BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location...

This topic has expert replies
Post new topic Post Reply
Previous Topic Next Topic
Moderator
Posts: 2599
Joined: Sun Oct 29, 2017 2:08 pm
Followed by:2 members

Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location...

by AAPL » Tue May 05, 2020 1:20 pm

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Veritas Prep

Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location. If Pavel travels only along streets and does not travel diagonally, the shortest possible route connecting the two points is exactly 14 blocks. How many different 14-block routes may Pavel take to travel the shortest possible distance to his aunt’s house?

A. 14
B. (14!)/(8!6!)
C. (22!)/(14!8!)
D. 8!6!
E. 14!8!6!

The OA is B
Top
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 3008
Joined: Mon Aug 22, 2016 6:19 am
Location: Grand Central / New York
Thanked: 470 times
Followed by:34 members

Re: Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location...

by Jay@ManhattanReview » Tue May 05, 2020 9:33 pm
AAPL wrote: ↑
Tue May 05, 2020 1:20 pm
 Veritas Prep

Pavel has to visit his aunt, who lives exactly eight blocks north and six blocks east of his current location. If Pavel travels only along streets and does not travel diagonally, the shortest possible route connecting the two points is exactly 14 blocks. How many different 14-block routes may Pavel take to travel the shortest possible distance to his aunt’s house?

A. 14
B. (14!)/(8!6!)
C. (22!)/(14!8!)
D. 8!6!
E. 14!8!6!

The OA is B
Given the information, we deduce that Pavel can travel the 14-block distance in many possible ways. To understand this, draw an 8*6 rectangle, with 8 equally spaced horizontal lines, with each depicting eastern direction and the gap between them, depicting 1-black distance.

Similarly, draw 6 vertical lines, as shown in the attached image.

Say each eastern side 1-block distance = E and each northern side distance = N; thus, Pavel has to travel 6 Es and 8 Ns. However, these Es and Ns can be in any combination. For example, in the image, Pavel travels NENENENENNEENNEE.

So, there are 8 + 6 = 14 blocks

No. of ways to choose them = 14!; however, since 8 Ns and 6Es are identical, we must divide 14! by 8! and 6!.

So, the required no. of ways = 14!/(8!.6!)

The correct answer: B

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review Mumbai | Hyderabad | GRE Prep Warangal | Begumpet GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.
Attachments
Picture1.png
Top
Post new topic Post Reply
• Page 1 of 1