Tag: business skills

Using weighted average: (2*50 + 3*40) / (2+3) = (100 + 120) / 5 = 220/5 = 44. With 2 boys and 3 girls, the boys contribute 100 and girls contribute 120 to total weight, divided by 5 students gives 44.

A square inscribed in a circle has a diagonal equal to the circle's diameter. With radius 5, the diameter is 10. The area of a square is (diagonal^2)/2, so (10^2)/2 = 100/2 = 50 square units.

Using allegation method: difference from 47% gives (50-47):(47-40) = 3:7. So Solution I (40%) and Solution II (50%) mix in ratio 3:7. Alternatively: (40x + 50y)/(x+y) = 47 gives x/y = 3/7.

The series follows the pattern of n^3 + 1. For n=1, 1^3+1=2; for n=2, 2^3+1=9; for n=3, 3^3+1=28; for n=4, 4^3+1=65. The next term for n=5 is 5^3+1, which equals 125+1 = 126.

The sum of interior angles in any triangle is always 180 degrees. This is a fundamental theorem in geometry - angle sum is constant regardless of triangle type (equilateral, isosceles, or scalene).

To get 125 = 5^3 cubes, make 4 cuts along each dimension. Total cuts = 4+4+4 = 12. Each set of parallel cuts creates one more piece than cuts: 4 cuts → 5 pieces. 5 × 5 × 5 = 125 cubes.

This is a trick question testing attention to detail. Jack started with 2 rabbits, and receiving a turtle doesn't change the number of rabbits he has. The total number of animals is 3, but the question specifically asks about rabbits only.