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# A basketball is dropped from a height of 20 feet. If it bounces back

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Manager
Joined: 14 Jun 2012
Posts: 111
GMAT 1: 560 Q36 V31
GMAT 2: 580 Q39 V31
GMAT 3: 630 Q41 V35
GPA: 4
A basketball is dropped from a height of 20 feet. If it bounces back  [#permalink]

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10 Jul 2016, 16:43
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Difficulty:

25% (medium)

Question Stats:

76% (01:29) correct 24% (01:03) wrong based on 46 sessions

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A basketball is dropped from a height of 20 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces.

A) 50
B) 55
C) 60
D) 75
E) 80

In my opinion the "right" answer is the distance for 4 bounces, not 3. The question asks for the distance after 3 full bounces.
what are 3 full bounces? 3 times down + 3 times up... whenever the ball has hit the ground 3 times not 4 times.

Can someone please explain the logic behind this?

Thank you.
Intern
Joined: 30 Jun 2016
Posts: 7
Re: A basketball is dropped from a height of 20 feet. If it bounces back  [#permalink]

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10 Jul 2016, 20:10
In my opinion, Full bounce starts from the time the ball hits ground to next time it hits ground again.
So 3 full bounces is calculated from the first time to the 4th time it hits ground (when it stops bouncing also)

The total distance that the ball travels will be = 20+2*20/2+2*20/4+2*20/8 = 55.
Director
Joined: 20 Feb 2015
Posts: 790
Concentration: Strategy, General Management
Re: A basketball is dropped from a height of 20 feet. If it bounces back  [#permalink]

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11 Jul 2016, 01:36
initial height = 20 feet
total bounces = 3 (after the initial 20 feet fall)
total distance covered 20+2(10+5+2.5)
(note that the ball has to cover the distance twice before the next bounce---something as
20 feet drop + (10 feet up +10 feet down) +(5 feet up +5 feet down) + (2.5 feet up + 2.5 feet down) )
=20+35=55 feet
Director
Joined: 04 Jun 2016
Posts: 562
GMAT 1: 750 Q49 V43
Re: A basketball is dropped from a height of 20 feet. If it bounces back  [#permalink]

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30 Jul 2016, 03:48
Silviax wrote:
A basketball is dropped from a height of 20 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces.

In my opinion the "right" answer is the distance for 4 bounces, not 3. The question asks for the distance after 3 full bounces.
what are 3 full bounces? 3 times down + 3 times up... whenever the ball has hit the ground 3 times not 4 times.

Can someone please explain the logic behind this?

Thank you.

A) 50
B) 55
C) 60
D) 75
E) 80

Initial distance = 20 feet
first bounce = 10 feet up + 10 feet down = 20 feet
second bouche = 5 feet up + 5 feet down = 10 feet
third bounce = 2.5 feet up and 2.5 feet down= 5 feet
total distance covered = 20+20+10+5 = 55
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FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.
Director
Joined: 27 May 2012
Posts: 816
Re: A basketball is dropped from a height of 20 feet. If it bounces back  [#permalink]

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24 Sep 2018, 03:08
Silviax wrote:
A basketball is dropped from a height of 20 feet. If it bounces back up to a height that is exactly half of its previous height, and it stops bouncing after hitting the ground for the fourth time, then how many total feet will the ball have traveled after 3 full bounces.

In my opinion the "right" answer is the distance for 4 bounces, not 3. The question asks for the distance after 3 full bounces.
what are 3 full bounces? 3 times down + 3 times up... whenever the ball has hit the ground 3 times not 4 times.

Can someone please explain the logic behind this?

Thank you.

A) 50
B) 55
C) 60
D) 75
E) 80

Ball drops from 20 feet - distance traveled 20 feet
first bounce :
rises up 10 feel and drops 10 feet - Distance traveled 20 feet
Second bounce :
Travels up 5 feet and drops 5 feet - Distance traveled 10 feet
Third Bounce . ( At the moment of the third bounce distance traveled is 20+20+10=50)
After the third bounce , balls goes up 2.5 feet and drops 2.5 feet
fourth bounce ( At the moment of the fourth bounce distance traveled is 20+20+10 +5=55)
Question could have simply asked what is the total distance traveled at the moment of fourth bounce.
_________________
- Stne
Re: A basketball is dropped from a height of 20 feet. If it bounces back   [#permalink] 24 Sep 2018, 03:08
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