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Dan and Karen, who live 10 miles apart meet at a cafe that
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31 Mar 2012, 21:07
Question Stats:
75% (02:06) correct 25% (02:14) wrong based on 281 sessions
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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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Dan and Karen, who live 10 miles apart meet at a cafe that
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01 Apr 2012, 02:40
boomtangboy wrote: 14. 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 Look at the diagram below: As you can see we have a right triangle with the sides of x, x2 and hypotenuse of 10. If you can not recognize on sight that this triangel must be 6810 right triangle, you can use Pythagoras theorem and find x: x^2+(x2)^2=10^2 > x=8. Answer: C. Attachment:
The distance.png [ 4.31 KiB  Viewed 11697 times ]
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Re: Dan and Karen, who live 10 miles apart meet at a cafe that
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08 Aug 2012, 11:09
Its a question on Pythagoras triangles. the most familiar is 543. Here also if u notice, its a multiple of basic Pythagoras triangle 2(543) or 1086.
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Dan and Karen, who live 10 miles apart, meet at a cafe that is
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24 Aug 2017, 22:17
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 x2 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, \(10^2 = x^2 + (x2)^2\)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)
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Dan and Karen, who live 10 miles apart, meet at a cafe that is
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24 Aug 2017, 22:18
Bunuel 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 From the figure it is evident that \(10^2 = x^2 +(x2)^2\) solving this we will get \(x^2  4x + 4 = 100\) or \(x^2  2x  48 = 0\) Hence \(x = 8\) option C
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Re: Dan and Karen, who live 10 miles apart, meet at a cafe that is
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24 Aug 2017, 23:02
Bunuel 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 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 306090 triangle or 1:1:\(\sqrt{2}\), a 454590 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
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Re: Dan and Karen, who live 10 miles apart meet at a cafe that
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08 Oct 2018, 10:38
Hey guys the simplest approach is to plug in the answer choices and you immediately see that the correct answer has to be C.



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Re: Dan and Karen, who live 10 miles apart meet at a cafe that
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09 Oct 2018, 21:08
Hi,
Could someone explain with an algebraic equation as to how the distance between Dan's house and the cafe is x2?
Thanks



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Re: Dan and Karen, who live 10 miles apart meet at a cafe that
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10 Oct 2018, 18:48
boomtangboy 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 We see that the three locations (Dan’s house, Karen’s house and the cafe) will form a 6810 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
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Re: Dan and Karen, who live 10 miles apart meet at a cafe that
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