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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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20 Oct 2018, 09:09
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65% (hard)

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57% (03:57) correct 43% (02:55) wrong based on 36 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

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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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

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

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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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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 [ 1.57 MiB | Viewed 769 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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20 Oct 2018, 10:03
D.

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

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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
One night Mark had a dream in which he grew a constant amount each hou   [#permalink] 09 Feb 2020, 14:14