Difficulty: Easy

Average Score: 100%

Martin, a student who has been diagnosed with autism spectrum disorder, receives a variety of services detailed in his Individualized Education Program (IEP). Toward the end of the school year, the IEP team meets to discuss strategies for how Martin can continue to get support over the summer months when school is not in session.

If the range of the average annual earthquake frequencies in the table shown is 9.7, which of the following could be the value of x? (The range of a set of numbers is the difference between the greatest and the least numbers.)

Rationale

15 could be the value of x.

The range of a set of numbers is calculated as the difference between the highest and lowest values. If the average annual earthquake frequency has a range of 9.7, this means that the difference between the largest number and the smallest number in the set must equal 9.7. Therefore, if we assume the smallest number is x, the largest number can be determined as x + 9.7, allowing 15 to be a valid potential maximum.

A (1.3) YOUR ANSWER

If we consider 1.3 as the smallest number (x), the largest number would be 1.3 + 9.7 = 11. This results in a range of 11 - 1.3 = 9.7, which is valid. However, if x is 1.3, it does not provide a maximum value that could result in 15, making it incompatible with the question.

B (9.7) YOUR ANSWER

If we take 9.7 as x, the largest number would be 9.7 + 9.7 = 19.4, resulting in a range of 19.4 - 9.7 = 9.7. While this satisfies the range condition, it does not yield a maximum value of 15, which is specified in the choices.

C (12.7) YOUR ANSWER

Assuming 12.7 as x, the largest number would be 12.7 + 9.7 = 22.4, resulting in a range of 22.4 - 12.7 = 9.7. While this maintains the range, it does not allow for a maximum value of 15, thus failing to meet the criteria set by the question.

D (15) CORRECT

If x is set to 15, the smallest number must be 15 - 9.7 = 5.3. Thus, the range calculation would be 15 - 5.3 = 9.7. This scenario fulfills the requirement of achieving the specified range with 15 as the highest number.

Conclusion

In this multiple-choice question regarding the range of earthquake frequencies, the only option that allows for the maximum value to be 15 while maintaining a range of 9.7 is D. The other options either do not result in a maximum value of 15 or do not fit the criteria for the range calculation. Hence, 15 is the only feasible candidate for x.

If the range of the average annual earthquake frequencies in the table shown is 9.7, which of the following could be the value of x? (The range of a set of numbers is the difference between the greatest and the least numbers.)

15 could be the value of x.

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