Brain teaser

Question

From a basket of mangoes when counted in twos there was one extra,counted in threes there were two extra,counted in fours there were three extra, counted in fives there were four extra, counted in sixes there were five extra. But when counted in seven there were no extra. Atleast how many mangoes were there in the basket? (show the process)

Answer 1

find the LCM of 2, 3, 4, 5, and 6

2=2

3=3

4=2*2

5=5

6=2*3

LCM=2*3*2*5=60

60-1=59, but 59 is not divisible by 7

try 120

120-1=119 and 119/7=17

there are at least 119 mangoes in the basket