Question
Akhilesh has a collection of toys, and he tries
arranging them in different group sizes. Whenever he groups them in pairs (2s), triplets (3s), sets of four (4s), bundles of five (5s), or groups of six (6s), he always has one toy left over. However, when he arranges them in groups of seven (7s), there are no toys left ungrouped. What is the smallest number of toys Akhilesh could possibly have?Solution
L.C.M of (2, 3, 4, 5, 6) = 60
So according to the first condition total number of toys with Akhil = 60p + 1
Now according to the second condition, total number of toys = 7q
Since number of toys is same hence, 60p + 1 = 7q
When p = 5 then q = 43
Therefore minimum number of toys = 60 X 5 + 1 = 301
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