Problem Solving

I am very inconsistent with solving AP questions. Please advise the best way to approach the following problem:

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

a)3/10
b)2/5
c)1/2
d)2/3
e)6/5

Thanks for your help.

gmatgirl12 wrote:I am very inconsistent with solving AP questions. Please advise the best way to approach the following problem:

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

a)3/10
b)2/5
c)1/2
d)2/3
e)6/5

Thanks for your help.

I am not sure if this is the correct solution, but here is what I did.

In 2 years the tree grew 1/5 taller. So the rate is 1/5 per 2 years or 1/5 divided by 2 (or multiplied by 1/2) = 1/10th rate per year.

Multiply 1/10th by the starting height of 4 feet and you get the growth rate in feet per year of 2/5 (or answer choice B)

I hope that was a clear explanation (and most importantly, I hope it was correct).

chipbmk wrote:

gmatgirl12 wrote:I am very inconsistent with solving AP questions. Please advise the best way to approach the following problem:

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

a)3/10
b)2/5
c)1/2
d)2/3
e)6/5

Thanks for your help.

I am not sure if this is the correct solution, but here is what I did.

In 2 years the tree grew 1/5 taller. So the rate is 1/5 per 2 years or 1/5 divided by 2 (or multiplied by 1/2) = 1/10th rate per year.

Multiply 1/10th by the starting height of 4 feet and you get the growth rate in feet per year of 2/5 (or answer choice B)

I hope that was a clear explanation (and most importantly, I hope it was correct).

Hi chipbmk,
That is the method that I used as well, but somehow the answer was d) 2/3. This was a question on the gmatprep software and it did not have any explanations with the answer. Thank you for replying though.

Sol :
Here
a=4
n=6
d=?
Length of tree after 6 years would be
a6 = a+(6-1)d
=> a6 = a+5d

and after 4 years would be
a4 = a+3d

given a6 = 1/5 (a4)+a4
=> a+5d = [1/5(a+3d)]+a+3d
=>5a+25d = 6(a+3d)
=> 7d = a
=> d=4/7

csbhargavi wrote:Sol :
Here
a=4
n=6
d=?
Length of tree after 6 years would be
a6 = a+(6-1)d
=> a6 = a+5d

and after 4 years would be
a4 = a+3d

given a6 = 1/5 (a4)+a4
=> a+5d = [1/5(a+3d)]+a+3d
=>5a+25d = 6(a+3d)
=> 7d = a
=> d=4/7

Just a slight change in this.
Initial height is 4 ft.
So after one yr, is is 4+d
after 2nd year - 4+2d,

nth term in this case is a+nd and not a+(n-1)d.
ans - 2/3

jaspreet_takhar wrote:

csbhargavi wrote:Sol :
Here
a=4
n=6
d=?
Length of tree after 6 years would be
a6 = a+(6-1)d
=> a6 = a+5d

and after 4 years would be
a4 = a+3d

given a6 = 1/5 (a4)+a4
=> a+5d = [1/5(a+3d)]+a+3d
=>5a+25d = 6(a+3d)
=> 7d = a
=> d=4/7

Just a slight change in this.
Initial height is 4 ft.
So after one yr, is is 4+d
after 2nd year - 4+2d,

nth term in this case is a+nd and not a+(n-1)d.
ans - 2/3

That makes sense and it works out to 2/3, which is the answer. Thank you for your help!

jaspreet_takhar wrote:

csbhargavi wrote:Sol :
Here
a=4
n=6
d=?
Length of tree after 6 years would be
a6 = a+(6-1)d
=> a6 = a+5d

and after 4 years would be
a4 = a+3d

given a6 = 1/5 (a4)+a4
=> a+5d = [1/5(a+3d)]+a+3d
=>5a+25d = 6(a+3d)
=> 7d = a
=> d=4/7

Just a slight change in this.
Initial height is 4 ft.
So after one yr, is is 4+d
after 2nd year - 4+2d,

nth term in this case is a+nd and not a+(n-1)d.
ans - 2/3

Hey Jaspreet,

I haven't understand it.
Initial height is 4 ft (right)
After 1 Year - 4+d
After 2 Years - 4+2d
After 3 Years - 4+3d
After 4 Years - 4+4d
After 5 Years - 4+5d
After 6 Years - 4+6d

As per question ->> (4+6d)-(4+4d)=1/5. IMO 1/10

CrackGMAC wrote:

jaspreet_takhar wrote:

csbhargavi wrote:Sol :
Here
a=4
n=6
d=?
Length of tree after 6 years would be
a6 = a+(6-1)d
=> a6 = a+5d

and after 4 years would be
a4 = a+3d

given a6 = 1/5 (a4)+a4
=> a+5d = [1/5(a+3d)]+a+3d
=>5a+25d = 6(a+3d)
=> 7d = a
=> d=4/7

Just a slight change in this.
Initial height is 4 ft.
So after one yr, is is 4+d
after 2nd year - 4+2d,

nth term in this case is a+nd and not a+(n-1)d.
ans - 2/3

Hey Jaspreet,

I haven't understand it.
Initial height is 4 ft (right)
After 1 Year - 4+d
After 2 Years - 4+2d
After 3 Years - 4+3d
After 4 Years - 4+4d
After 5 Years - 4+5d
After 6 Years - 4+6d

As per question ->> (4+6d)-(4+4d)=1/5. IMO 1/10

Hi there--

The height at the 6th year, is .20 greater than the height of the 4th year.

It should be (4+6d)= (4+4d)+1/5(4+4d)-->
(4+6d)= 6/5(d+4d)
multiple each side by 5:
(5)(4+6d)= 6(4+4d)---> 20+30d=24+24d
solve for d:
6d=4---> d= 4/6---> 2/3