GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 11 Dec 2018, 11:23

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
  • Free GMAT Prep Hour

     December 11, 2018

     December 11, 2018

     09:00 PM EST

     10:00 PM EST

    Strategies and techniques for approaching featured GMAT topics. December 11 at 9 PM EST.
  • The winning strategy for 700+ on the GMAT

     December 13, 2018

     December 13, 2018

     08:00 AM PST

     09:00 AM PST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Manager
Manager
avatar
Status: May The Force Be With Me (D-DAY 15 May 2012)
Joined: 06 Jan 2012
Posts: 220
Location: India
Concentration: General Management, Entrepreneurship
Reviews Badge
Dan and Karen, who live 10 miles apart meet at a cafe that  [#permalink]

Show Tags

New post 31 Mar 2012, 20:07
2
6
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

76% (01:30) correct 24% (01:54) wrong based on 251 sessions

HideShow 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

_________________

Giving +1 kudos is a better way of saying 'Thank You'.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 51100
Dan and Karen, who live 10 miles apart meet at a cafe that  [#permalink]

Show Tags

New post 01 Apr 2012, 01:40
1
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:

Image

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.

Attachment:
The distance.png
The distance.png [ 4.31 KiB | Viewed 10382 times ]

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
Joined: 15 Jun 2010
Posts: 300
Schools: IE'14, ISB'14, Kellogg'15
WE 1: 7 Yrs in Automobile (Commercial Vehicle industry)
Reviews Badge
Re: Dan and Karen, who live 10 miles apart meet at a cafe that  [#permalink]

Show Tags

New post 08 Aug 2012, 10:09
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.
_________________

Regards
SD
-----------------------------
Press Kudos if you like my post.
Debrief 610-540-580-710(Long Journey): http://gmatclub.com/forum/from-600-540-580-710-finally-achieved-in-4th-attempt-142456.html

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3325
Location: India
GPA: 3.12
Premium Member CAT Tests
Dan and Karen, who live 10 miles apart, meet at a cafe that is  [#permalink]

Show Tags

New post 24 Aug 2017, 21:17
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 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)
_________________

You've got what it takes, but it will take everything you've got

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Dan and Karen, who live 10 miles apart, meet at a cafe that is  [#permalink]

Show Tags

New post 24 Aug 2017, 21:18
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 1615 times ]

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7099
Re: Dan and Karen, who live 10 miles apart, meet at a cafe that is  [#permalink]

Show Tags

New post 24 Aug 2017, 22:02
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 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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

Intern
Intern
avatar
B
Joined: 12 Sep 2018
Posts: 3
Re: Dan and Karen, who live 10 miles apart meet at a cafe that  [#permalink]

Show Tags

New post 08 Oct 2018, 09:38
1
Hey guys the simplest approach is to plug in the answer choices and you immediately see that the correct answer has to be C.
Manager
Manager
User avatar
B
Joined: 24 Jan 2015
Posts: 53
Location: India
Reviews Badge
Re: Dan and Karen, who live 10 miles apart meet at a cafe that  [#permalink]

Show Tags

New post 09 Oct 2018, 20:08
Hi,

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

Thanks
Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4278
Location: United States (CA)
Re: Dan and Karen, who live 10 miles apart meet at a cafe that  [#permalink]

Show Tags

New post 10 Oct 2018, 17:48
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 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
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: Dan and Karen, who live 10 miles apart meet at a cafe that &nbs [#permalink] 10 Oct 2018, 17:48
Display posts from previous: Sort by

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

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.