Baa Ram Ewe...
A flock of less than 200 sheep lived together in a distant farm.
One day, 3 sheep were killed by the wolves, and the remaining sheep could be herded in equal rows of 7.
Then 2 sheep were sold off by their owner, and the remaining sheep could be herded in equal rows of 6.
Finally, 1 new lamb was born, and now the herd could get in equal rows of 5.
What was the total number of sheep at the start?
The answer is 59.
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1 solution
Let the total no. of sheep be x, then ATQ, 7|x-3, 6|x-5 and 5|x-4. So, there are three consecutive numbers which are divisible by 6, 5 and 7 in increasing order. If we go on checking the multiples of 5, we can easily get 55 as the number where the condition is satisfied, i.e. 6|54, 5|55 and 7|56, or we can say that 7|59-3, 6|59-5 and 5|59-4. Thus, the answer is 59 .