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A large rectangular decorative panel of 45 meters (horizontal dimensio

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GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
A large rectangular decorative panel of 45 meters (horizontal dimensio  [#permalink]

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27 Feb 2019, 14:17
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Difficulty:

45% (medium)

Question Stats:

63% (02:27) correct 38% (03:15) wrong based on 32 sessions

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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

_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMATH Teacher
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 935
Re: A large rectangular decorative panel of 45 meters (horizontal dimensio  [#permalink]

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28 Feb 2019, 05:44
fskilnik wrote:
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

$${\rm{panel}}\,\,:\,\,\,4500\,{\rm{cm}}\,\, \times \,\,\,600\,{\rm{cm}}$$

$$M\,\,{\rm{squares}}\,\,{\rm{:}}\,\,\,k\,{\rm{cm}}\,\, \times \,\,\,k\,{\rm{cm}}\,\,\,{\rm{each}}\,\,\,\,\,\,\,\left( {k \ge 1\,\,{\mathop{\rm int}} } \right)$$

$${\rm{?}}\,\, = \,\,\,\min \left( M \right)$$

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

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

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

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
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Re: A large rectangular decorative panel of 45 meters (horizontal dimensio  [#permalink]

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28 Feb 2019, 10:03
fskilnik wrote:
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

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
Re: A large rectangular decorative panel of 45 meters (horizontal dimensio   [#permalink] 28 Feb 2019, 10:03
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