linear growth need help

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linear growth need help

by Winner2013 » Thu Jan 30, 2014 9:19 am
A certain kudzu plant was 11 feet long on the day it was planted, and the length grows
by a constant amount every day (including the first day it was planted). If this plant
grew 40% between the fourth day after it was planted and the tenth day after it was
planted, how many feet per day does it grow?

answer 1 foot per day.

My logic : it increases by a constant amount(say d) each day. so if 1st day it is a, on subsequent days it will be a+d, a+2d, a+3d ....

therefore, on 4th day it will be a+3d and on 10th -> a+9d

and,
a+9d= 1.4(a+3d)
a+9d = 1.4 a + 4.2d
0.4a = 4.8 d
a=11
therefore 4.8d= 4.4
so d = 11/12 foot

where am i going wrong? can someone help please....
thanks,
pooja
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by Brent@GMATPrepNow » Thu Jan 30, 2014 9:34 am
You were almost there. You just missed your calculations by 1 day.

Initial height = 11
Let d = daily height increase (in feet)

So, height 1 day after planting = 11 + d
Height 2 days after planting = 11 + 2d
Height 3 days after planting = 11 + 3d
Height 4 days after planting = 11 + 4d
.
.
.
Height 10 days after planting = 11 + 10d

The plant grew 40% between the fourth day after it was planted and the tenth day after it was
planted

In other words, the height on day 10 is 40% greater than the height on day 4
So, we can write: 11 + 10d = 1.4(11 + 4d)
Expand: 11 + 10d = 15.4 + 5.6d
Simplify: 4.4d = 4.4
Solve, d = 1

Cheers,
Brent
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by Winner2013 » Thu Jan 30, 2014 1:41 pm
Hello Brent,

yeah just realized that I totally ignored this line - 'including the first day it was planted' from the question. got it now. Thank you for your help :-)

regards,
pooja

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by GMATGuruNY » Thu Jan 30, 2014 3:27 pm
Winner2013 wrote:A certain kudzu plant was 11 feet long on the day it was planted, and the length grows by a constant amount every day (including the first day it was planted). If this plant grew 40% between the fourth day after it was planted and the tenth day after it was planted, how many feet per day does it grow?

1
2
3
4
5
An alternate approach would be to PLUG IN THE ANSWERS, which an actual GMAT problem would provide.

On the 10th day, the plan is 40% taller than on the 4th day.
Since 40/100 = 2/5, it is very likely that the height on the 4th day is a multiple of 5.
The answer choices imply the following heights on the 4th day:
A: 11 + 4(1) = 15.
B: 11 + 4(2) = 19.
C: 11 + 4(3) = 23.
D: 11 + 4(4) = 27.
E: 11 + 4(5) = 31.
Only the option in red yields a multiple of 5.

Answer choice A: 1 foot per day
Here, the height on the 4th day = 15.
6 days later, the height on the 10th day = 15 + 6(1) = 21.
(height increase)/(4th day height) = (21-15)/15 = 6/15 = 2/5 = 40%.
Success!

The correct answer is A.
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