You grossly underestimated the time this question took you. You actually solved it in 6 minutes and 43 seconds.
Numbers in the answer choices and a specific question ("How many candies...") call for Plugging In The Answers. You may feel like jotting down an equation or more. This is just your algebraic urge, which is another stop sign for Reverse PI problems.
Start with answer choice C - assume the amount in the answer choice is the number of candies Rebecca has now, and then follow the story in the problem. If everything fits - stop. Pick it. Otherwise - POE and move on, until you find an answer that works.
Start with answer choice C. If Rebecca has 54 candies, then she had 54-24=30 candies to begin with. Since the question states that Tina and Rebecca had the same number of candies originally, this means that Tina also had 30 candies. Therefore, after giving 24 candies to Rebecca, Tina should now have 30-24=6 left and Rebecca 54, but that means that Rebecca has 9 times more than Tina, not 5 (as the question stipulates). So you should eliminate C. Which direction should you go now?
The answer is 'not sure', so test either way. Check answer choice B. If Rebecca has 48 candies now, she and Tina had 24 each to begin with, so now Rebecca has all the candies and Tina has none, which doesn't fit the question. POE B and A as well, because A would result in even less candies for Tina. Plug in D or E to check which is correct.
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The correct answer is E.
If Rebecca has 60 candies, it means that she and Tina had 36 candies. Now Tina has 36-24=12, exactly a fifth of the amount Rebecca has.
Note: knowing that the number of Rebecca's candies is a multiple of 5, you can also automatically eliminate all the answer choices which are not divisible by 5. Noticing that makes your life a whole lot easier, as it leaves you with D or E.