Join us for MBA Spotlight – The Top 20 MBA Fair      Schedule of Events | Register

 It is currently 06 Jun 2020, 07:18

### 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

# The figure above shows a zebra crossing made of alternate black and

Author Message
TAGS:

### Hide Tags

Alum
Joined: 19 Mar 2012
Posts: 4551
Location: United States (WA)
Schools: Ross '20 (M)
GMAT 1: 760 Q50 V42
GMAT 2: 740 Q49 V42 (Online)
GPA: 3.8
WE: Marketing (Non-Profit and Government)
The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 07:42
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:39) correct 45% (02:01) wrong based on 125 sessions

### HideShow timer Statistics

GST Week 1 Day 1 Exampal Question 1

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and Exampal Premium GMAT Package. See the GMAT Spring Training Thread for all details

The figure above shows a zebra crossing made of alternate black and white stripes. A frog sits on the middle black stripe and on each jump, it can only move from one stripe to a stripe next to it, right or left. What is the probability that after 25 jumps the frog returns to the middle black stripe?

A. 0
B. 1/25
C. 2/25
D. 13/25
E. 1

Attachment:

zXMsDmQ.png [ 5.04 KiB | Viewed 2979 times ]

_________________
Manager
Joined: 05 Feb 2016
Posts: 151
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 07:56
[quote="souvik101990"]

GST Week 1 Day 1 Exampal Question 1

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and Exampal Premium GMAT Package. See the GMAT Spring Training Thread for all details

The figure above shows a zebra crossing made of alternate black and white stripes. A frog sits on the middle black stripe and on each jump, it can only move from one stripe to a stripe next to it, right or left. What is the probability that after 25 jumps the frog returns to the middle black stripe?

A. 0
B. 1/25
C. 2/25
D. 13/25
E. 1

For moving forward and backward each trip will be a factor of 2.

but total 25 is odd .So probability that after 25 jumps the frog returns to the middle black is 0

option A
Current Student
Joined: 03 Aug 2017
Posts: 19
Location: United States (NY)
GMAT 1: 720 Q49 V39
GPA: 3.76
The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 08:14
souvik101990 wrote:

GST Week 1 Day 1 Exampal Question 1

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and Exampal Premium GMAT Package. See the GMAT Spring Training Thread for all details

The figure above shows a zebra crossing made of alternate black and white stripes. A frog sits on the middle black stripe and on each jump, it can only move from one stripe to a stripe next to it, right or left. What is the probability that after 25 jumps the frog returns to the middle black stripe?

A. 0
B. 1/25
C. 2/25
D. 13/25
E. 1

Attachment:
zXMsDmQ.png

The answer is A. 0 percent chance.
If you tried to figure this out mathematically it may give you a headache. Instead using logic you will find that it is impossible to land on any black stripe with 0 moves left.

Assuming | = black strip, _ = white stripe , and x= Frog, and that the chart looks like this |_|_|_X_|_|_|

On the first move, the frog will land a white stripe (or _) with an even amount of moves left: |_|_|_|X|_|_| or |_|_|X|_|_|_|

Considering 0 is even, that means with 1 move left you NEED to land on a white stripe which cannot happen.

To further explain this lets make this problem easier: Lets change the strips to |_X_| and only allow 5 moves.

5 moves left: |_X_|
4 moves left: |_|X| or |X|_|
3 moves left: |_X_| or X_|_| or |_|_X
2 moves left: |_|X| or |X|_|
1 moves left: |_X_| or X_|_| or |_|_X
0 moves left: |_|X| or |X|_|
Senior Manager
Joined: 15 Oct 2017
Posts: 291
GMAT 1: 560 Q42 V25
GMAT 2: 570 Q43 V27
GMAT 3: 710 Q49 V39
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 08:47
1
Every to and fro move of frog will be a multiple of 2. To come back to the initial positions, the number of jumps required will therefore always be in multiples of two. For example, 2, 4, 6, 8..2*n (n=no of jumps). Hence, as 25 is odd, it will always result in frog moving away from the previous positions of jump.

Therefore, A=0 is the probability.
Manager
Joined: 03 Oct 2016
Posts: 118
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 09:28
2
souvik101990 wrote:

GST Week 1 Day 1 Exampal Question 1

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and Exampal Premium GMAT Package. See the GMAT Spring Training Thread for all details

The figure above shows a zebra crossing made of alternate black and white stripes. A frog sits on the middle black stripe and on each jump, it can only move from one stripe to a stripe next to it, right or left. What is the probability that after 25 jumps the frog returns to the middle black stripe?

A. 0
B. 1/25
C. 2/25
D. 13/25
E. 1

Attachment:
zXMsDmQ.png

Scenario 1: If the frog jumps to the right black strip and comes back then it takes 2 jumps.
Scenario 2: If the frog jumps to second right black strip and comes back then it takes 4 jumps.
Scenario 3: If the frog jumps to third right black strip and comes back then it takes 6 jumps.

Please note that above scenarios are valid for black strips to the left of frog.

We see here that for jumping and coming back to the center the frog takes even jumps (2,4,6) so, for given odd jumps .i.e. 25 the frog will never come back to the center black strip.

The probability is 0. (A).
Retired Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 1040
Location: India
GPA: 3.64
The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

Updated on: 10 Apr 2018, 00:09
souvik101990 wrote:

GST Week 1 Day 1 Exampal Question 1

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and Exampal Premium GMAT Package. See the GMAT Spring Training Thread for all details

The figure above shows a zebra crossing made of alternate black and white stripes. A frog sits on the middle black stripe and on each jump, it can only move from one stripe to a stripe next to it, right or left. What is the probability that after 25 jumps the frog returns to the middle black stripe?

