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

Question

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

lostboy · Answer

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

yenbh · Answer

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

raghavshekhar · Answer

D.

Equating 15+x to 1/4 less than 15/4 + 9x

pk123 · Answer

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

shameekv1989 · Answer

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

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

GMATWhizTeam · Answer

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

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