Aptitude - Puzzle

Questions 

1) x**(1/3) - x**(1/9) = 60 note: ** is power of symbol find x? ans: 4**9. or 64*64*64 both ans are same.

2)x,y,z are different digits.find them using the following addition
  x y z
  x z y
  -----
  z y x
  -----
 ans: x=4, y=5, z=9;

3)One person chooses a number between 1 - 1000 including 1 and 1000. Then other person chooses a number from same limit. then what is the probability that other person chooses the number less than first one. 

     ans:999/2000 =0.4995

4)51 teams are there and they are to play basketball matches. A team is out of the tournament if that looses 2 games. what is the maximum number of games to be played to decide one winner. ans:101 matches

5) Two persons A and B met. A told B " myself and my 3 cousins have ages which are prime numbers and sum of our ages is 50. If you know my age then you can tell their ages. what are the ages of cousins?" ans: 3,2,2 and myself is 43
6)Two ships start from the opposite banks of river perpendicular to banks. Both are going at constant speed. One is faster than the other. They meet at 720 m from nearest bank. Then they go ahead upto the other end of banks and wait there for 10 minutes. Then they again comeback and meet 400m farfrom the other bank. find out what is the width of river. ans: 1720 check again

7)the following balance is perfectly balanced with weights.

2m  6m
----------------

15kg c

----------------
5m   3m 
----------- 80kg

B A
find values of A, B and C (some lengths of arms are not available with us) ans: 100,60,85.

8)Both the guptas and sinhas have two young sons whose ages are under eleven. The names of the boys, whose ages roundedoff to the nearest year are all different, are rajesh, praveen, lalith and prathap. taking the ages of the boys only to the nearest year, the following statements are true
1) rajesh is 3 years younger than his brother is
2) praveen is the oldest
3) prathap is 5 years older than the younger sinhas boy.
4) lalith is half as old as one of the gupta boys.
5) the total ages of the boys in each family differ by the same amount today as they did five years ago.
   ans: gupta sinha
  pratap=10 praveen=11
   rajesh=7 lalit=5

9)A,B.C are 3 students. they have taken 3 subjects out of 4 subjects biology, maths,history,chemistry. A,B,C given
following statements of four each. out of those 2 are true and 2 are false of each one. find out the subjects taken by them.
A statements:
a)we take only one subjects in common.
b)no two of us have all subjects common.
c)only i take maths
d)if c tells that me and B are taken chemistry,then it is wrong.
B statements:
a)we only take biology common
b)me and c have all subjects common
c)two of us have taken both biology and chemistry.
d)
C statements:
a)we only take maths
b)A and B are taking chemistry
c)A has taken a subject that i have not taken

10)6 students are there. they are friends since childhood. after they grown us they became 3 couples. that is they are 3 boys and 3 girls. say a,b,c,d,e,f.the following are the statements given
1)b is the oldest girl
2)some of the ages of any two couples are same
3) d is the brother of a
4) sum of the ages of b and e equal to that of c and f. find out the couples. essay: internet revolution.