CAT 2011 LR-DI thread

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:cheers: here we discuss logical reasoing question and DI which appear in different mocs and in different books so guys be ready to answer the question and to ask the question ::
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@ All kindly continye posting questions in CAT 2012 thread

http://www.pagalguy.com/discussions/cat-2012-lr-di-thread-25074663/3048616

JCU Singapore 2012 - 2013
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My solution:
when initially the 125 cubes are taken together to form a cube ,it will be formed 5*5*5 ways.

1)now for cubes having exactly three sides painted:

it is obvious that smaller cubes that emerge from the corners of the re-coloured big cube are coloured exactly 3 sides(handa sir article).their number is 8
now taking the cube which was cut and smaller cubes that emerge from the corners of the this cut cube are also three sided coloured.this number is also 8.but subtract 1 from it as one corner was included already in the above statement.
now in the exposed cubes you can visualise 3 cubes,each on the farthest edges which are coloured 3 sided...
so the total no. is 8+8-1+3=18.

3.)cubes which are zero sided painted....
as u can see only one cube which is in the cut cube is not painted at all...rest all r painted fr atleast one side..
so answer is 1.

2.)now for cubes which are one sided painted:

For 1 face to be painted, we will have to consider the smaller cubes that emerge from the face of the big cube (leaving out the corners and the edges).
so der number is 27 in the cube excluding the cut cube(3 faces,9 cubes each)(refer ravi sir concepts in the link i gave) and now we will add in this cubes of exposed parts which were coloured one sided.
so cubes in exposed part which are one sided coloured are: 4+4+4(4 each in the three exposed squares of the form 3*3).
now in this we all also add the one sided coloured cubes of the cut cube which is equal to 6(1 each in every face)
so the answer is 27+12+6=45.

Please tell if any mistake i committed....there is a chance as i visualised and did after reading handa sir concepts again..


Answer for 2nd question should be 48...u got 27+12+6...But missed +3(1 at each face of Larger Cube from where small Cube is truncated.

Answer for 3rd question is 6+...not getting the exact number....:-(
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Dear timeschange --- first of all thanks for posting the detailed answer. Though I have not gone through the detailed answer I am posting the answers as per the Answer Sheet
1) c that is 18
2) e that is 48
3) b that is 8

My Take is
1)18
2) 48 = (27+12+6+3)
3) 6 (not getting 2 more)


Plz provide some explanation (if available) for ur 3rd answer as 8..
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My solution:
when initially the 125 cubes are taken together to form a cube ,it will be formed 5*5*5 ways.

1)now for cubes having exactly three sides painted:

it is obvious that smaller cubes that emerge from the corners of the re-coloured big cube are coloured exactly 3 sides(handa sir article).their number is 8
now taking the cube which was cut and smaller cubes that emerge from the corners of the this cut cube are also three sided coloured.this number is also 8.but subtract 1 from it as one corner was included already in the above statement.
now in the exposed cubes you can visualise 3 cubes,each on the farthest edges which are coloured 3 sided...
so the total no. is 8+8-1+3=18.

3.)cubes which are zero sided painted....
as u can see only one cube which is in the cut cube is not painted at all...rest all r painted fr atleast one side..
so answer is 1.

2.)now for cubes which are one sided painted:

For 1 face to be painted, we will have to consider the smaller cubes that emerge from the face of the big cube (leaving out the corners and the edges).
so der number is 27 in the cube excluding the cut cube(3 faces,9 cubes each)(refer ravi sir concepts in the link i gave) and now we will add in this cubes of exposed parts which were coloured one sided.
so cubes in exposed part which are one sided coloured are: 4+4+4(4 each in the three exposed squares of the form 3*3).
now in this we all also add the one sided coloured cubes of the cut cube which is equal to 6(1 each in every face)
so the answer is 27+12+6=45.

Please tell if any mistake i committed....there is a chance as i visualised and did after reading handa sir concepts again..


Dear timeschange --- first of all thanks for posting the detailed answer. Though I have not gone through the detailed answer I am posting the answers as per the Answer Sheet
1) c that is 18
2) e that is 48
3) b that is 8
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From TIME Mock test
Q: 125 small unpainted cubes are arranged to form a large cube. All the six faces of the large cube are painted white. Now, a 3*3 cube, comprising 27 small cubes, is removed out from one of the corners of the large cube. The 3*3 cube is now painted blue on all six faces, while all the three surfaces (each of which a is a 3*3 square) of the large cube exposed due to the removal of the 3*3 cube are painted black. Then, the 3*3 cube is put back in its original position in the large cube and the large cube is finally painted yellow on all the six faces.

1) What is the number of small cubes which have exactly three faces painted ?
a) 8 b) 16 c) 18 d) 19 e) 6
2) What is the number of small cubes with exactly one face painted ?
a) 36 b) 39 c) 42 d) 45 e) 48
3) What is the number of small cube with no face painted
a) 1 b) 8 c) 10 d) 4 e) 12

Please provide the concept of solving this Caselet

My solution:
when initially the 125 cubes are taken together to form a cube ,it will be formed 5*5*5 ways.

