1) A 31" x 31" square metal plate needs to be fixed by a carpenter on to a wooden board. The carpenter uses nails all along the edges of the square such that there are 32 nails on each side of the square. Each nail is at the same distance from the neighboring nails. How many nails does the carpenter use? 

Solution:
32*2 + 30*2=124

2) It was vacation time, and so I decided to visit my cousin's home. What a grand time we had! In the mornings, we both would go for a jog. The evenings were spent on the tennis court. Tiring as these activities were, we could manage only one per day, i.e., either we went for a jog or played tennis each day. There were days when we felt lazy and stayed home all day long. Now, there were 12 mornings when we did nothing, 18 evenings when we stayed at home, and a total of 14 days when we jogged or played tennis. For how many days did I stay at my cousin's place?

Solution :
Use sets and venn diagram to solve such questions.a,b ,aub,anb etc.
12=tennis+leave
18=jog+leave
so jog-tennis=6
again jog+tennis=14.so solve and get jog=10,leave=8,tennis=4.so tot=22

3) Glenn and Jason each have a collection of cricket balls. Glenn said that if Jason would give him 2 of his balls they would have an equal number; but, if Glenn would give Jason 2 of his balls, Jason would have 2 times as many balls as Glenn. How many balls does Jason have?

Solution:
R 14
1. G+2=j-2
2. 2(G-2)=J+2.
solve these 2 to get
J=14

4) How many even integers n, where , are divisible neither by seven nor by nine?
                                                                                              

Solution:
There are 101 integers in all, of which 51 are even.From 100 to 200, there are 14 multiples of 7, of which 7 are even. There are 11 multiples of 9, of which 6 are even.But there is one integer (i.e. 126) that is a multiple of both 7 and 9 and also even.Hence the answer is (51 – 7 – 6 + 1) = 39