A tree.

64

The series consists of squares and cubes of consecutive natural numbers i.e. 1^2, 1^3, 2^2, 2^3, 3^2, 3^3.
4^3 = 64.

A catcher and an umpire.

Fly.

A spider.

155 is the least number when divided by 36, 24 and 16 leaves 11 as remainder in each case.

Given numbers: 16, 24, 26

Finding LCM which is Lowest Common Factor is
LCM = 2 × 2 × 2 × 3 × 1 × 2 = 144

144 is the LCM of 36, 24 and 16.

Given condition leaving 11 as reminder

By adding 11 to LCM = 11+144 = 155

155 is the least number when divided by 36, 24 and 16 leaves 11 as remainder in each case.

I’m nuts about you!

He goes up to one guard and asks " If I ask the other guard which door leads too freedom, what will he say?" he then goes into the opposite door.
So if he asks the lying guard the guard, the guard would say the prison door, because he lies. But if he asks the truthful guard, knowing his companion would lie, points to the prison door.

20, 22, 24, 26

2n + (2n + 2) + (2n + 4) + (2n + 6) = 92
8n + 12 = 92 => 8n = 80 => n = 10
2n = 20

Hold its nose.

6 because 10 divided by 2 is 5 then minus one from friend and add one from me and I have 6.

1.

30/45 of 144 = 6/9 x 144 = 96
19/57 of 96 = 1/3 x 96 = 32
12.5% of 32 = 4
17/68 of 4 = 1/4 x 4 = 1