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Dan and Karen, who live 10 miles apart meet at a cafe that

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Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink]

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New post 11 Oct 2012, 08:26
. Dan and Karen, who live 10 miles apart meet at a cafe that is directly north of Dan’s house and directly east of Karen’s house. If the cafe is 2 miles closer to Dan’s house than to Karen’s house, how many miles is the cafe from Karen’s house?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
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Re: misecellaneous [#permalink]

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New post 16 Oct 2012, 09:19
Shouldn't it be 8 km from Karen’s house. Ans choice (c)

They form a right triangle with the hypotenuse as 10 and then the possible values are 6 and 8 , given that the coffee house is 2 km closer to Daren house; so distance b/w daren and the coffee house would be 6
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Re: misecellaneous [#permalink]

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New post 16 Oct 2012, 09:46
abhishek1990p wrote:
. Dan and Karen, who live 10 miles apart meet at a cafe that is directly north of Dan’s house and directly east of Karen’s house. If the cafe is 2 miles closer to Dan’s house than to Karen’s house, how many miles is the cafe from Karen’s house?
(A) 6
(B) 7
(C) 8
(D) 9
(E) 10


Incorrect OA. what is the source?
Also this should be in quants

Let K represent Karen's house, D represent Dan's house and C represent Cafe. Then the problem can be shown as given in image here.

we need a value of x. Using pyth theorem
\(x^2 + (x-2)^2=10^2\)
=>\(2x^2 -4x -96=0^2\)
=>\(x^2 -2x-48=0\)
=>\((x-8)(x+6)=0\)
Hence x = 8 (since x can not be negative)
The correct Ans is C.

Another simpler approach is to just notice,one of the common right angle triangle is 3:4:5 or 6:8:10
Second one fits exactly in our problem.. since hypotenuse is 10, and difference in 2 other sides is 2.

We can again reach to correct ans C.
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Re: misecellaneous   [#permalink] 16 Oct 2012, 09:46
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