A ball is dropped from a height of 1640.25 centimeters. Every time it

Question

Source: e-GMAT

A ball is dropped from a height of 1640.25 centimeters. Every time it touches the ground, it rebounds two-third of the distance it falls and then falls on the ground again. If “count of fall” represents the count of the number of times it falls on the ground, then find out the relevant 'Count of Fall’, & 'Distance Traveled' by the ball in the table, which is consistent with information provided. 
 Make only two selections, one in each column.

zhanbo · Answer

Equipped with a calculator, we can list the table below rather quickly

1 1640.25
2 1093.5
3 729
4 486
5 324
6 216
7 144
8 96

So, the answer is
Count of fall -  8  
Distance travelled -  96

Sajjad1994 · Answer

Competition mode is off now.

OAs is:

Count of fall:  8
 Distance travelled:  96

Good job  zhanbo

Hoehenheim · Answer

Is there a trick to doing this without using the calculator?

1111fate · Answer

why does the ball stop rebounding 2/3rd of its distance after 96?

cheshire · Answer

We are looking for the 2 numbers that match up. The ball doesn't stop rolling but lines up with 8 at 96. If you make a table it's easier to see.

kashishbulani · Answer

Didn't understand the explanation here. Can you please provide the solution in detail. 
As I can think, the ball with bounce infinitely, there is no cap specifically asked in the problem statement. I am still stuck on this

Dereno · Answer

Yeah, there is a greater chance the ball might bounce repeatedly, but there cannot be a ball that bounces infinitely. In the question it’s mentioned that the ball dropped from a height, for example say 300m. It rebounces back to (2/3)rd of the original distance.

That’s, the new height will be 300*(2/3) = 200m

The next new height will be 200* (2/3) = 133.33 m.

So, the question asks the number of times the ball rebounds and the height at that time.

So, seeing the options the logical guess should be the count should fall between options 7 or 8.

When a ball is dropped from a height of 1640.25, it travels a distance of 1640.25 that’s count 1, from then on the distance is (2/3)rd of its height.

Count 2: 1640.25 *(2/3) = 1093.5

Count 3: 1093.5 *(2/3) = 729

Count 4: 729 *(2/3) = 486

Count 5: 486 *(2/3) = 324

Count 6: 324*(2/3) = 216

Count 7 : 216*(2/3) = 144

We are given option starting from 7 only,

Count 8: 144*(2/3) = 96

So the answer is 8 and 96.

Hope this clears your doubt.

Danielmm · Answer

How did you get 3280.5?

cheshire · Answer

It's wrong, not sure how it could bounce higher than what it started at... The correct table of values is listed earlier in the replies.

Dereno · Answer

Danielmm   cheshire

Extremely sorry from my end. In a hurry have mistyped it altogether and didn’t recheck too. My apologies for that. Have corrected the post now.

MinhHoang31 · Answer

What is travelled distance? In my first attempt, I thought it was the total length of the path the ball had moved (For example: the 2nd time the ball touches the ground, it has travelled 1640.25 + 1640.25 x 2/3 x 2 according to my understanding) and thus I came up with a very complex expression to calculate 
After reading comments, I see that travelled distance is the current height of the ball at a particular moment. Am i right? Do you think the original question is a bit confusing and should be rephrased?

cheshire · Answer

I could see how you could interpret it that way and "height bounced" would probably be a better way of stating it. However, one look at the answer choices should tell you it's not the total distance traveled.

Danielmm · Answer

Thanks!

A ball is dropped from a height of 1640.25 centimeters. Every time it

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A ball is dropped from a height of 1640.25 centimeters. Every time it

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