A large rectangular decorative panel of 45 meters (horizonta

[fskilnik@GMATH]

GMATH practice exercise (Quant Class 16)

A large rectangular decorative panel of 45 meters (horizontal dimension) by 6 meters (vertical dimension) is to be completely divided into M identical squares, all of them with horizontal and vertical edges. If the smallest measure of length considered for the edges is centimeters (1 meter = 100 centimeters), what is the minimum possible value of M?

(A) 30
(B) 60
(C) 75
(D) 150
(E) 180

Answer: [spoiler]_____(A)___[/spoiler]

[fskilnik@GMATH]

GMATH practice exercise (Quant Class 16)

A large rectangular decorative panel of 45 meters (horizontal dimension) by 6 meters (vertical dimension) is to be completely divided into M identical squares, all of them with horizontal and vertical edges. If the smallest measure of length considered for the edges is centimeters (1 meter = 100 centimeters), what is the minimum possible value of M?

(A) 30
(B) 60
(C) 75
(D) 150
(E) 180

$${\rm{panel}}\,\,:\,\,\,4500\,{\rm{cm}}\,\, \times \,\,\,600\,{\rm{cm}}$$
$$M\,\,{\rm{squares}}\,\,{\rm{:}}\,\,\,k\,{\rm{cm}}\,\, \times \,\,\,k\,{\rm{cm}}\,\,\,{\rm{each}}\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)$$
$${\rm{?}}\,\, = \,\,\,\min \left( M \right)$$

$$\left. \matrix{
{{4500} \over k} = {{{2^2} \cdot {3^2} \cdot {5^3}} \over k} = {{\mathop{\rm int}} _1}\,\,\,\,\left[ {\# \,\,{\rm{columns}}} \right]\,\, \hfill \cr
{{600} \over k} = {{{2^3} \cdot 3 \cdot {5^2}} \over k} = {{\mathop{\rm int}} _2}\,\,\,\,\,\,\left[ {\# \,\,{\rm{rows}}} \right] \hfill \cr} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = \min \left( {{{{\mathop{\rm int}} }_1} \cdot {{{\mathop{\rm int}} }_2}} \right)$$

$$?\,\,\,:\,\,\,k = GCF\left( {4500,600} \right) = {2^2} \cdot 3 \cdot {5^2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{
\,{{\mathop{\rm int}} _1} = 3 \cdot 5 \hfill \cr
\,{{\mathop{\rm int}} _2} = 2 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 30$$


The correct answer is (A).


We follow the notations and rationale taught in the GMATH method.

Regards,
Fabio.