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Schools: Johnson (Cornell) (A) IIMB EPGP'22 (A) Emory Goizueta (A$) Cambridge '22 (D) Fuqua '23 (D) Sloan Fellows '22 (WL) Owen '23 (A$) Schulich Sept '23 (A)
GMAT 1: 720 Q50 V37
Posts: 113
26 Apr 2020, 00:37
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At times questions on Painted Cubes are tested on GMAT. It is better to understand the concept-
SHORTCUT FORMULA'S-
A cube of side n painted on all sides which is uniformly cut into smaller cubes of dimension 1 units
1. Number of cubes with 0 side painted= (n-2) ^3
2. Number of cubes with 1 sides painted =6(n - 2) ^2
3. Number of cubes with 2 sides painted= 12(n-2)
4. Number of cubes with 3 sides painted= 8(always)
A cuboid of dimension a*b*c painted on all sides which is cut into smaller cubes of dimension 1*1*1,
Number of cubes with 0 side painted= (a-2) (b-2) (c-2)
Number of cubes with 1 sides painted =2[(a-2) (b-2) + (b-2)(c-2) + (a-2)(c-2) ]
Number of cubes with 2 sides painted= 4(a+b+c -6)
Number of cubes with 3 sides painted= 8
Questions for Practice-
Q1: A cube having a side of 6 cm is painted red on all the faces and then cut into smaller cubes of 1 cm each. Find the total number of smaller cubes so obtained.
Q 2: In the above example, how many cubes will have three faces painted?
Q 3: In the above example, how many cubes will have only two faces painted?
Q 4: In the above example, how many cubes will have only one face and no side painted?
Q 5: A cube having an edge of 12 cm each. It is painted red on two opposite faces, blue on one other pair of opposite faces, black on one more face and one face is left unpainted. Then it is cut into smaller cubes of 1 cm each. Answer the following questions:
1. The total no. of smaller cubes/
2. The no. of smaller cubes which are having three-faces painted.
3. The no. of smaller cubes which are having two-faces painted.
4. The no. of smaller cubes which are having one-face painted.
5. The no. of smaller cubes which are having zero-face painted.
SOLUTIONS-
Q1- 216
Q2- 8
Q3- 48
Q4- 64
Q5:
1. 1728
2. 4
3. 84
4. 540
5. 1100
Try solving this, I will share the detailed answers in next posts.
SHORTCUT FORMULA'S-
A cube of side n painted on all sides which is uniformly cut into smaller cubes of dimension 1 units
1. Number of cubes with 0 side painted= (n-2) ^3
2. Number of cubes with 1 sides painted =6(n - 2) ^2
3. Number of cubes with 2 sides painted= 12(n-2)
4. Number of cubes with 3 sides painted= 8(always)
A cuboid of dimension a*b*c painted on all sides which is cut into smaller cubes of dimension 1*1*1,
Number of cubes with 0 side painted= (a-2) (b-2) (c-2)
Number of cubes with 1 sides painted =2[(a-2) (b-2) + (b-2)(c-2) + (a-2)(c-2) ]
Number of cubes with 2 sides painted= 4(a+b+c -6)
Number of cubes with 3 sides painted= 8
Questions for Practice-
Q1: A cube having a side of 6 cm is painted red on all the faces and then cut into smaller cubes of 1 cm each. Find the total number of smaller cubes so obtained.
Q 2: In the above example, how many cubes will have three faces painted?
Q 3: In the above example, how many cubes will have only two faces painted?
Q 4: In the above example, how many cubes will have only one face and no side painted?
Q 5: A cube having an edge of 12 cm each. It is painted red on two opposite faces, blue on one other pair of opposite faces, black on one more face and one face is left unpainted. Then it is cut into smaller cubes of 1 cm each. Answer the following questions:
1. The total no. of smaller cubes/
2. The no. of smaller cubes which are having three-faces painted.
3. The no. of smaller cubes which are having two-faces painted.
4. The no. of smaller cubes which are having one-face painted.
5. The no. of smaller cubes which are having zero-face painted.
SOLUTIONS-
Q1- 216
Q2- 8
Q3- 48
Q4- 64
Q5:
1. 1728
2. 4
3. 84
4. 540
5. 1100
Try solving this, I will share the detailed answers in next posts.
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