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13 Mar 2019, 07:54
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GMATH practice exercise (Quant Class 2)
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
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
13 Mar 2019, 10:07
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Try to imagine the given graph as it would be plotted on the first quadrant region. Then,
\(A (1,5); \\
C(9,3);\\
B(12,0)\)
Let's compute the distance. Roughly,
\(AC = \sqrt{(9-1)^2 + (3-5)^2}= \sqrt{64 + 4} = \sqrt{68}\)
\(CB = \sqrt{3^2 + 3^2} = \sqrt{18}\)
Hence \(\sqrt{68} + \sqrt{18} = 2\sqrt{17} + 3\sqrt{2} = 8 + 4.5 = 12.5 cm\)
\(12.5cm = 1250 km\)
\(A (1,5); \\
C(9,3);\\
B(12,0)\)
Let's compute the distance. Roughly,
\(AC = \sqrt{(9-1)^2 + (3-5)^2}= \sqrt{64 + 4} = \sqrt{68}\)
\(CB = \sqrt{3^2 + 3^2} = \sqrt{18}\)
Hence \(\sqrt{68} + \sqrt{18} = 2\sqrt{17} + 3\sqrt{2} = 8 + 4.5 = 12.5 cm\)
\(12.5cm = 1250 km\)
13 Mar 2019, 11:40
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fskilnik
\(?\,\,\, \cong \,\,\,AC + CB\,\,\,\,\left[ {{\rm{km}}} \right]\)
\(\left[ {{\rm{cm}}} \right]\,\,\,::\,\,\,\left\{ \matrix{\\
AC = \sqrt {{2^2} + {8^2}} = \sqrt {{2^2} \cdot 17} = 2\sqrt {17} \,\,\,\mathop > \limits^ \approx \,\,\,8\,\,\,\,\left[ { = 2\sqrt {16} } \right] \hfill \cr \\
CB = \,\,3\sqrt 2 \,\, \cong \,\,3 \cdot 1.41 = 4.23 \hfill \cr} \right.\)
\(? = AC + CB\,\,\,\, \cong \,\,\,12.23 \cdot 100\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\text{B}} \right)\,\,{\text{or}}\,\,\left( C \right)\,\,\, \ldots \,\,\,\,\underline {{\text{approx}}{\text{.}}\,\,{\text{improvement}}\,\,\,{\text{needed}}} !\)
\(\left\{ \matrix{\\
\sqrt {17} \cong 4 + {a \over {10}}\,\,\,\, \Rightarrow \,\,\,\,\,17 = 16 + {8 \over {10}}a + {{{a^2}} \over {100}}\,\,\,\, \Rightarrow \,\,\,a = 1 \hfill \cr \\
2\sqrt {17} \cong 2 \cdot 4.1 = 8.2 \hfill \cr} \right.\)
\(? = AC + CB\,\,\,\, \cong \,\,\,12.43 \cdot 100\,\,\,\,\, \Rightarrow \,\,\,\,\,\left( {\rm{B}} \right)\,\)
We follow the notations and rationale taught in the GMATH method.
Regards,
Fabio.
