GMATprep. Exam 1. Question 31

When a certain tree was first planted, it was 4 feet tall, and the heigth of the tree increased by 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 of the tree increased each year?

Answers: 3/10, 2/5, 1/2, 2/3, 6/5

The correct answer is 2/3 but I have no idea how to solve it. Any help?

thanks

This is essentially a sequence problem in disguise. Let x = amount of yearly growth, in feet.

Yr0 = 4
Yr1 = 4+x
Yr2 = 4+x+x=4+2x
Yr3 = 4+x+x+x=4+3x
Yr4 = 4+x+x+x+x=4+4x
Yr5 = 4+x+x+x+x+x=4+5x
Yr6 = 4+x+x+x+x+x+x=4+6x

We are told the amount at the end of Year 6 is 6/5 of the amount at the end of year 4. Thus we can write:

4+6x = 6/5 (4+4x)
5(4+6x) = 6(4+4x)
20+30x = 24+24x
6x=4
x=2/3

Hi Condenach,

You're right, there was a typo in Stacey's original explanation. I edited her explanation, so I deleted your follow-up question.

Thanks.

-Jad

How can we say 6/5 when the question mentions 1/5 ? Please explain :(

I agree the statement 6th year is 1/5 tall 4th year is confusing.

For e.g. one could assume

6th year - 4th year = 1/5 ; which leads you to nowhere

actually the correct equation is similar to %change i.e. (6th year - 4th year)/4th year = 1/5 and this leads to 2/3

wrong.
the gmat is extremely fastidious about words and details. if this were the intended meaning, then the problem would have to say "1/5 foot". it doesn't, so the 1/5 MUST refer to a fraction of the aforementioned original quantity.

think about other examples and you'll see that this is correct: you can't, for instance, say "tim is 4 older than joe" if you mean "tim is 4 years older than joe".

--

DIGRESSION - caveat lector: the rest of this post has nothing to do directly with the original problem

there are, however, a couple of instances of genuine ambiguity, in which foreign readers must simply learn the common interpretation of certain phrasings. for instance,
temperature X is more than 20 degrees below the melting point of substance Y is, strictly speaking, genuinely ambiguous.
it could be read as
(1) temperature X is more than 20 degrees below the melting point of substance Y
or as
(2) temperature X is more than 20 degrees below the melting point of substance Y

if the melting point of substance Y were 87 degrees, then (1) would mean X < 67, and (2) would mean X > 67.
frustratingly - and dangerously, if X is a dangerous chemical - you MUST know that the correct interpretation is #1. native english speakers, even if they aren't that smart, will understand this without even stopping to think about it, but second-language english learners will be understandably confused.