A. 0
B. 1/25
C. 2/25
D. 13/25
E. 1

Attachment:
zXMsDmQ.png

Let us number the black and white stripes as follows, with the number 0 representing the middle black stripe, and 1, 3, 5 representing black stripes. Similarly, 0,2,4,6 represents the black stripes.

5 4 3 2 1 0 1 2 3 4 5 6

Observe that 25 is an odd number, and hence the frog cannot reach the center black stripe even if it makes 25 jumps.
Hence the probability must be 0.

Originally posted by souvonik2k on 09 Apr 2018, 09:52.
Last edited by souvonik2k on 10 Apr 2018, 00:09, edited 1 time in total.
Intern
Status: Preparing for GMAT
Joined: 07 Nov 2016
Posts: 16
Location: India
Concentration: Technology, Economics
GPA: 3.1
WE: Analyst (Consulting)
The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 11:12
souvik101990 wrote:

GST Week 1 Day 1 Exampal Question 1

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and Exampal Premium GMAT Package. See the GMAT Spring Training Thread for all details

The figure above shows a zebra crossing made of alternate black and white stripes. A frog sits on the middle black stripe and on each jump, it can only move from one stripe to a stripe next to it, right or left. What is the probability that after 25 jumps the frog returns to the middle black stripe?

A. 0
B. 1/25
C. 2/25
D. 13/25
E. 1

Attachment:
zXMsDmQ.png

As the number of jumps is odd-25, there is 0% chance of the frog returning to the starting position
Intern
Joined: 10 May 2016
Posts: 16
Location: India
GMAT 1: 690 Q49 V35
GPA: 3.9
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 12:05
The answer is Option A : 0

Here is the solution:
For questions like these which seem impossible to solve it is usually trying to count is the way to go - these usually lead to a pattern.
1. Say it jumps 1 left and then jumps back to the middle stripe - that's 2 jumps. Repeating the same it's 4, then 6.... so essentially multiples of 2. So this way it will need either 24 or 26 jumps to return to the middle stripe.

2. Next consider that it jumps 2 left and then back 2 to the middle stripe - that's 4 jumps. Repeating the same it's 8 jumps, then 12. Again multiples of 4 - So either 24 or 28 jumps this way

Similarly try by adding one extra jump to the left - you will see a pattern in the number of jumps required to return - 2, 4,6, 8, 10, 12....etc. Note that since the frog is at the center - moving left or right will be symmetrical.

Finally, there may be cases that the frog not repeat the same pattern i.e. it may do 2 left and 4 right and return to the middle stripe i.e. in any combination of the above mentioned jumps. However, if you recall - sum of two even numbers is even. So any combination will result in an even number - meaning that the 25th jump will always be away from the middle stripe.

Hence, 0 cases where the frog returns to the middle stripe after the 25 jumps. So the probability is 0.
Senior Manager
Joined: 31 Jul 2017
Posts: 499
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 18:48
souvik101990 wrote:

GST Week 1 Day 1 Exampal Question 1

Give your best shot at writing a top notch application and you will have the chance to win GMAT Club tests daily and Exampal Premium GMAT Package. See the GMAT Spring Training Thread for all details

The figure above shows a zebra crossing made of alternate black and white stripes. A frog sits on the middle black stripe and on each jump, it can only move from one stripe to a stripe next to it, right or left. What is the probability that after 25 jumps the frog returns to the middle black stripe?

A. 0
B. 1/25
C. 2/25
D. 13/25
E. 1

Attachment:
zXMsDmQ.png

Every Jump to the Middle Black Stripe is a multiple of 2. Hence, Probability = 0.
Moderator
Joined: 28 Mar 2017
Posts: 1192
Location: India
GMAT 1: 730 Q49 V41
GPA: 4
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 21:03
Answer must be 0 because frog will be on black strip every even number of jump. Since 25 is odd, the frog will be on white.

Posted from my mobile device
Intern
Joined: 23 Sep 2016
Posts: 1
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

09 Apr 2018, 22:07
A. 0 percent

Assuming that the middle black stripe is 0, and each right jump or left jump equals +1 or -1 respectively. If you want 0 as the final result, you need as many positive value as negative value, which means an equal number of left and right jump made. Consequently, the total number of left and right jump will be a multiple of 2, which can never be an odd number like 25.
Intern
Joined: 10 Apr 2018
Posts: 4
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

10 Apr 2018, 03:27
The probability is 0.
The zebra needs steps in the multiple of 2 to come back to the middle black strip and 25 is an odd no and not a multiple of 2.

Posted from my mobile device
Alum
Joined: 19 Mar 2012
Posts: 4551
Location: United States (WA)
Schools: Ross '20 (M)
GMAT 1: 760 Q50 V42
GMAT 2: 740 Q49 V42 (Online)
GPA: 3.8
WE: Marketing (Non-Profit and Government)
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

10 Apr 2018, 04:47
Thanks for answering, everyone! kunalcvrce - I am happy to report you are our first daily winner! Shoot me a PM to redeem your reward.
_________________
Non-Human User
Joined: 09 Sep 2013
Posts: 15104
Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

### Show Tags

26 Apr 2019, 00:28
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: The figure above shows a zebra crossing made of alternate black and   [#permalink] 26 Apr 2019, 00:28