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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