BTGmoderatorDC 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
Source: Magoosh
\[N,J \geqslant 1\,\,\,{\text{ints}}\]
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.
