NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 09:52 It is currently 24 Apr 2024, 09:52
Decision Tracker
My Rewards
New posts
New comers' posts

Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

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

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
B
boomtangboy
Manager
Manager
Joined: 06 Jan 2012
Status:May The Force Be With Me (D-DAY 15 May 2012)
Posts: 165
Own Kudos [?]: 2093 [27]
Given Kudos: 33
Location: India
Concentration: General Management, Entrepreneurship
Schools: ISB '14 (D) INSEAD Jan '13 (D) Tuck '15 (D) Ross '15 (D) Duke '15 (D) NUS '15 (D) NTU '15 (WL) Ivey '15 (D) Johnson '16 (S)
Send PM
Reviews Badge
Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink] New post   31 Mar 2012, 21:07
3
Kudos
24
Bookmarks
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

78% (02:11) correct 22% (02:13) wrong based on 934 sessions
Hide Show timer Statistics
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
ShowHide Answer
Official Answer
C
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618772 [5]
Given Kudos: 81587
Send PM
CAT Tests Forum Quiz Mode
Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink] New post   01 Apr 2012, 02:40
3
Kudos
1
Bookmarks
Expert Reply
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, 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.

Show Spoiler
Attachment:
The distance.png
The distance.png [ 4.31 KiB | Viewed 35034 times ]
User avatar
SOURH7WK
Manager
Manager
Joined: 15 Jun 2010
Posts: 242
Own Kudos [?]: 1175 [0]
Given Kudos: 50
Concentration: Marketing
Schools:IE'14, ISB'14, Kellogg'15
 Q47  V26 GMAT 2: 540  Q45  V19 GMAT 3: 580  Q48  V23
GPA: 3.2
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Send PM
Reviews Badge
Re: Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink] New post   08 Aug 2012, 11:09
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.
User avatar
L
pushpitkc
Senior PS Moderator
Joined: 26 Feb 2016
Posts: 2873
Own Kudos [?]: 5205 [1]
Given Kudos: 47
Location: India
GPA: 3.12
Send PM
Dan and Karen, who live 10 miles apart, meet at a cafe that is [#permalink] New post   24 Aug 2017, 22:17
1
Bookmarks
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)
User avatar
D
niks18
Retired Moderator
Joined: 25 Feb 2013
Posts: 895
Own Kudos [?]: 1526 [0]
Given Kudos: 54
Location: India
GPA: 3.82
Send PM
GMAT ToolKit User Reviews Badge
Dan and Karen, who live 10 miles apart, meet at a cafe that is [#permalink] New post   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
\(10^2 = x^2 +(x-2)^2\) solving this we will get

\(x^2 - 4x + 4 = 100\) or \(x^2 - 2x - 48 = 0\)

Hence \(x = 8\)

option C
Attachments

File comment: Cafe
Cafe.jpg
Cafe.jpg [ 18.43 KiB | Viewed 22629 times ]

User avatar
L
chetan2u
RC & DI Moderator
Joined: 02 Aug 2009
Status:Math and DI Expert
Posts: 11169
Own Kudos [?]: 31888 [0]
Given Kudos: 290
Send PM
Reviews Badge
Re: Dan and Karen, who live 10 miles apart, meet at a cafe that is [#permalink] New post   24 Aug 2017, 23:02
Expert Reply
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 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
avatar
B
jHue
Intern
Intern
Joined: 12 Sep 2018
Posts: 3
Own Kudos [?]: 2 [1]
Given Kudos: 20
Send PM
Re: Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink] New post   08 Oct 2018, 10:38
1
Kudos
Hey guys the simplest approach is to plug in the answer choices and you immediately see that the correct answer has to be C.
User avatar
B
Amirfunc
Intern
Intern
Joined: 24 Jan 2015
Posts: 41
Own Kudos [?]: 5 [1]
Given Kudos: 51
Location: India
Send PM
Reviews Badge
Re: Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink] New post   09 Oct 2018, 21:08
1
Kudos
Hi,

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

Thanks
User avatar
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18754
Own Kudos [?]: 22044 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink] New post   10 Oct 2018, 18:48
Expert Reply
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 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
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32647
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink] New post   09 Jan 2024, 20:44
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Dan and Karen, who live 10 miles apart meet at a cafe that [#permalink]
09 Jan 2024, 20:44
Moderators:
Bunuel
Math Expert
92902 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions