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?

(1) More than 5 individuals volunteer to walk the dogs.

(2) Fewer than 8 individuals volunteer to walk the dogs.

Kudos for a correct solution.
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number of volunteers are unknown. Dogs can be 43, 44, 45, 46, or 47.
Basically we need to know the number of volunteers and/or number of dogs to see if the two are divisible by each other.

Statement 1: more than 5 volunteers walk the dogs.
if volunteers=11 and dogs equal 44, 44/11 works. Yes
if volunteers equal 6, then none of the dog numbers (43 through 47) would be divisible and and the dogs could not be divided equally. No.
Insufficient

Statement 2: Fewer than 8 volunteers.
if volunteers=5 and dogs equal 45, 45/5 works. Yes
if volunteers=4 and dogs equal 43, 43/4 is not divisible. No
Insufficient

Combined, volunteers equal 6 or 7. None of the potential numbers for dogs, 43, 44, 45, 46, or 47 is divisible by 6 or 7.
So that means the dogs could not be equally distributed among the volunteers.
Sufficient

Answer: C

Actually, both statements together are sufficient.
The number of volunteers is either 6 or 7.
The number of dogs is 43 or 44 or 45 or 46 or 47. All these numbers are not divisible by 6. All of them are also not divisible by 7.
So it doesn't matter exactly how many dogs there are, they will NOT be divisible by the number of volunteers. So the dogs definitely CANNOT be equally divided among the volunteers. We have a definite 'NO' answer and hence the two statements together are sufficient.

Answer (C)
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VERITAS PREP OFFICIAL SOLUTION:


This is a yes/no divisibility question. If we use the variable d to represent the number of dogs, and v to represent the number of volunteers, then the question is whether d/v is an integer.

Obviously, d and v must be integers, because half a dog or volunteer would make no sense. According to the question stem, then, d = 43, 44, 45, 46, or 47.

Testing numbers is probably the best way to evaluate the statements. Start with Statement 1. If v > 5, v could equal 6. If v=6, then d/v is definitely not an integer, because none of the possible values of d are multiples of 6. But what if v=9? If v=9 and d=45, d/v would be an integer. Thus, it’s possible that d=43 and v=6 and the answer is “no”, or that d=45 and v=9 and the answer is “yes”. Statement 1 alone is not sufficient. Eliminate A and D.

Test numbers again to evaluate Statement 2. If v < 8, v could equal 6. We already tried v=6 for Statement 1 alone, and we found that the answer would be “no” when v=6. But what if v=2? If v=2 and d=44, then d/v would be an integer. Thus, it’s possible that d=43 and v=6 and the answer is “no”, or that d=44 and v=2 and the answer is “yes”. Statement 2 alone is not sufficient. Eliminate B.

With both statements combined, we know that v=6 or v=7. If v=6, then every value of d would yield a “no” to the yes/no question. What if v=7? Same scenario. None of the possible values of d – 43, 44, 45, 46, or 47 – is divisible by 7. Thus, with the question stem and both statements combined, we have sufficient information to answer the yes/no question. Specifically, the answer to the yes/no question is a definite “no”, d/v is definitely not an integer. The correct answer is C.
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