Last visit was: 12 Sep 2024, 22:59 It is currently 12 Sep 2024, 22:59
Toolkit
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

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.

# What is the number of the shortest routes from X to Y through Z?

SORT BY:
Tags:
Show Tags
Hide Tags
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10131
Own Kudos [?]: 17271 [32]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
GMAT Club Legend
Joined: 12 Sep 2015
Posts: 6803
Own Kudos [?]: 31293 [14]
Given Kudos: 799
General Discussion
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10131
Own Kudos [?]: 17271 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Manager
Joined: 06 Oct 2019
Status:BELIEVE IN YOURSELF
Posts: 100
Own Kudos [?]: 178 [0]
Given Kudos: 90
Location: India
What is the number of the shortest routes from X to Y through Z? [#permalink]
MathRevolution
What is the number of the shortest routes from X to Y through Z?

Attachment:
12.jpg

A. 8
B. 12
C. 16
D. 18
E. 20

No matter what, you have to take 2 horizontal steps and 2 vertical steps to reach point "Z" from "X".

let's Horizontal step=H
vertical step= V

"HHVV" the no. of ways to arrange them= $$\frac{4!}{2!*2!} = 6$$ ways to reach Z

the no. of ways to reach Y from Z only $$2 ways$$

now, multiply the results= $$6*2= 12$$ ways total

Manager
Joined: 18 Jun 2010
Posts: 83
Own Kudos [?]: 86 [0]
Given Kudos: 28
Re: What is the number of the shortest routes from X to Y through Z? [#permalink]
If I see a question like this again, how do I tell it is a combination question?
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10131
Own Kudos [?]: 17271 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: What is the number of the shortest routes from X to Y through Z? [#permalink]
KashishBansal

=> Best Approach: Regard the different parts of the shortest route as repeated letters in a word
=> Start at X, End at Y, Stop at Z

Two parts: Shortest route (X to Z) & Shortest route (Z to Y)

Modify the question: X to Z
Stretches of vertical roads/ steps = ‘a’
Stretches of horizontal roads/ steps = ‘b’
=> List all stretches of roads: b,b,a,a

=> Total number of roads: 4 (2 b^′ s & 2 a^′ s)

=> "∴" Formula: 4!/(2! 2! ) = 6

=> Modify the question: Z to Y
Stretches of vertical roads/steps = ‘p’
Stretches of horizontal roads/steps = ‘q’

=> List all stretches of roads: p,q

=> Total number of roads: 2 (1 p^′ s & 1 q^′ s)

=> " ∴" Formula: 2! = 2

=> Shortest routes: 6 routes (X~Z) and 2 routes (Z~Y)

=> " ∴" Total possible shortest routes: 6 * 2 = 12

Thanks
Non-Human User
Joined: 09 Sep 2013
Posts: 34824
Own Kudos [?]: 878 [0]
Given Kudos: 0
Re: What is the number of the shortest routes from X to Y through Z? [#permalink]
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.
Re: What is the number of the shortest routes from X to Y through Z? [#permalink]
Moderator:
Math Expert
95478 posts