Random Puzzles 

Workings

Hint
This is a tricky question related to number bases.

Answer
200.

Each number in the sequence is a representation of the number 32 in different bases, starting with base 10.
Base 10: 32  = 3 x 10^1 + 2 x 10^0          = 3 x 10 + 2         = 32
Base 9 : 35  = 3 x 9^1  + 5 x 9^0           = 3 x 9 + 5          = 32
Base 8 : 40  = 4 x 8^1  + 0 x 8^0           = 4 x 8 + 0          = 32
Base 7 : 44  = 4 x 7^1  + 4 x 7^0           = 4 x 7 + 4          = 32
Base 6 : 52  = 5 x 6^1  + 2 x 6^0           = 5 x 6 + 2          = 32
Base 5 : 112 = 1 x 5^2  + 1 x 5^1 + 2 x 5^0 = 1 x 25 + 1 x 5 + 2 = 32
Base 4 : 200 = 2 x 4^2  + 0 x 4^1 + 0 x 4^0 = 2 x 16 + 0 + 0     = 32

Workings

Hint
A little algebra might help.

Answers
Drew is 7 years old. Glen is 4 years old.
Answer #1
The first question involves Drew (D) and Alex (A).

Drew is currently one fifth of Alex's age, so:

(1)      A = D x 5

In 21 years, Alex will be twice their age, so:

(2) A + 21 = (D + 21) x 2

Using (1) in (2) gives:

  A + 21 = (D + 21) x 2

 5D + 21 = (D + 21) x 2

 5D + 21 = 2D + 42

      3D = 21

       D = 7

So Drew is 7 (and Alex is 35).

Answer #2
The second question involves Glen (G) and Billie (B).

Billie is exactly seven times the age of Glen:

(3)     B = G x 7

In 8 years, Billie will be three times the age of Glen, so:

(4) B + 8 = (G + 8) x 3

Using (3) in (4) gives:

  B + 8 = (G + 8) x 3

 7G + 8 = (G + 8) x 3

 7G + 8 = 3G + 24

     4G = 16

      G = 4

So Glen is 4 (and Billie is 28).

Workings

Hints
The first letters of the words are: C, A, C, B, L, L, P, S, C.

Answers
coagulate = catalogue cavitates = activates bacterial = calibrate balancers = barnacles headlamps = lampshade milestone = limestone or lemoniest telephony = polythene dignifies = signified unnoticed = continued

Workings

Hint
The sequence involves both adding and multiplying in some way.

Answer
153.

The sequence is created using: +1 x1 +2 x2 +3 x3 +4 x4 +5.