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

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

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New post 09 Apr 2018, 08:42
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58% (00:54) correct 42% (01:30) wrong based on 127 sessions

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GST Week 1 Day 1 Exampal Question 1


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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
zXMsDmQ.png [ 5.04 KiB | Viewed 2075 times ]

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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 08:56
[quote="souvik101990"]

GST Week 1 Day 1 Exampal Question 1


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Image

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

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New post 09 Apr 2018, 09:14
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


Image

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|_|
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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 09:47
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.
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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 10:28
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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


Image

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).
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The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post Updated on: 10 Apr 2018, 01:09
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


Image

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.
Answer A.
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Originally posted by souvonik2k on 09 Apr 2018, 10:52.
Last edited by souvonik2k on 10 Apr 2018, 01:09, edited 1 time in total.
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The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 12:12
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


Image

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
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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 13:05
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.
Lets see how the frog may return to the middle stripe:
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.
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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 19:48
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


Image

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.
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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 22:03
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.

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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 09 Apr 2018, 23:07
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.
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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 10 Apr 2018, 04:27
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.

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Re: The figure above shows a zebra crossing made of alternate black and  [#permalink]

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New post 10 Apr 2018, 05:47
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