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30 May 2026, 08:19
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Two animal shelters, Cedar Shelter and Harbor Shelter, each house only cats and dogs. Cedar Shelter has more cats than dogs while Harbor Shelter has more dogs than cats. Does Cedar Shelter have more animals in total than Harbor Shelter?
(1) The number of cats at Harbor Shelter is 2 more than twice the number of dogs at Cedar Shelter.
(2) The number of cats at Cedar Shelter is 2 more than twice the number of dogs at Harbor Shelter.
(1) The number of cats at Harbor Shelter is 2 more than twice the number of dogs at Cedar Shelter.
(2) The number of cats at Cedar Shelter is 2 more than twice the number of dogs at Harbor Shelter.
30 May 2026, 08:19
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Official Solution:
Two animal shelters, Cedar Shelter and Harbor Shelter, each house only cats and dogs. Cedar Shelter has more cats than dogs while Harbor Shelter has more dogs than cats. Does Cedar Shelter have more animals in total than Harbor Shelter?
(1) The number of cats at Harbor Shelter is 2 more than twice the number of dogs at Cedar Shelter.
Let \(x\) be the number of dogs at Cedar. Then Harbor has \(2x + 2\) cats, but Harbor’s number of dogs is still unknown other than being greater than its cats. Cedar’s number of cats is also unknown other than being greater than \(x\). So Cedar’s total could be smaller than Harbor’s or larger than Harbor’s. Not sufficient.
(2) The number of cats at Cedar Shelter is 2 more than twice the number of dogs at Harbor Shelter.
Harbor Shelter has more dogs than cats, so if it has \(y\) dogs, then it has fewer than \(2y\) animals in total. Statement (2) says Cedar Shelter has \(2y + 2\) cats. Since Cedar Shelter has at least \(2y + 2\) animals in total, Cedar must have more animals than Harbor. Sufficient.
Answer: B
Two animal shelters, Cedar Shelter and Harbor Shelter, each house only cats and dogs. Cedar Shelter has more cats than dogs while Harbor Shelter has more dogs than cats. Does Cedar Shelter have more animals in total than Harbor Shelter?
(1) The number of cats at Harbor Shelter is 2 more than twice the number of dogs at Cedar Shelter.
Let \(x\) be the number of dogs at Cedar. Then Harbor has \(2x + 2\) cats, but Harbor’s number of dogs is still unknown other than being greater than its cats. Cedar’s number of cats is also unknown other than being greater than \(x\). So Cedar’s total could be smaller than Harbor’s or larger than Harbor’s. Not sufficient.
(2) The number of cats at Cedar Shelter is 2 more than twice the number of dogs at Harbor Shelter.
Harbor Shelter has more dogs than cats, so if it has \(y\) dogs, then it has fewer than \(2y\) animals in total. Statement (2) says Cedar Shelter has \(2y + 2\) cats. Since Cedar Shelter has at least \(2y + 2\) animals in total, Cedar must have more animals than Harbor. Sufficient.
Answer: B
