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

Question

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

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

Bunuel · Accepted Answer

Look at the diagram below: https://gmatclub.com/forum/download/file.php?id=16983 As you can see we have a right triangle with the sides of x, x-2 and hypotenuse of 10. If you can not recognize on sight that this triangel must be 6-8-10 right triangle, you can use Pythagoras theorem and find x: x^2+(x-2)^2=10^2 --> x=8. Answer: C. The distance.png

SOURH7WK · Answer

Its a question on Pythagoras triangles. the most familiar is 5-4-3. Here also if u notice, its a multiple of basic Pythagoras triangle 2(5-4-3) or 10-8-6.

pushpitkc · Answer

Since the cafe is directly east to Karen's house and directly north to Dan's house,
they form the two legs of a right angled triangle. From the question stem,
If we assume that the distance between Karen's house and the cafe is x,
then, distance between Dan's house and the cafe is x-2

Also, the distance between their houses is the hypotenuse of the triangle(which is 10)

In a right triangle,   Hyp^2 = Side1^2 + Side2^2  
Substituting the values,   10^2 = x^2 + (x-2)^2  
6,8,10 is a Pythagorean triplet which satisfies this equation

Therefore, the distance from Karen's house to the cafe is 8 miles (Option C)

niks18 · Answer

From the figure it is evident that 
 10^2 = x^2 +(x-2)^2  solving this we will get

x^2 - 4x + 4 = 100  or  x^2 - 2x - 48 = 0

Hence  x = 8

option  C

chetan2u · Answer

Hi..

ofcourse one method is the algebraic as explained above..

the other is to realize that MORE than often, you may be tested for triplet is 3:4:5.. or may be 1: \sqrt{3} :2, a 30-60-90 triangle or 1:1: \sqrt{2} , a 45-45-90 triangle 
and so when you see the HYPOTENUSE here as 10, a multiple of 5, try out this triplet ( may save some time)

so 3:4:5 has 5 as hypotenuse and with 10 as hypotenuse it becomes 3*2:4*2:5*2 = 6:8:10..
so Karens distance is TWO more and 6:8 perfectly fit in..
ans 8
C

jHue · Answer

Hey guys the simplest approach is to plug in the answer choices and you immediately see that the correct answer has to be C.

Amirfunc · Answer

Hi,

Could someone explain with an algebraic equation as to how the distance between Dan's house and the cafe is x-2?

Thanks

ScottTargetTestPrep · Answer

We see that the three locations (Dan’s house, Karen’s house and the cafe) will form a 6-8-10 right triangle. That is, Dan’s and Karen’s houses are 10 miles apart (which is given) and the cafe is 6 miles from Dan’s house and 8 miles from Karen’s house (notice that this makes the cafe 2 miles closer to Dan’s house than to Karen’s house). Therefore, the cafe is 8 miles from Karen’s house.

Answer: C

rak08 · Answer

what if i solve like this
karen (d) = kd
dan (d) = dd

dd+2=kd
dd+kd=10

2 equations

dd+2 = kd
10-kd+2=kd
12=2kd
kd=6

subhashsavalia · Answer

Until its not Clearfield about 10 Km is straight distance, rules of Trigo fails to evaluate. alternatively cafe may be 4 and 6 Km away respective home with given conditions.

TheYagami · Answer

Its a right triangle and the Hypotenuse is 10 units
The triplet is (3 4 5) and has been multiplied by 2 
so the triplet is (6 8 10), where 10 is the hypotenuse
Therefore other sides will be 6 units and 8 units
We have been asked about the longer distance 
OA 8 units

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

Prep Toolkit

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