A group of students met in the lobby of their school. First, 1/3 of the students were sent to the gym. Then, 1/3 of the remaining students were sent to the cafeteria. Finally, 1/3 of the students still in the lobby were sent to the auditorium, and all the remaining students were sent home. Which of the following could not have been the number of students who originally met in the school lobby? 81 135 162 207 243

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A group of students met in the lobby of their school. First, 1/3 of the students were sent to the gym. Then, 1/3 of the remaining students were sent to the cafeteria. Finally, 1/3 of the students still in the lobby were sent to the auditorium, and all the remaining students were sent home. Which of the following could not have been the number of students who originally met in the school lobby? 81 135 162 207 243

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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let no. of students=x students sent to the gym=x/3 students remaining=x-x/3=2x/3 students sent to cafteria\[=\frac{ 1 }{ 3 }\times \frac{ 2x }{ 3 }=\frac{ 2x }{ 9 }\] remaining students\[=\frac{ 2x }{ 3 }-\frac{ 2x }{ 9 }=\frac{ 4x }{ 9 }\] students sent to auditorium\[=\frac{ 1 }{ 3 }\times \frac{ 4x }{ 9 }=\frac{ 4x }{ 27 }\] students sent home\[=\frac{ 4x }{ 9 }-\frac{ 4x }{ 27 }=\frac{ 8x }{ 27 }\] as no. of students is a natural no. so x should be a multiple of 27 81=27*3 135=27*5 162=27*6 207= 23*9 243=27*9 so 207 is not a multiple of 27 hence 207 is the reqd. no. of students

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