4)20

5)A cube is decorated in such a way that, a diamond is placed at each corner, six diamonds at each edge and a diamond at the centre of every face.How many diamonds are there on the cube?
1)74 2)70 3)62 4)64

The next questions 6-14 are based on the following information:

A large cube is taken and one pair of opposite faces is painted in blue, one pair of adjacent faces is painted in green and among the remaining faces, one is painted in red and the other in blue. Now , the cube is cut into 125 small and identical pieces.

6)How many smaller cubes have all the three colours?
1)0 2)1 3)2 4)4

7)How many smaller cubes have only one colour on them?
1)54 2)57 3)60 4)63

8)How many smaller cubes have exactly one face painted?
1)54 2)96 3)63 4)75

9)How many smaller cubes have exactly two colours on them?
1)27 2)33 3)36 4)30

10)How many smaller cubes have exactly two painted faces?
1)30 2)36 3)33 4)27

11)How many smaller cubes have exactly two painted faces in exactly two colours?
1)24 2)27 3)30 4)33

12)How many smaller cubes have no blue colour on them?
1)45 2)57 3)65 4)60

13)How many smaller cubes have only blue and green on them?
1)19 2)15 3)23 4)27

14)How many smaller cubes have red or green but not blue?
1)36 2)30 3)60 4)33

The next 15-18 questions are based on the following information:

216 small but identical cubes are put together to form a large cube. This large cube is now painted on all six faces.

15)How many of the smaller cubes have no face painted at all?
1)125 2)27 3)64 4)49

16)How many of the smaller cubes have exactly one face painted?
1)96 2)16 3)120 4)112

17)How many of the smaller cubes have exactly two faces painted?
1)56 2)60 3)64 4)48

18)How many of the smaller cubes have exactly three faces painted?
1)8 2)9 3)16 4)27

The next 19-20 questions are based on the following information:

In a class of 150 students, 40 passed in Social Studies, 90 passed in Science and 30 failed in both the subjects.

19)How many students passed in at most one subject among Science and Social Science?
1)100 2)110 3)140 4)150

20)How many students passed in Science but failed in Social Studies?
1)70 2)10 3)90 4)80