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An airplane leaves city A to make a connection in city C, be

by fskilnik@GMATH » Wed Mar 13, 2019 6:44 am

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GMATH practice exercise (Quant Class 2)

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An airplane leaves city A to make a connection in city C, before going on to city B (as shown in the map). If the map scale is 1cm=100km, which of the following is closest to the minimum possible distance covered by the airplane from city A to city B, through city C?

(A) 1300 km
(B) 1250 km
(C) 1200 km
(D) 1150 km
(E) 1100 km

Answer: [spoiler]_____(B)__[/spoiler]
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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by fskilnik@GMATH » Wed Mar 13, 2019 10:31 am
fskilnik@GMATH wrote:GMATH practice exercise (Quant Class 2)


Image

An airplane leaves city A to make a connection in city C, before going on to city B (as shown in the map). If the map scale is 1cm=100km, which of the following is closest to the minimum possible distance covered by the airplane from city A to city B, through city C?

(A) 1300 km
(B) 1250 km
(C) 1200 km
(D) 1150 km
(E) 1100 km
Image

$$?\,\,\, \cong \,\,\,AC + CB\,\,\,\,\left[ {{\text{km}}} \right]$$
$$\left[ {{\rm{cm}}} \right]\,\,\,::\,\,\,\left\{ \matrix{
AC = \sqrt {{2^2} + {8^2}} = \sqrt {{2^2} \cdot 17} = 2\sqrt {17} \,\,\,\mathop > \limits^ \approx \,\,\,8\,\,\,\,\left[ { = 2\sqrt {16} } \right] \hfill \cr
CB = \,\,3\sqrt 2 \,\, \cong \,\,3 \cdot 1.41 = 4.23 \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\,\,$$
$$? = AC + CB\,\,\,\, \cong \,\,\,12.23 \cdot 100\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\text{B}} \right)\,\,{\text{or}}\,\,\left( C \right)\,\,\, \ldots \,\,\,\,\underline {{\text{approx}}{\text{.}}\,\,{\text{improvement}}\,\,\,{\text{needed}}} !$$

$$\left\{ \matrix{
\sqrt {17} \cong 4 + {a \over {10}}\,\,\,\, \Rightarrow \,\,\,\,\,17 = 16 + {8 \over {10}}a + {{{a^2}} \over {100}}\,\,\,\, \Rightarrow \,\,\,a = 1 \hfill \cr
2\sqrt {17} \cong 2 \cdot 4.1 = 8.2 \hfill \cr} \right.$$
$$? = AC + CB\,\,\,\, \cong \,\,\,12.43 \cdot 100\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\text{B}} \right)\,$$

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

Regards,
Fabio.
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
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