3 & 4 Legged Tables

Question

Several three-legged tables and four-legged table have a total of 23 legs. If there is more than one table of each type, what is the number of three-legged tables?

A) 6

B) 7

C) 3

D) 4

E)  5

Answer
The simplest way of doing this is by writing out the number of legs in a table (shown below)

Tables	‘3 Legged’ Tables	‘4 Legged’ Tables	To Make 23
1	3	4
2	6	8	15
3	9	12	11 (not a multi. of 3)
4	12	16	7 (not a multi. of 3)
5	15	20
6	18	24
7	21
8	24

As shown above:

• 8 legs are allowed '4 legged table'
• 15 legs are allowed '3 legged table'

So: 5 = 3 'legged table'

       2 = 4 'legged table'   

E = 5