A cube painted green on all faces is cut into 216 cubes of equal sizes. how many cubes are painted on one face only?

Registration gives you: • Tests Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan Prep. All are free for GMAT Club members. • Applicant Stats View detailed applicant stats such as GPA, GMAT score, work experience, location, application status, and more • Books/Downloads Download thousands of study notes, question collections, GMAT Club’s Grammar and Math books. All are free! and many more benefits! Hi Salvetor, I'm going to give you a couple of hints so that you can try this question again: 1) Draw a simple cube 2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes. 3) Remember that the OUTSIDE of the cube is the part that's painted.... While the question asks for the number of min-cubes that have paint on 2 sides, here's a critical thinking exercise (you can use the drawing to help you; remember that the cube has 6 sides and you're not allowed to count a min-cube more than once): Which of the 27 mini-cubes have paint on just 1 side? Which of the 27 mini-cubes have paint on 2 sides? Which of the 27 mini-cubes have paint on 3 sides? Final Answer The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A GMAT assassins aren't born, they're made, Rich __...

Painted Cubes Painted Cubes Task 160 ... Years 4 - 12 Summary A cube made from unit cubes is spray painted on all faces, when deconstructed into its unit cubes, how many of these have 3, 2, 1, 0 faces painted. This classic problem is full of pattern and algebra investigations and yet the students don't have to be experienced algebraists to 'get it'. The generalisations may be developed from the tabulated data or they may be developed by visual inspection combined with knowledge of the number of faces, edges and vertices of a cube. This cameo has a Materials • 3 wooden cubes of different sizes • board, marker & cloth Content • multiplication calculations in context • number patterns • linear, quadratic & cubic functions • generalisation • symbolic representation • substituting into equations • solving equations • graphing ordered pairs • isometric drawing Iceberg A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. The opening question may seem a little straight forward, but its intent is to encourage students to see 'into' the scored cube - to deconstruct it. This visual separation of the whole into parts is important in developing the patterns in the main problem. If you have 2cm cubes (or similar) in the room it can be useful to ask students to show you how their calculation methods can be demonstrated. Two ways to calculate are: • 3 layers, each with 9 unit cubes • 9 towers each with 3 unit cubes and there may be more. Th...

Given:Numbers of small cubes of equal sides are 64. Therefore, The sidesof cubes will be (64) (1/3) = 4 Now, the numbers of cubes with no colored surfaces = (4 - 2) 3 = 2 3 = 8 Hence, the correct answer should be "8". Shortcut Trick For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1, Number of cubes with 0 side painted= (n-2) ^3 Number of cubes with 1 side painted =6(n - 2) ^2 Number of cubes with 2 sides painted= 12(n-2) Number of cubes with 3 sides painted= 8(always)

There is a cube in which one pair of opposite faces is painted red; another pair of opposite faces is painted blue and the third pair of opposite faces is painted pink. This cube is now cut into 216 smaller but identical cubes. 12. How many small cubes will be there with no red paint at all? (A) 121 (B) 144 (C) 169 (D) 100 13. How many small cubes will be there with at least two different colours on their faces? (A) 49 (B) 64 (C) 56 (D) 81 14. How many small cubes will be there without any face painted? (A) 64 (B) 49 (C) 36 (D) 25 how to solve these types of questions 216 small cubes means assume each small cube having 1cm length. 12. small cubes without red=216-(8 cubes having 3 colors+red is with 8 edges *4+16*2) =216-8-32-32=144 13. at least 2 face colors = cube with 2 face colors + cube with 3 colors cube with 2 face color = 12*4 = 48 cube with 3 face color = 8 at least 2 face colors = 48+8=56 14. small cubes without face color = total small cubes - face with at least one color cube with color on one face = 6*16=96 cube with color on 2 faces = 12*4 = 48 cube with color on 3 faces = 8 cube with no face painting = 216-96-48-8= 64

Given:Numbers of small cubes of equal sides are 64. Therefore, The sidesof cubes will be (64) (1/3) = 4 Now, the numbers of cubes with no colored surfaces = (4 - 2) 3 = 2 3 = 8 Hence, the correct answer should be "8". Shortcut Trick For a cube of side n*n*n painted on all sides which is uniformly cut into smaller cubes of dimension 1*1*1, Number of cubes with 0 side painted= (n-2) ^3 Number of cubes with 1 side painted =6(n - 2) ^2 Number of cubes with 2 sides painted= 12(n-2) Number of cubes with 3 sides painted= 8(always)

There is a cube in which one pair of opposite faces is painted red; another pair of opposite faces is painted blue and the third pair of opposite faces is painted pink. This cube is now cut into 216 smaller but identical cubes. 12. How many small cubes will be there with no red paint at all? (A) 121 (B) 144 (C) 169 (D) 100 13. How many small cubes will be there with at least two different colours on their faces? (A) 49 (B) 64 (C) 56 (D) 81 14. How many small cubes will be there without any face painted? (A) 64 (B) 49 (C) 36 (D) 25 how to solve these types of questions 216 small cubes means assume each small cube having 1cm length. 12. small cubes without red=216-(8 cubes having 3 colors+red is with 8 edges *4+16*2) =216-8-32-32=144 13. at least 2 face colors = cube with 2 face colors + cube with 3 colors cube with 2 face color = 12*4 = 48 cube with 3 face color = 8 at least 2 face colors = 48+8=56 14. small cubes without face color = total small cubes - face with at least one color cube with color on one face = 6*16=96 cube with color on 2 faces = 12*4 = 48 cube with color on 3 faces = 8 cube with no face painting = 216-96-48-8= 64

