Non-Verbal Reasoning: Figure Series and Mirror Images — MCQs with Answers (Set 2)

Count only the upward-pointing triangles, one size at a time. Start with the smallest, unit-sized upward triangles, then the next size up, and so on. Adding every size of upward-pointing triangle gives 20 in total. The downward-pointing triangles, which total 7, are not part of this count. The correct number of upward-pointing triangles is 20.

Count only the upward-pointing triangles, one size at a time. Start with the smallest, unit-sized upward triangles, then the next size up, and so on. Adding every size of upward-pointing triangle gives 10 in total. The downward-pointing triangles, which total 3, are not part of this count. The correct number of upward-pointing triangles is 10.

Count the upward-pointing triangles first, one size at a time, from smallest to largest. For this figure, that comes to 56 upward-pointing triangles in total. Now count the downward-pointing triangles the same way, size by size. That comes to 22 downward-pointing triangles in total. A common mistake is to count only the upward-pointing ones and stop there. Add both directions together: 56 plus 22 equals 78. The correct total, counting every size and both directions, is 78.

Count the upward-pointing triangles first, one size at a time, from smallest to largest. For this figure, that comes to 35 upward-pointing triangles in total. Now count the downward-pointing triangles the same way, size by size. That comes to 13 downward-pointing triangles in total. A common mistake is to count only the upward-pointing ones and stop there. Add both directions together: 35 plus 13 equals 48. The correct total, counting every size and both directions, is 48.

Count the upward-pointing triangles first, one size at a time, from smallest to largest. For this figure, that comes to 20 upward-pointing triangles in total. Now count the downward-pointing triangles the same way, size by size. That comes to 7 downward-pointing triangles in total. A common mistake is to count only the upward-pointing ones and stop there. Add both directions together: 20 plus 7 equals 27. The correct total, counting every size and both directions, is 27.

Count the upward-pointing triangles first, one size at a time, from smallest to largest. For this figure, that comes to 10 upward-pointing triangles in total. Now count the downward-pointing triangles the same way, size by size. That comes to 3 downward-pointing triangles in total. A common mistake is to count only the upward-pointing ones and stop there. Add both directions together: 10 plus 3 equals 13. The correct total, counting every size and both directions, is 13.

Count the upward-pointing triangles first, one size at a time, from smallest to largest. For this figure, that comes to 4 upward-pointing triangles in total. Now count the downward-pointing triangles the same way, size by size. That comes to 1 downward-pointing triangles in total. A common mistake is to count only the upward-pointing ones and stop there. Add both directions together: 4 plus 1 equals 5. The correct total, counting every size and both directions, is 5.

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 4 rows has 5 horizontal lines, so there are C(5,2) = 10 ways to pick 2 of them. A grid with 4 columns has 5 vertical lines, so there are C(5,2) = 10 ways to pick 2 of them. Multiply these two counts together: 10 times 10 equals 100. A common mistake is counting only the 16 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 100.

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 3 rows has 4 horizontal lines, so there are C(4,2) = 6 ways to pick 2 of them. A grid with 5 columns has 6 vertical lines, so there are C(6,2) = 15 ways to pick 2 of them. Multiply these two counts together: 6 times 15 equals 90. A common mistake is counting only the 15 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 90.

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 2 rows has 3 horizontal lines, so there are C(3,2) = 3 ways to pick 2 of them. A grid with 5 columns has 6 vertical lines, so there are C(6,2) = 15 ways to pick 2 of them. Multiply these two counts together: 3 times 15 equals 45. A common mistake is counting only the 10 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 45.

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 3 rows has 4 horizontal lines, so there are C(4,2) = 6 ways to pick 2 of them. A grid with 4 columns has 5 vertical lines, so there are C(5,2) = 10 ways to pick 2 of them. Multiply these two counts together: 6 times 10 equals 60. A common mistake is counting only the 12 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 60.

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 3 rows has 4 horizontal lines, so there are C(4,2) = 6 ways to pick 2 of them. A grid with 3 columns has 4 vertical lines, so there are C(4,2) = 6 ways to pick 2 of them. Multiply these two counts together: 6 times 6 equals 36. A common mistake is counting only the 9 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 36.

A rectangle in this grid is fixed by choosing 2 horizontal lines and 2 vertical lines. A grid with 2 rows has 3 horizontal lines, so there are C(3,2) = 3 ways to pick 2 of them. A grid with 3 columns has 4 vertical lines, so there are C(4,2) = 6 ways to pick 2 of them. Multiply these two counts together: 3 times 6 equals 18. A common mistake is counting only the 6 smallest unit cells, and missing every larger rectangle. The correct total, across every size, is 18.

Count squares one size at a time, from smallest to largest. A size k square fits in (n-k+1) positions along each side of an n by n grid. For this 6 by 6 grid, here is each size’s count. 1 by 1 gives 36, 2 by 2 gives 25, 3 by 3 gives 16. 4 by 4 gives 9, 5 by 5 gives 4, 6 by 6 gives 1. Add every size together to get the total. The sum is 91. A common mistake is counting only the 36 smallest unit squares, and forgetting the larger squares made by combining them. The correct total, across every size, is 91.

Count squares one size at a time, from smallest to largest. A size k square fits in (n-k+1) positions along each side of an n by n grid. For this 5 by 5 grid, here is each size’s count. 1 by 1 gives 25, 2 by 2 gives 16, 3 by 3 gives 9. 4 by 4 gives 4, 5 by 5 gives 1. Add every size together to get the total. The sum is 55. A common mistake is counting only the 25 smallest unit squares, and forgetting the larger squares made by combining them. The correct total, across every size, is 55.

