SSAT Math Question 651: Answer and Explanation

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Question: 651

6. One six-foot Italian hero serves either 12 children or 8 adults. Approximately how many sandwiches do you need to feed a party of 250, 75 of whom are children?

  • A. 21
  • B. 24
  • C. 29
  • D. 30

Correct Answer: C

Explanation:

Take this question one step at a time. If there are 250 people and 75 are children, then there are 175 adults. If one hero sandwich could feed 12 children and there are 75 children at the party, find how many sandwiches are needed for the 75 children: 12 goes into 75 six times evenly since 6 × 12 = 72, which leaves a remainder of 3 children. Part of another sandwich will be needed to feed those children. Therefore, the 75 children will need 6+ sandwiches. Now, do the same for the adults. There are 175 adults at the party. Each hero sandwich can feed 8 adults. 8 only goes into 175 twenty-one times evenly since 8 × 21 = 168. That will leave a remainder of 7 adults (175 - 168 = 7). Remember, 1 sandwich feeds 8 adults, so if there are 7 adults left, you need almost an entire sandwich more. That makes about 22 sandwiches to feed all the adults. 22 + 6 = 28. Remember that a little more than 6 sandwiches were needed to feed all the children (no half-sandwich orders allowed!). Round up, so 29 sandwiches will be needed to feed the entire group. The correct answer is (C). Ballparking is okay here! Note that the next closest answer is 30, which is too many (3 extra sandwiches are not needed), so both (D) and (E) are too large. Choices (A) and (B) are too small even before taking the remainders into account, which makes (C) is the best answer!

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