alanforde800Maximus wrote:
A lecture course consists of 595 students. The students are to be divided into discussion sections, each with an equal number of students.
Which of the following cannot be the number of students in a discussion section.
a) 17
b) 35
c) 45
d) 85
e) 119
\(\frac{{N\,\,{\text{students}}}}{{{\text{section}}}}\)
\(?\,\,:\,\,N\,\,{\text{impossible}}\)
\({\text{595}}\,\,{\text{students}}\,\,\,\,{\text{ = }}\,\,\,\,{\text{M}}\,\,{\text{sections}}\,\,\left( {\frac{{N\,\,{\text{students}}}}{{{\text{section}}}}} \right)\)
\(\left\{ \begin{gathered}
M \cdot N = 595 \hfill \\
M,N\,\, \geqslant 1\,\,{\text{ints}} \hfill \\
\end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,\,M\,\,{\text{and}}\,\,N\,\,{\text{are}}\,\,{\text{pairs}}\,\,{\text{of}}\,\,\underline {{\text{divisors}}} \,\,{\text{of}}\,\,595\)
\(\frac{{500 + 50 + 45}}{5} = 119\,\,\,\, \Rightarrow \,\,\,\,595 = 5 \cdot 119\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{refute}}\,\,\left( E \right)\)
\(\frac{{119}}{7} = \frac{{70 + 28 + 21}}{7} = 17\,\,\,\, \Rightarrow \,\,\,\,119 = 7 \cdot 17\,\,\,\,\,\, \Rightarrow \,\,\,\,\,{\text{refute}}\,\,\left( A \right),\left( B \right),\left( D \right)\,\,\,\,\,\,\left[ {\frac{{85}}{5} = \frac{{50 + 35}}{5} = 17 \Rightarrow 85 = 5 \cdot 17} \right]\)
The correct answer is therefore (C).
We follow the notations and rationale taught in the
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Regards,
Fabio.
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