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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
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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


GMATbuster's Weekly GMAT Quant Quiz #5 Ques No 3


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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
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Denote t is the height Brian grew each hour.

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


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

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New post 09 Feb 2020, 14:14
One night Mark had a dream in which he grew a constant amount each hour from his original height \(3\frac{3}{4}\) feet. At the end of the third hour, Mark's height was \(\frac{1}{4}\) less than his height at the end of the ninth hour. What was Mark's height, in feet, after the seventh hour?

a) 4\(\frac{3}{4}\)
b) 5\(\frac{1}{8}\)
c) 5\(\frac{1}{3}\)
d) 5\(\frac{1}{2}\)
e) 6
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Re: One night Mark had a dream in which he grew a constant amount each hou  [#permalink]

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New post 09 Feb 2020, 22:11
1
shameekv1989 wrote:
One night Mark had a dream in which he grew a constant amount each hour from his original height \(3\frac{3}{4}\) feet. At the end of the third hour, Mark's height was \(\frac{1}{4}\) less than his height at the end of the ninth hour. What was Mark's height, in feet, after the seventh hour?

a) 4\(\frac{3}{4}\)
b) 5\(\frac{1}{8}\)
c) 5\(\frac{1}{3}\)
d) 5\(\frac{1}{2}\)
e) 6


Solution:


    • The original height of Mark =\( 3\frac{ 3}{4}=15/4\) feet
    • Mark’s height is increasing at a constant rate each hour.
      o Let \(x\) be the increase in height of mark each hour.
    • Now, the question says at the end of the third hour Mark’s height is \(\frac{1}{4}\)th less than his height at the end of nine-hour.
      Note:-The question states \(\frac{1}{4}\) less not \(\frac{1}{4}\) feet less
      o Mark’s height at the end of the third hour = \(\frac{15}{4} + 3*x\)
      o Marks' height at the end of nine-hour = \(\frac{15}{4} + 9*x\)
         According to the condition given.
        \(\frac{15}{4}+3*x=(1-\frac{1}{4}) (\frac{15}{4}+9*x)\)
        \(15+12*x=\frac{(45+108*x)}{4} \)
        \(60+48*x=45+108*x \)
        \(108*x-48*x=60-45\)
        \(60*x=15 \)
        \(x=\frac{15}{60}=\frac{1}{4}\) feet
    • Now, the height of mark at the end of the seventh hour = \(\frac{15}{4}+7*x=\frac{15}{4}+7*\frac{1}{4}=\frac{22}{4}=\frac{11}{2}=5\frac{ 1}{2}\) feet.
Hence, the correct answer is Option D.
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Re: One night Mark had a dream in which he grew a constant amount each hou   [#permalink] 09 Feb 2020, 22:11

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

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