When a certain tree was first planted, it was 4 feet tall and the heig

Question

When a certain tree was first planted, it was 4 feet tall and the height of the tree increased by a constant amount each year for the next 6 years. At the end of 6 year the tree was 1/5 taller then it was at the end of 4 year. By how many feet did the height of the tree increase each year

A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5

A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5

avigutman · Answer

Video solution from Quant Reasoning starts at 8:06 Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=u_OSUyDBonc

vatsal323 · Answer

Does the question stem say that it was 1/5 times taller or was 1/5 feet taller. It's not clear!

avigutman · Answer

Would it be less confusing if it said:
the tree was  20%  taller than it was at the end of the 4th year.
If so, remember: 20% is the same thing as 1/5.

avigutman · Answer

In the absence of the word "feet" following the fraction, the meaning is the same as "20% taller", or "6/5 as tall".

CrackverbalGMAT · Answer

Solution:

Let the tree increase by x units every year

Growth in 6 years are (4+x),(4+2x),(4+3x),(4+4x),(4+5x) ,(4+6x)

Given 6th -4th year = 1/5 (4+4x)

=> 4+6x-4-4x = 4/5 + 4x/5

=> 2x = 4/5 +4x/5

=>6x/5= 4/5

=>x=4/6 = 2/3  (option d)

Devmitra Sen
GMAT SME

jabhatta2 · Answer

Hi  avigutman  - Tried doing this with ratios

Tried 3 attempts with ratios as the pic shows.

In All 3 attempts - the ratio is the same.

I was surprised to see how in every attempt -- the scale factor was coming up different.

It seems  my take-away  should be to 
- Attempt # 2 -  reduce down as much as possible  so every cell is an integer but its reduced down as much as possible 
OR 
- Attempt # 1 -  increase up  so every cell with a decimal/ fraction has an integer

It seems like this reduction / integer constraint is vital for ratios (Which really surprised me)

Why do we need to (reduce down as much as possible) or (increase up so no decimals exists) in the ratio system when finding the scale factor

Technically - it should not matter if my starting ratio is 3x or 6x or 30x (as 3 ratio's are the same)

avigutman · Answer

Note the exact wording of the question,  jabhatta2 :
 
Your solutions all show that you're solving for x, but is the question asking for x? That depends on your definition of x. In attempt #1 you should have been solving for 0.5x. In attempt #2 you should have been solving for 5x.
I also noticed that you have inches in your solution, rather than feet. Your takeaway ought to be that you need to pay more attention to what is being asked, and be precise about it. In general, though, yes, best practice is to use the smallest integers possible when constructing a ratio, and avoiding fractions.

ADisHere · Answer

Hi Can someone explain me why my approach is wrong..
 I used AP as it the height of the tree increased by a constant amount
4+5d=6/5(4+3k)
20+25k=24+18k
7k=4
k=4/7

Bunuel · Answer

Should be 4 + 6x = 6/5(4 + 4x), which leads to x = 2/3.

ADisHere · Answer

Ohkkk so year 0 4 ft year 1 4+k ft Got it! Thankss Bunnel!!

shvm_sin7 · Answer

Hi Bunuel,
Shouldn't we assume that since the tree was first planted, its height was 4 feet which increased by a constant amount in the consequent years? Therefore height at the 6 th year should be 4+5y?

Please help

Bunuel · Answer

Starting height = 4 feet
 
 Height after one years = 4 + x 
 Height after two years = 4 + 2x 
 Height after three years = 4 + 3x 
 Height after four years = 4 + 4x 
 Height after five years = 4 + 5x 
 height after six years = 4 + 6x

asingh91 · Answer

Hi Scott,

wondering why we arent applying (n-1) to this AP to find the 6th term

anindhio · Answer

Hi  Bunuel ,

I'm still confused the difference between the linear and exponential. I used the exponential way to calculate above question.

APram · Answer

Hi

We use exponential when question says the increase or decrease is due to certain factor.
We use linear when the question says the increase or decrease is by some amount.

Hope this clears the doubt.

sahiti220620 · Answer

bb  help me understand something.. i took year 6 to be 4+5d and year 3 to be 4+3d. what's going wrong??

Bunuel · Answer

The tree starts at 4 feet tall when it was first planted (that is year 0).

After 1 year the height is  4 + x . 
 After 2 years the height is  4 + 2x . 
 After 3 years the height is  4 + 3x . 
 After 4 years the height is  4 + 4x . 
 After 5 years the height is  4 + 5x .  
 After 6 years the height is  4 + 6x .

So the correct heights are  4 + 4x  at the end of year 4 and  4 + 6x  at the end of year 6.

If you wrote  4 + 5x  for year 6, you were off by one year of growth, since there are 6 increases, not 5.

Please review the previous discussion for more.

gmatcat8 · Answer

Hello,

I was wondering why my approach was wrong. I set up the sequence as follows and tried to form a pattern.

a6 = a4 +(1/5)a4

So,

a3 = a1 + (1/5)*a1 (Essentially, a(n) = a(n-2) + (1/5)*a(n-2))

Plugging in for a1, which is 4ft, I get:

a3 = 4 + (1/5)*4, therefore a3 = 4.8

So, if the tree grows 0.8 in 2 years, it will grow 0.4 or 2/5 each year.

Clearly, this is wrong. Just trying to understand why I cannot solve it this way. Is it because the question clearly says the 1/5 relationship only applies to year 4 and 6, and not to the other years?

Bunuel · Answer

Yes, your last sentence is exactly right:  the 1/5 relationship applies only between year 4 and year 6, not to other years . For more review the two pages of the discussion.

When a certain tree was first planted, it was 4 feet tall and the heig

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