In a city where all streets run east-to-west, all avenues run north-to

Question

https://gmatclub.com/forum/download/file.php?id=24412 In a city where all streets run east-to-west, all avenues run north-to-south, and all intersections are right angles as shown below, Jenn needs to walk from the corner of 1st Street and 1st Avenue to the corner of 6th Street and 3rd Avenue. If her friend Amanda is sitting on a bench on 4th Street halfway between 1st and 2nd Avenues, and Jenn chooses her path randomly from any route that will allow her to walk exactly seven blocks to her destination, what is the probability that Jenn will walk down 4th St. past Amanda? A. 1/42 B. 1/21 C. 1/7 D. 1/3 E. 1/2 Street_Map.png

Bunuel · Accepted Answer

https://gmatclub.com/forum/download/file.php?id=24414 Jenn needs to walk from red dot to green dot in seven moves. So, she should walk 5 blocks UP and 2 blocks LEFT: UUUUULL. She can do this in 7!/(5!2!) = 21 ways, which is the number of permutations of 5 U's and 2 L's. How many roots go through the black dot? To walk from red to blue Jenn needs to walk 3 blocks UP: UUU. So, 1 way. To walk from yellow to green Jenn needs to walk 2 blocks UP and 1 blocks LEFT: UUL. She can do this in 3!/2! = 3 ways. So, only 1*3 = 3 ways pass through black dot. Probability = 3/21 = 1/7. Answer: C. Similar questions to practice: https://gmatclub.com/forum/every-morning ... 04236.html https://gmatclub.com/forum/josh-has-to-r ... 99962.html https://gmatclub.com/forum/as-per-the-gi ... 34453.html https://gmatclub.com/forum/pat-will-walk ... 68374.html https://gmatclub.com/forum/alicia-lives- ... 26920.html https://gmatclub.com/forum/in-city-a-the ... 36949.html https://gmatclub.com/forum/the-diagram-a ... 44271.html https://gmatclub.com/forum/in-a-city-wh ... 94692.html Untitled.png

srezar · Answer

All routs between (1,1) to (3,6) = 7!/(2!*5!) = 21
Routs which pass 4th st. between 1st and 2nd avenue = routs between (1,1) to (1,4) * routs between (2,4) to (3,6) 
= 1 * (3!/(2!*1!)) = 3
the probability that Jenn will walk down 4th St. past Amanda= 3 / 21 = 1 / 7

C is correct.

hsbinfy · Answer

hi srezar,

i get ur approach..but can u explain graphically how u found the favourble outcomes(Routs which pass 4th st. between 1st and 2nd avenue = routs between (1,1) to (1,4) * routs between (2,4) to (3,6)
= 1 * (3!/(2!*1!)) = 3)??

-h

Thoughtosphere · Answer

Thanks a lot  Bunuel , I got his one.

While searching for explanations, I came across another explanation.

The destination can be reached in minimum steps by going 5 up and 2 L.
Thus from the 7 choices, we need to choose how can we select the 5 Ups or the two downs

So, it would be  7C5 or 7C2 = 7! / (5! * 2!)

Thanks

Thoughtosphere · Answer

Bunuel , Thanks a lot for sharing the similar types of questions, they come as life savers - help me understand the topic well... :-)

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

C. Given the diagram, you should see that Jenn will make it to her destination by traveling 5 "up" blocks (from 1st to 6th St.) and 2 "left" blocks (from 1st to 3rd Ave.). How can you find all the routes? Using permutations - how many ways would you arrange 5 up and 2 left? 
7!/(5!2!), which equals 21. Then to pass Amanda, she has to go up 1st Ave. to 4th St. and make her first left there, leaving 2 "up" streets and 1 "left" street left to go after she passes Amanda. That's 3 ways of the 21 (LUU, ULU, UUL) that will take her past Amanda, for an answer of 1/7.

Funsho84 · Answer

Hi  Bunuel ,

I solved this problem the same way you did but I got hung up at the end. The portion of the question that says  "what is the probability that Jenn will walk down 4th St. past Amanda?'  confused me for a second because I mapped out the path as being NNNW which came out to 4!/3!. That would have resulted in an answer of 4/21. Do we assume that she takes the left, knowing that she is really moving half the distance to the left? If the question read "If her friend Amanda is sitting on a bench on  4th Street and 2nd Avenue " would 4/21 have been correct?

Adit_ · Answer

Do we still get such questions under GMAT Focus?

Bunuel · Answer

This is a probability and combinations question, both of which are still tested on GMAT Focus. So yes, you can still get such questions on the exam.

Adit_ · Answer

Was curious since I rarely ever see diagram based questions in quants these days. Has the rarity of such questions gone up since Focus edition?

In a city where all streets run east-to-west, all avenues run north-to

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