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One night Bran had a dream in which he grew a constant amount each hou

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One night Bran had a dream in which he grew a constant amount each hou  [#permalink]

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New post 20 Oct 2018, 09:09
3
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A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

47% (04:08) correct 53% (02:47) wrong based on 25 sessions

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One night Bran had a dream in which he grew a constant amount each hour from his original height of 15/4 feet. At the end of the third hour, Bran's height was 1/4 less than his height at the end of the ninth hour. What was Bran's height, in feet, after the seventh hour?
A) 19/4
B) 41/8
C) 16/3
D) 11/2
E) 6


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Re: One night Bran had a dream in which he grew a constant amount each hou  [#permalink]

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New post 20 Oct 2018, 09:18
B:

we're given that 15/4(r)^3 = 3/4 * 15/4 (r^9)
solve we get r = 6sqrt (4/3)

plug that in to 15/4 (r)^7 we get 5 * (4/3)^1/6
So it's a bit bigger than 5
Therefore B
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Re: One night Bran had a dream in which he grew a constant amount each hou  [#permalink]

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New post 20 Oct 2018, 09:25
Posted from my mobile device

Denote t is the height Brian grew each hour.

After 7th hour, Brian’s height is 11/2. Details are in the file attached
Attachments

image.jpg
image.jpg [ 1.57 MiB | Viewed 393 times ]

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Re: One night Bran had a dream in which he grew a constant amount each hou  [#permalink]

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New post 20 Oct 2018, 10:03
D.

Equating 15+x to 1/4 less than 15/4 + 9x
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Re: One night Bran had a dream in which he grew a constant amount each hou  [#permalink]

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New post 20 Oct 2018, 10:42
1
One night Bran had a dream in which he grew a constant amount each hour from his original height of 15/4 feet. At the end of the third hour, Bran's height was 1/4 less than his height at the end of the ninth hour. What was Bran's height, in feet, after the seventh hour?
A) 19/4
B) 41/8
C) 16/3
D) 11/2
E) 6


So lets say every hour it is growing by x, so 1 hour it becomes 15/4+x.
now 3 rd hour = 15/4+3x
9th hour=15/4+9x
so 3rd hour = 3/4(9th hour) as it is 1/4 less height of 9th hour
so it becomes 15/4 + 3x = 3/4 (15/4+9x)
after solving it becomes x =1/4
so after 7th hour height is 15/4 +7/4= 22/4 = 11/2

hence D is the answer
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Re: One night Bran had a dream in which he grew a constant amount each hou   [#permalink] 20 Oct 2018, 10:42
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One night Bran had a dream in which he grew a constant amount each hou

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