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Two students played a game of catch on the roof of the chemistry build

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Bunuel
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Two students played a game of catch on the roof of the chemistry build [#permalink] New post   07 Jul 2020, 03:01
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Two students played a game of catch on the roof of the chemistry building, which was 1,750 feet high. Unfortunately, after a bad throw, the ball fell to the ground and bounced several times. With each consecutive bounce, the ball reaches a height that is the same fraction of the height it reached on its previous bounce. If the ball reaches a height of 897 feet after its fifth bounce, what is this fraction?

A. 1/8
B. 1/6
C. 3/4
D. 5/6
E. 7/8
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E
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Re: Two students played a game of catch on the roof of the chemistry build [#permalink] New post   07 Jul 2020, 03:24
Let the fraction be X

1750x^5 = 897
X^5 = 897/1750
X^5 = 3*13*23/2*5*5*5*7
X^5 = 0.51257
Taking 5th root
X = 0.1025

Value of options in decimal =

A. 1/8 = 0.125
B. 1/6 = 0.166
C. 3/4 = 0.750
D. 5/6 = 0.833
E. 7/8 = 0.875 (Closest Value)

IMO E

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Re: Two students played a game of catch on the roof of the chemistry build [#permalink] New post   07 Jul 2020, 04:34
yashikaaggarwal wrote:
Let the fraction be X

1750x^5 = 897
X^5 = 897/1750



Hi yashikaaggarwal

How did you come up with this highlighted part?

Thanks
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Re: Two students played a game of catch on the roof of the chemistry build [#permalink] New post   07 Jul 2020, 04:42
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Mo2men wrote:
yashikaaggarwal wrote:
Let the fraction be X

1750x^5 = 897
X^5 = 897/1750



Hi yashikaaggarwal

How did you come up with this highlighted part?

Thanks

We know the ball bounce back at the same fractional distance it traveled last time. For ex if a ball is bouncing 1/2 time every time.
At 3rd time it will bounce from x meter. When the height of building = 100
The first bounce= 100*1/2 = 50
Second bounce= 50/2 = 25
Third bounce = 25/2 = 12.5
Or we can write.
100*(1/2)^3 = 100/8 = 12.5

Hopefully that clears.

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Re: Two students played a game of catch on the roof of the chemistry build [#permalink] New post   07 Jul 2020, 05:00
Height reached after 5th consecutive bounce = 897

The final height of 897 is more than half of 1750. We can discard A and B.

(3/4)^3 = 27/64 which is less than 0.5. Discard C.

(5/6)^4 = 625/1296 which is less than 0.5. Discard D.

Left with option E.

Ans: E
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Re: Two students played a game of catch on the roof of the chemistry build [#permalink] New post   07 Jul 2020, 21:39
Bunuel wrote:
Two students played a game of catch on the roof of the chemistry building, which was 1,750 feet high. Unfortunately, after a bad throw, the ball fell to the ground and bounced several times. With each consecutive bounce, the ball reaches a height that is the same fraction of the height it reached on its previous bounce. If the ball reaches a height of 897 feet after its fifth bounce, what is this fraction?

A. 1/8
B. 1/6
C. 3/4
D. 5/6
E. 7/8


As the height of the fifth bounce is more than half the height of the building.

By POE, Answer is 1750*(7/8)^5 = 897

OA: E
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Re: Two students played a game of catch on the roof of the chemistry build [#permalink] New post   09 Nov 2022, 01:19
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Re: Two students played a game of catch on the roof of the chemistry build [#permalink]
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