1)now for cubes having exactly three sides painted:

it is obvious that smaller cubes that emerge from the corners of the re-coloured big cube are coloured exactly 3 sides(handa sir article).their number is 8
now taking the cube which was cut and smaller cubes that emerge from the corners of the this cut cube are also three sided coloured.this number is also 8.but subtract 1 from it as one corner was included already in the above statement.
now in the exposed cubes you can visualise 3 cubes,each on the farthest edges which are coloured 3 sided...
so the total no. is 8+8-1+3=18.

3.)cubes which are zero sided painted....
as u can see only one cube which is in the cut cube is not painted at all...rest all r painted fr atleast one side..
so answer is 1.

2.)now for cubes which are one sided painted:

For 1 face to be painted, we will have to consider the smaller cubes that emerge from the face of the big cube (leaving out the corners and the edges).
so der number is 27 in the cube excluding the cut cube(3 faces,9 cubes each)(refer ravi sir concepts in the link i gave) and now we will add in this cubes of exposed parts which were coloured one sided.
so cubes in exposed part which are one sided coloured are: 4+4+4(4 each in the three exposed squares of the form 3*3).
now in this we all also add the one sided coloured cubes of the cut cube which is equal to 6(1 each in every face)
so the answer is 27+12+6=45.

Please tell if any mistake i committed....there is a chance as i visualised and did after reading handa sir concepts again..
IIM Shillong
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From TIME Mock test
Q: 125 small unpainted cubes are arranged to form a large cube. All the six faces of the large cube are painted white. Now, a 3*3 cube, comprising 27 small cubes, is removed out from one of the corners of the large cube. The 3*3 cube is now painted blue on all six faces, while all the three surfaces (each of which a is a 3*3 square) of the large cube exposed due to the removal of the 3*3 cube are painted black. Then, the 3*3 cube is put back in its original position in the large cube and the large cube is finally painted yellow on all the six faces.

1) What is the number of small cubes which have exactly three faces painted ?
a) 8 b) 16 c) 18 d) 19 e) 6
2) What is the number of small cubes with exactly one face painted ?
a) 36 b) 39 c) 42 d) 45 e) 48
3) What is the number of small cube with no face painted
a) 1 b) 8 c) 10 d) 4 e) 12

Please provide the concept of solving this Caselet


are the answers
1.)18
2.)45
3.)1

if these are the correct answers ,pls tell me i will try to post my solution...
IIM Shillong
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go through this post...it will surely clear all your concepts like it did to me in these type of problems...
Of Cubes and Matchsticks Logical Reasoning Tricks for CAT 2011 | PaGaLGuY.com - India's biggest website for MBA in India, International MBA, CAT, XAT, SNAP, MAT

all the best


Already gone through that post of Ravi Sir but the same was generic in nature while this is a particular problem and that logic cannot be applied here.
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From TIME Mock test
Q: 125 small unpainted cubes are arranged to form a large cube. All the six faces of the large cube are painted white. Now, a 3*3 cube, comprising 27 small cubes, is removed out from one of the corners of the large cube. The 3*3 cube is now painted blue on all six faces, while all the three surfaces (each of which a is a 3*3 square) of the large cube exposed due to the removal of the 3*3 cube are painted black. Then, the 3*3 cube is put back in its original position in the large cube and the large cube is finally painted yellow on all the six faces.

1) What is the number of small cubes which have exactly three faces painted ?
a) 8 b) 16 c) 18 d) 19 e) 6
2) What is the number of small cubes with exactly one face painted ?
a) 36 b) 39 c) 42 d) 45 e) 48
3) What is the number of small cube with no face painted
a) 1 b) 8 c) 10 d) 4 e) 12

Please provide the concept of solving this Caselet



go through this post...it will surely clear all your concepts like it did to me in these type of problems...
Of Cubes and Matchsticks - Logical Reasoning Tricks for CAT 2011 | PaGaLGuY.com - Indias biggest website for MBA in India, International MBA, CAT, XAT, SNAP, MAT

all the best
IIM Shillong
Commenting on this post has been disabled by the moderator.

From TIME Mock test
Q: 125 small unpainted cubes are arranged to form a large cube. All the six faces of the large cube are painted white. Now, a 3*3 cube, comprising 27 small cubes, is removed out from one of the corners of the large cube. The 3*3 cube is now painted blue on all six faces, while all the three surfaces (each of which a is a 3*3 square) of the large cube exposed due to the removal of the 3*3 cube are painted black. Then, the 3*3 cube is put back in its original position in the large cube and the large cube is finally painted yellow on all the six faces.

1) What is the number of small cubes which have exactly three faces painted ?
a) 8 b) 16 c) 18 d) 19 e) 6
2) What is the number of small cubes with exactly one face painted ?
a) 36 b) 39 c) 42 d) 45 e) 48
3) What is the number of small cube with no face painted
a) 1 b) 8 c) 10 d) 4 e) 12

Please provide the concept of solving this Caselet

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hariluvsu Says
Ans is D...the least number of engineers for whom the details of exactly four features are available can be 0...draw 6 lines of each % given with common reference...and then try to move the lines so as to (take 100% line as reference) minimize the area where 4 lines are overlapped(which represents the % of engineers with exactly 4 details are available)...im not sure...neways whats the OS

OA is D only....can u explain approach clearly:-(
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