ISEE Word Problems Question 249: Answer and Explanation

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Question: 249

13. In a certain city, the average height for men over 18 years old is 70 inches. All men in the city are within 5 inches of the average height. If m represents the height of a man in the city, which best describes the man's height?

  • A. |m – 5| ≤ 70
  • B. |m – 5| ≥ 70
  • C. |m – 70| ≥ 5
  • D. |m – 70| ≤ 5

Correct Answer: D

Explanation:

The answer is D

To determine whether a specified value is within a given range around a middle or average value, subtract the middle value from the specific value, take the absolute value of that difference, and determine whether the result is less than or equal to the given range. That is |specific - middle| ≤ range. In this case, m is the specified value, 70 is the middle value, and 5 is the given range, so |m - 70| ≤ 5.

Plug in a permitted value for m, such as 72. Test 72 in each answer. For choice (A), |72 - 5| ≤ 70. This is true, so keep choice (A). For choice (B), |72 - 5| ≥ 70. This is false, so eliminate choice (B). For choice (C), |72 - 70| ≥ 5. This is false, so eliminate choice (C). For choice (D), |72 - 70| ≤ 5. This is true, so keep choice (D). As two answers remain, try a value for m that is not permitted, such as 60. In this case, the equation should fail, as 60 is not permitted. For choice (A), |60 -

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