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City B is 5 miles east of the city A, city C is 10 miles southeast of

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Joined: 02 Sep 2009
Posts: 62499
City B is 5 miles east of the city A, city C is 10 miles southeast of  [#permalink]

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New post 11 Nov 2019, 00:50
1
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A
B
C
D
E

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  95% (hard)

Question Stats:

29% (02:57) correct 71% (02:09) wrong based on 52 sessions

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Re: City B is 5 miles east of the city A, city C is 10 miles southeast of  [#permalink]

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New post 10 Feb 2020, 01:09
2
Bunuel wrote:
City B is 5 miles east of the city A, city C is 10 miles southeast of city B. Which of the following is the closest to the distance from city A to city C?

A. 11 miles
B. 12 miles
C. 13 miles
D. 14 miles
E. 15 miles


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Solution:
    • Here, the keyword is Southeast, which means DBC is exactly 45 degrees.
    Image
    • In right-angle triangle DBC,
      o \(∠DBC = ∠DCB = 45\)
      o It means triangle DBC is an isosceles triangle, and \(BD = CD = x\) (say)
      \(10^2=x^2+x^2\)
      \(x=\frac{10}{√2} \)
    • Now, in right angle triangle ADC,
      o \(AD = AB+BD=5 + \frac{10}{√2}\)
      o \(CD=\frac{10}{√2}\)
      o \(AC^2=(5+\frac{10}{√2})^2+(\frac{10}{√2})^2\)
      \(AC^2=25+\frac{100}{√2}+\frac{100}{2}+\frac{100}{2} \)
      \(AC^2=125+\frac{100}{√2}=125+70 \) \(\ \ \ \ \ \ \ [\frac{100}{√2}=50√2=70(approx.)]\)
      \(AC=√195\), which is nearest to \(14\).
Hence, the correct answer is Option D.
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Re: City B is 5 miles east of the city A, city C is 10 miles southeast of   [#permalink] 10 Feb 2020, 01:09
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