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

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Manager
Status: Gmat Prep
Joined: 22 Jul 2011
Posts: 74

Kudos [?]: 63 [0], given: 39

In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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17 Mar 2015, 11:26
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Difficulty:

95% (hard)

Question Stats:

42% (02:02) correct 58% (02:14) wrong based on 85 sessions

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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, Jessica needs to walk from the corner of 6th Street and 3rd Avenue to the corner of 1st Street and 1st Avenue. If Jessica will randomly choose from any route that allows her to walk the fewest number of blocks, what is the probability that she walks exactly two blocks on 1st Avenue?

a) 1/21
b) 1/7
c) 4/21
d) 10/21
e) 12/21
[Reveal] Spoiler: OA

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Street_Map.png [ 5.64 KiB | Viewed 2501 times ]

Kudos [?]: 63 [0], given: 39

Math Expert
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129048 [0], given: 12187

Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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17 Mar 2015, 11:33
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ynaikavde wrote:
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, Jessica needs to walk from the corner of 6th Street and 3rd Avenue to the corner of 1st Street and 1st Avenue. If Jessica will randomly choose from any route that allows her to walk the fewest number of blocks, what is the probability that she walks exactly two blocks on 1st Avenue?

a) 1/21
b) 1/7
c) 4/21
d) 10/21
e) 12/21

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Manager
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Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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10 Apr 2015, 08:18
Bunuel, could you please explain how do we deal with the restriction ? (Only two blocks on 1st avenue).

Kudos [?]: 12 [0], given: 139

Director
Joined: 07 Aug 2011
Posts: 583

Kudos [?]: 538 [7], given: 75

GMAT 1: 630 Q49 V27
In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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10 Apr 2015, 10:09
7
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ynaikavde wrote:
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, Jessica needs to walk from the corner of 6th Street and 3rd Avenue to the corner of 1st Street and 1st Avenue. If Jessica will randomly choose from any route that allows her to walk the fewest number of blocks, what is the probability that she walks exactly two blocks on 1st Avenue?

a) 1/21
b) 1/7
c) 4/21
d) 10/21
e) 12/21

She choose a route which allows her to walk fewest number of blocks
there are 2 blocks she will cross towards east moves represented by E,E and there will be 5 blocks she will cross towards south represented by S,S,S,S,S

total number of ways $$\frac{7!}{5!2!}$$

there are 4 ways she can cross 2 blocks on av.1 as shown in attached image.

in order to reach from black dot to blue dot she has to make 1 E and 3 S moves .. total 4!/3! = 4Ways . now from Blue dot to Maroon dot there is only 1 way . so there are only 4 ways .

A
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gclub.jpg [ 44.12 KiB | Viewed 2263 times ]

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Kudos [?]: 538 [7], given: 75

Manager
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Kudos [?]: 12 [0], given: 139

Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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10 Apr 2015, 11:40
Thank you Lucky2783 for the detailed explanation.

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GMAT Club Legend
Joined: 09 Sep 2013
Posts: 16637

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Re: In a city where all streets run east-to-west, all avenues run north-to [#permalink]

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07 Oct 2017, 06:21
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).

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Re: In a city where all streets run east-to-west, all avenues run north-to   [#permalink] 07 Oct 2017, 06:21
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