Count squares one size at a time, from smallest to largest. A size k square fits in (n-k+1) positions along each side of an n by n grid. For this 4 by 4 grid, here is each size’s count. 1 by 1 gives 16, 2 by 2 gives 9, 3 by 3 gives 4. 4 by 4 gives 1. Add every size together to get the total. The sum is 30. A common mistake is counting only the 16 smallest unit squares, and forgetting the larger squares made by combining them. The correct total, across every size, is 30.

Count squares one size at a time, from smallest to largest. A size k square fits in (n-k+1) positions along each side of an n by n grid. For this 3 by 3 grid, here is each size’s count. 1 by 1 gives 9, 2 by 2 gives 4, 3 by 3 gives 1. Add every size together to get the total. The sum is 14. A common mistake is counting only the 9 smallest unit squares, and forgetting the larger squares made by combining them. The correct total, across every size, is 14.

Count squares one size at a time, from smallest to largest. A size k square fits in (n-k+1) positions along each side of an n by n grid. For this 2 by 2 grid, here is each size’s count. 1 by 1 gives 4, 2 by 2 gives 1. Add every size together to get the total. The sum is 5. A common mistake is counting only the 4 smallest unit squares, and forgetting the larger squares made by combining them. The correct total, across every size, is 5.

The cube’s six faces show Circle, Square, Triangle, Diamond, Cross and Arrow. In View 1, Circle sits with Square and Triangle, so Circle is adjacent to both. In View 2, Circle sits with Cross and Arrow, so Circle is adjacent to both as well. Circle is now adjacent to four faces: Square, Triangle, Cross and Arrow. So Circle’s opposite must be Diamond. In View 1, Square sits with Circle and Triangle, so Square is adjacent to both. In View 3, Square sits with Diamond and Arrow, so Square is adjacent to both as well. Square is now adjacent to four faces: Circle, Triangle, Diamond and Arrow. So Square’s opposite must be Cross. Two opposite pairs are now fixed: Circle-Diamond, and Square-Cross. Only Triangle and Arrow remain unpaired. Since every face has exactly one opposite, Triangle and Arrow must be opposite each other. The symbol opposite Triangle is Arrow.

The cube’s six faces show Sun, Moon, Star, Cloud, Leaf and Wave. In View 1, Sun sits with Moon and Star, so Sun is adjacent to both. In View 2, Sun sits with Cloud and Leaf, so Sun is adjacent to both as well. Together, Sun is now known to be adjacent to four different faces: Moon, Star, Cloud and Leaf. A cube face can be adjacent to at most four others, touching every face except its opposite. Since Sun is already adjacent to Moon, Star, Cloud and Leaf, only Wave is left. So Wave must be the face opposite Sun. The symbol opposite Sun is Wave.

The cube’s six faces are P, Q, R, S, T and W. In View 1, P sits with Q and R, so P is adjacent to both. In View 2, P sits with S and T, so P is adjacent to both as well. Together, P is now known to be adjacent to four different faces: Q, R, S and T. A cube face can be adjacent to at most four others, touching every face except its opposite. Since P is already adjacent to Q, R, S and T, the only face left is W. So W must be the one face opposite P. The letter opposite W is P.

The cube has side 7, so N-2 = 7-2 = 5. Edge cubes touch exactly two outer faces. Their count is 12 x (N-2) = 12 x 5 = 60. Corner cubes always number 8, regardless of the cube’s size. Face-center cubes, with one painted face, number 6 x (N-2)^2 = 6 x 25 = 150. Fully hidden cubes, with zero painted faces, number (N-2)^3 = 5^3 = 125. The cubes with exactly two painted faces number 60.

The cube has side 6, so it is cut into 6 x 6 x 6 = 216 unit cubes. Fully hidden cubes touch none of the outer faces. Their count is (N-2)^3, using N as the side length. Here N-2 = 6-2 = 4, so (N-2)^3 = 4^3 = 64. Face-center cubes, with one painted face, number 6 x (N-2)^2 = 6 x 16 = 96. Edge cubes, with two painted faces, number 12 x (N-2) = 12 x 4 = 48. The total of 216 unit cubes is not the number asked for here. The fully unpainted cubes number 64.

The cube has side 3, so it is cut into 3 x 3 x 3 = 27 unit cubes. Face-center cubes touch exactly one outer face. Their count is 6 x (N-2)^2, using N as the side length. Here N-2 = 3-2 = 1, so (N-2)^2 = 1. Face-center cubes = 6 x 1 = 6. Corner cubes always number 8, no matter the cube’s size. Edge cubes, with two painted faces, number 12 x (N-2) = 12 x 1 = 12. Fully hidden cubes, with zero painted faces, number (N-2)^3 = 1. The cubes with exactly one painted face number 6.

The cube has side 4, so it is cut into 4 x 4 x 4 = 64 unit cubes. Edge cubes touch exactly two outer faces. Their count is 12 x (N-2), using N as the side length. Here N-2 = 4-2 = 2. So edge cubes = 12 x 2 = 24. A common mistake is using (N-1) instead of (N-2) in the formula. That wrongly gives 12 x 3 = 36. Corner cubes always number 8, since every cube has 8 corners. The total number of unit cubes here is 64, not the answer to this question. The cubes with exactly two painted faces number 24.

The cube has side 3, so it is cut into 3 x 3 x 3 = 27 unit cubes. Corner cubes always touch three outer faces, so they get 3 painted faces. There are always exactly 8 corner cubes, regardless of the cube’s size. Edge cubes touch two outer faces. Their count is 12 x (N-2), where N is the side length. Here N-2 = 1, so edge cubes = 12 x 1 = 12. Face-center cubes touch one outer face. Their count is 6 x (N-2)^2 = 6 x 1 = 6. Fully hidden cubes touch no outer face. Their count is (N-2)^3 = 1^3 = 1. Only the very center cube is untouched by paint. So the answer is 1.