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27 Feb 2019, 15:17
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A
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Difficulty:
35%
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Question Stats:
73% (02:21) correct
27%
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wrong
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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
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
28 Feb 2019, 06:44
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fskilnik
\({\rm{panel}}\,\,:\,\,\,4500\,{\rm{cm}}\,\, \times \,\,\,600\,{\rm{cm}}\)
\(M\,\,{\rm{squares}}\,\,{\rm{:}}\,\,\,k\,{\rm{cm}}\,\, \times \,\,\,k\,{\rm{cm}}\,\,\,{\rm{each}}\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)\)
\({\rm{?}}\,\, = \,\,\,\min \left( M \right)\)
\(\left. \matrix{\\
{{4500} \over k} = {{{2^2} \cdot {3^2} \cdot {5^3}} \over k} = {{\mathop{\rm int}} _1}\,\,\,\,\left[ {\# \,\,{\rm{columns}}} \right]\,\, \hfill \cr \\
{{600} \over k} = {{{2^3} \cdot 3 \cdot {5^2}} \over k} = {{\mathop{\rm int}} _2}\,\,\,\,\,\,\left[ {\# \,\,{\rm{rows}}} \right] \hfill \cr} \right\}\,\,\,\, \Rightarrow \,\,\,\,? = \min \left( {{{{\mathop{\rm int}} }_1} \cdot {{{\mathop{\rm int}} }_2}} \right)\)
\(?\,\,\,:\,\,\,k = GCF\left( {4500,600} \right) = {2^2} \cdot 3 \cdot {5^2}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left\{ \matrix{\\
\,{{\mathop{\rm int}} _1} = 3 \cdot 5 \hfill \cr \\
\,{{\mathop{\rm int}} _2} = 2 \hfill \cr} \right.\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,? = 30\)
The correct answer is (A).
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
Archit3110
Major Poster
28 Feb 2019, 11:03
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fskilnik
length = 45* 100 ; 4500 mtrs ; 3^2 *5^3 * 2^2
width= 600 mtrs; 2^3* 3*5^2
GCF ; 2^2*3*5^2
2*3*5 ; 30 min value ..
IMO A
