SSAT Math Question 398: Answer and Explanation

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Question: 398

9. At the beginning of March, Alice gave Luke 40% of her baseball card collection. At the end of that month, she decides to give Luke 40% of the remaining cards in her baseball card collection. Out of her original collection, what percent of it does Alice still have?

  • A. 20%
  • B. 24%
  • C. 36%
  • D. 60%

Correct Answer: C

Explanation:

C

Let x represent the number of baseball cards Alice has. When she gives away 40% of those cards, she has 60% left or 0.6x. She then gives away 40% of 0.6x, which is (0.4)(0.6x) or 0.24x. Thus, she has 0.6x – 0.24x left, or 0.36x. That is 36% of the original amount.

As the original amount is not given, plug in a number, such as 100. If she gives Luke 40% of her collection, she gives away 40 baseball cards, leaving Alice with 60 baseball cards. If she gives Luke 40% of the 60 cards she has left, she gives away 24 of her cards, leaving Alice with 36 baseball cards, As she started with 100, 36 represents 36%.

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