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Tree problem from GMATPrep 1

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by Mjkourtis » Wed Jul 11, 2012 7:35 am
When a tree was first planted, it was 4 ft. tall. The height increased by a constant each year for the next 6 years. At end, it was 1/5 taller than it was at the end of 4 years. By how many feet did the height increase each year?

A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5
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by Birottam Dutta » Wed Jul 11, 2012 7:45 am
Let the constant increase in height be X.

So, after 1st year, height = 4+X
2nd year, height = 4+2X
3rd year, height = 4+3X
4th year, height = 4+4X
5th year, height = 4+5X
6th year, height = 4+6X
By the question, height at 6th year is 1/5th more or 6/5th of height at 4th year

=> 4+6X = 6/5(4+4X)
Solving, we get, X=2/3.

Hence, answer is D!
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by GMATGuruNY » Wed Jul 11, 2012 10:13 am
Mjkourtis wrote:When a tree was first planted, it was 4 ft. tall. The height increased by a constant each year for the next 6 years. At end, it was 1/5 taller than it was at the end of 4 years. By how many feet did the height increase each year?

A. 3/10
B. 2/5
C. 1/2
D. 2/3
E. 6/5
We can plug in the answers, which represent the growth each year.
Since the height in the 6th year is 6/5 the height in the 4th year, the needed ratio is 6th year : 4th year = 6:5.

Answer choice C: 1/2 each year.
4th year = 4 + 4(1/2) = 6.
6th year = 6 + 2(1/2) = 7.
6th : 4th = 7:6.
Since 7/6 is just a bit less than 6/5, the difference between the 6th year and the 4th year needs to increase by just a little.

The correct answer is D.

Note that, to determine the correct answer, we had to try only ONE answer choice -- a very efficient way to solve the problem.

Answer choice D: 2/3 each year.
4th year = 4 + 4(2/3) = 20/3.
6th year = 20/3 + 2(2/3) = 24/3.
6th : 4th = 24:20 = 6:5.
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by bubbliiiiiiii » Wed Jul 18, 2012 5:05 am
Is there a typo in the question? Both of you have taken 6/5 while the question says 1/5! ? or am I missing something?
Regards,

Pranay
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by GMATGuruNY » Wed Jul 18, 2012 5:12 am
bubbliiiiiiii wrote:Is there a typo in the question? Both of you have taken 6/5 while the question says 1/5! ? or am I missing something?
1/5 more than x means x + (1/5)x = (6/5)x.
Similarly, 1/5 TALLER means 6/5 of the preceding height.
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by bubbliiiiiiii » Fri Jul 20, 2012 12:34 am
GMATGuruNY wrote:
bubbliiiiiiii wrote:Is there a typo in the question? Both of you have taken 6/5 while the question says 1/5! ? or am I missing something?
1/5 more than x means x + (1/5)x = (6/5)x.
Similarly, 1/5 TALLER means 6/5 of the preceding height.
Thanks. :)
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Pranay
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