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At an animal shelter, each cat and each dog received exactly one treat: either Treat A or Treat B. 84 of the cats received Treat A, and 48 of the dogs received Treat B. How many of the animals received Treat A?
(1) 60% of the cats received Treat A.
(2) 60% of the dogs received Treat B.
(1) 60% of the cats received Treat A.
(2) 60% of the dogs received Treat B.
02 May 2025, 03:31
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Official Solution:
At an animal shelter, each cat and each dog received exactly one treat: either Treat A or Treat B. 84 of the cats received Treat A, and 48 of the dogs received Treat B. How many of the animals received Treat A?
(1) 60% of the cats received Treat A.
This gives \(0.6C = 84\), so \(C = 140\). Hence, 84 cats received Treat A, and the remaining 140 - 84 = 56 cats received Treat B. From this we can deduce that 56 (cats) + 48 (dogs) = 104 of the animals received Treat B. However, the number of dogs receiving Treat A is not known. Not sufficient.
(2) 60% of the dogs received Treat B.
This gives \(0.6D = 48\), so \(D = 80\). Hence, 48 dogs received Treat B, and the remaining 80 - 48 = 32 dogs received Treat A. Therefore, a total of 84 (cats) + 32 (dogs) = 116 of the animals received Treat A. Sufficient.
Answer: B
At an animal shelter, each cat and each dog received exactly one treat: either Treat A or Treat B. 84 of the cats received Treat A, and 48 of the dogs received Treat B. How many of the animals received Treat A?
(1) 60% of the cats received Treat A.
This gives \(0.6C = 84\), so \(C = 140\). Hence, 84 cats received Treat A, and the remaining 140 - 84 = 56 cats received Treat B. From this we can deduce that 56 (cats) + 48 (dogs) = 104 of the animals received Treat B. However, the number of dogs receiving Treat A is not known. Not sufficient.
(2) 60% of the dogs received Treat B.
This gives \(0.6D = 48\), so \(D = 80\). Hence, 48 dogs received Treat B, and the remaining 80 - 48 = 32 dogs received Treat A. Therefore, a total of 84 (cats) + 32 (dogs) = 116 of the animals received Treat A. Sufficient.
Answer: B
