A number of individuals volunteer to walk dogs at a certain kennel this afternoon. The kennel's dogs number between 43 and 47, inclusive. If each dog is walked by only one volunteer this afternoon, can the dogs be divided equally among the volunteers?Given: 43 ≤ number of dogs ≤ 47
i.e. number of dogs can be 43, 44, 45, 46, 47.
Can the dogs be divided equally among the volunteers = is number of dogs divisible by number of volunteers?
Statement 1: More than 5 individuals volunteer to walk the dogs.
We can have a case, in which number of volunteers = 6.
In this case, however, none of 43, 44, 45, 46, 47 is divisible by 6.
Hence, dogs cannot be equally divided among volunteers.
However, we can have another case, in which number of volunteers = 9
In this case, 45 is divisible by 9.
Hence, dogs can be equally divided among volunteers.
So, statement 1 alone is inconclusive
i.e. insufficient.
Statement 2: Fewer than 8 individuals volunteer to walk the dogs.
We can have a case, in which number of volunteers = 7.
In this case, however, none of 43, 44, 45, 46, 47 is divisible by 7.
Hence, dogs cannot be equally divided among volunteers.
However, we can have another case, in which number of volunteers = 4
In this case, 44 is divisible by 4.
Hence, dogs can be equally divided among volunteers.
So, statement 2 alone is inconclusive
i.e. insufficient.
Taking statement 1 and statement 2 together:
More than 5 individuals volunteer to walk the dogs. Also, fewer than 8 individuals volunteer to walk the dogs.
That means, number of volunteers can be either or 6, 7 or 8.
It is already given that number of dogs can be 43, 44, 45, 46, 47.
But, none of 43, 44, 45, 46, 47, 48 is divided by either of 6, 7 or 8.
So, we can conclude that number of dogs will NOT be divisible by number of volunteers.
In question's language, dogs can NOT be divided equally among volunteers.
Answer: CHope it helps.
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