ISEE Word Problems Question 298: Answer and Explanation

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Question: 298

17. The normal number of days of rain per year in City A is 20, and this year's number of days of rain was within 5 days of the normal number. If this year's number of days of rain was R, which one of the following best describes this scenario?

  • A. |R – 5| ≤ 20
  • B. |R – 5| ≥ 20
  • C. |R – 20| ≤ 5
  • D. |R – 20| ≥ 5

Correct Answer: C

Explanation:

C

To determine whether a specified value is within a given range around a middle or normal 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, R is the specified value, 20 is the middle value, and 5 is the given range, so |R – 20| ≤ 5.

Plug in a permitted value for R, such as 22. Test 22 in each answer. For choice (A), |22 – 5| ≤ 20. This is true, so keep choice (A). For choice (B), |22 – 5| ≥ 20. This is false, so eliminate choice (B). For choice (C), |22 – 20| ≤ 5. This is true, so keep choice (C). For choice (D), |22 – 20| ≥ 5. This is false, so eliminate choice (D). As two answers remain, try a value for R that is not permitted, such as 13. In this case, the equation should fail, as 13 is not permitted. For choice (A), |13 – 5| ≤ 20

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