Turkish wrote:

62 candies were equally distributed to a group of children. If the number of candies left were two less than the number of children then which of the following CANNOT be the number of candies received by each child?

a.1

b.3

c.7

d.9

e.15

\(\left. \matrix{

{\rm{\# children}}\,\,\,{\rm{:}}\,\,\,n \ge 2\,\,{\mathop{\rm int}} \hfill \cr

{\rm{\# candies/child}}\,\,\,{\rm{:}}\,\,\,c \ge 1\,\,{\mathop{\rm int}} \,\, \hfill \cr} \right\}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,nc\,\,\,{\rm{candies}}\,\,{\rm{distributed}}\)

\(?\,\,\,:\,\,\,c\,\,\,\underline {{\text{CANNOT}}}\)

\(62 - nc = n - 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,n\left( {c + 1} \right) = 64\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\text{FOCUS}}\,!} \,\,\,\,c + 1\,\,{\text{is}}\,\,{\text{a}}\,\,{\text{positive}}\,\,{\text{divisor}}\,\,{\text{of}}\,\,64\,\,\,\,\left( * \right)\)

\(?\,\,\mathop = \limits^{\left( * \right)} \,\,\left( D \right)\,\,\,\,\,\,\,\left[ {\,10\,\,{\text{is}}\,\,{\text{not}}\,\,{\text{a}}\,\,{\text{positive}}\,\,{\text{divisor}}\,\,{\text{of}}\,\,64\,} \right]\,\,\,\,\,\)

This solution follows the notations and rationale taught in the GMATH method.

Regards,

Fabio.

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Fabio Skilnik :: GMATH method creator (Math for the GMAT)

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