At an animal shelter, the ratio of cats to dogs is 3 to 5. After 6 more dogs arrive, the ratio of cats to dogs becomes 1 to 2. How many cats are at the shelter?
- A12
- B15
- C18
- D21
- E24
Practice bank ยท Quant
Ratios after new arrivals: keep the multiplier
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Correct answer: C
Keep the ratio in multiplier form. Let cats = 3k and dogs = 5k for some positive number k. The cat count never changes, only the dogs increase.
Set up the new ratio:
3k / (5k + 6) = 1/2
Cross-multiply: 6k = 5k + 6, so k = 6.
Cats = 3k = 18.
Check: originally 18 cats and 30 dogs. Six dogs arrive, making 36 dogs, and 18:36 = 1:2. Correct.
The traps reward partial setups: (E), 24, treats the 6 new dogs as if the total grew in ratio (solving 3k/(5k+6) = 3/5 type errors). (A), 12, solves for dogs at the start using k = 4 from a cross-multiplication slip. (D), 21, comes from adding 3 to 18 after the check step.
Note the structure: one quantity fixed, one changing, and a new ratio. That template covers a large family of GMAT and GRE ratio problems, and the multiplier k is almost always the cleanest way in.