15. A total of 2021 people were interviewed concerning their breakfast-eating habits. Between 1/4 and 1/5 of the people interviewed indicated that they did not eat breakfast. Which of the following could be the number of people interviewed who indicated that they did not eat breakfast?
Answer: B
451 could be the number of people interviewed who indicated that they did not eat breakfast.
Between 1/4 and 1/5 of the total 2021 people interviewed represents a range of approximately 404 to 505 individuals. The number 451 falls within this range, making it a possible answer.
A) 398
398 is not a valid choice because it is below the lower limit of the range calculated from the fraction of people who do not eat breakfast. Since 1/4 of 2021 is approximately 505, 398 does not meet the requirement.
B) 451
451 is a valid option as it lies between the calculated limits of 404 and 505. This number fits within the specified range of 1/4 and 1/5 of the total interviewed individuals, confirming its correctness.
C) 511
511 exceeds the upper limit of 505, which corresponds to 1/4 of the total. Therefore, it cannot be the number of people who indicated they do not eat breakfast as it falls outside the defined range.
D) 546
546 is also outside the range derived from the fractions provided. It significantly exceeds the upper limit of 505, thereby invalidating it as a possible number of people who did not eat breakfast.
Conclusion
The correct answer is 451, as it is the only option that falls within the range of individuals who indicated they do not eat breakfast based on the given fractions. Other options fail to meet the criteria established by the percentages of the total interviewed.