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.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards