Bunuel wrote:

When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J?

A. 22

B. 56

C. 78

D. 112

E. 175

\(N,J \ge 1\,\,\,{\rm{ints}}\)

Let´s consider what the

Division Algorithm say!

\(N = QJ + 14\,\,,\,\,\,\left\{ \matrix{

\,Q\,\,{\mathop{\rm int}} \hfill \cr

\,J \ge 15\,\,\,\,\,,\,\,\,\,\,\,? = J\,\, \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\left( * \right)\)

\(134.08 = {N \over J} = Q + {{14} \over J}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\left\{ \matrix{

\,Q = 134 \hfill \cr

\,{{14} \over J} = 0.08 = {8 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = J = {{14 \cdot 100} \over 8} = 7 \cdot 25 = 175 \hfill \cr} \right.\,\,\,\,\)

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

Regards,

Fabio.

_________________

Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or GMATH.com.br (Portuguese version)

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