Registration gives you: • Tests Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan Prep. All are free for GMAT Club members. • Applicant Stats View detailed applicant stats such as GPA, GMAT score, work experience, location, application status, and more • Books/Downloads Download thousands of study notes, question collections, GMAT Club’s Grammar and Math books. All are free! and many more benefits! Hi Salvetor, I'm going to give you a couple of hints so that you can try this question again: 1) Draw a simple cube 2) Draw 9 squares on each face of the cube (so that it looks like a Rubik's Cube) - this is what the cube will look like when it's cut into 27 equal smaller cubes. 3) Remember that the OUTSIDE of the cube is the part that's painted.... While the question asks for the number of min-cubes that have paint on 2 sides, here's a critical thinking exercise (you can use the drawing to help you; remember that the cube has 6 sides and you're not allowed to count a min-cube more than once): Which of the 27 mini-cubes have paint on just 1 side? Which of the 27 mini-cubes have paint on 2 sides? Which of the 27 mini-cubes have paint on 3 sides? Final Answer The mini-cubes with 2 painted sides are ALL on the edge of the cube, in the "middle" of the edge. There are 4 in front, 4 in back and 4 more on the "strip" that runs around the left/top/right/bottom of the cube. 4 + 4 + 4 = 12. Answer A GMAT assassins aren't born, they're made, Rich __...

Painted Cubes Painted Cubes Task 160 ... Years 4 - 12 Summary A cube made from unit cubes is spray painted on all faces, when deconstructed into its unit cubes, how many of these have 3, 2, 1, 0 faces painted. This classic problem is full of pattern and algebra investigations and yet the students don't have to be experienced algebraists to 'get it'. The generalisations may be developed from the tabulated data or they may be developed by visual inspection combined with knowledge of the number of faces, edges and vertices of a cube. This cameo has a Materials • 3 wooden cubes of different sizes • board, marker & cloth Content • multiplication calculations in context • number patterns • linear, quadratic & cubic functions • generalisation • symbolic representation • substituting into equations • solving equations • graphing ordered pairs • isometric drawing Iceberg A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. The opening question may seem a little straight forward, but its intent is to encourage students to see 'into' the scored cube - to deconstruct it. This visual separation of the whole into parts is important in developing the patterns in the main problem. If you have 2cm cubes (or similar) in the room it can be useful to ask students to show you how their calculation methods can be demonstrated. Two ways to calculate are: • 3 layers, each with 9 unit cubes • 9 towers each with 3 unit cubes and there may be more. Th...

Painted Cubes Painted Cubes Task 160 ... Years 4 - 12 Summary A cube made from unit cubes is spray painted on all faces, when deconstructed into its unit cubes, how many of these have 3, 2, 1, 0 faces painted. This classic problem is full of pattern and algebra investigations and yet the students don't have to be experienced algebraists to 'get it'. The generalisations may be developed from the tabulated data or they may be developed by visual inspection combined with knowledge of the number of faces, edges and vertices of a cube. This cameo has a Materials • 3 wooden cubes of different sizes • board, marker & cloth Content • multiplication calculations in context • number patterns • linear, quadratic & cubic functions • generalisation • symbolic representation • substituting into equations • solving equations • graphing ordered pairs • isometric drawing Iceberg A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card. The opening question may seem a little straight forward, but its intent is to encourage students to see 'into' the scored cube - to deconstruct it. This visual separation of the whole into parts is important in developing the patterns in the main problem. If you have 2cm cubes (or similar) in the room it can be useful to ask students to show you how their calculation methods can be demonstrated. Two ways to calculate are: • 3 layers, each with 9 unit cubes • 9 towers each with 3 unit cubes and there may be more. Th...

There is a cube in which one pair of opposite faces is painted red; another pair of opposite faces is painted blue and the third pair of opposite faces is painted pink. This cube is now cut into 216 smaller but identical cubes. 12. How many small cubes will be there with no red paint at all? (A) 121 (B) 144 (C) 169 (D) 100 13. How many small cubes will be there with at least two different colours on their faces? (A) 49 (B) 64 (C) 56 (D) 81 14. How many small cubes will be there without any face painted? (A) 64 (B) 49 (C) 36 (D) 25 how to solve these types of questions 216 small cubes means assume each small cube having 1cm length. 12. small cubes without red=216-(8 cubes having 3 colors+red is with 8 edges *4+16*2) =216-8-32-32=144 13. at least 2 face colors = cube with 2 face colors + cube with 3 colors cube with 2 face color = 12*4 = 48 cube with 3 face color = 8 at least 2 face colors = 48+8=56 14. small cubes without face color = total small cubes - face with at least one color cube with color on one face = 6*16=96 cube with color on 2 faces = 12*4 = 48 cube with color on 3 faces = 8 cube with no face painting = 216-96-48-8= 64