Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: When a certain tree was first planted, it was 4 feet tall, [#permalink]

Show Tags

09 Sep 2013, 11:15

gameCode wrote:

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 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 increase each year?

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

if 4th year is say x and 6th year is x + x/5, the difference = x/5 for 2 years and hence for each year it will be x/10.

now if 4th year is x then the start of 1st year will be (x-(4x/10)) i.e. x- (2x/5) = 4 i.e. x = 20/3.

When a certain tree was first planted, it was 4 feet tall, [#permalink]

Show Tags

24 Aug 2014, 12:10

1

This post was BOOKMARKED

Bunuel wrote:

gameCode wrote:

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 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 increase each year?

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

There's something particular with the answer of this one which i don't understand, hence the posting.

Let the rate of increase be \(x\) feet per year.

At the end of the 4th year the height was \(4+4x\) and at the of the 6th year the height was \(4+6x\), which was "1/5 taller than it was at the end of the 4th year" --> \((4+4x)+\frac{1}{5}(4+4x)=4+6x\) --> \(\frac{1}{5}(4+4x)=2x\) --> \(x=\frac{2}{3}\).

Answer: D.

Hi Bunuel,

I used a different approach which led me to the wrong answer. I can't seem to figure out why?

1)Difference between EOY 6 and EOY 4 is 1/5, therefore, Y6=(6/5)Y4 2)By the same token, EOY 2 = (6/5) EOY0, therefore EOY2 = (6/5)*4 3)Since it's a constant increase every year, (24/5) / (2) since we are only concerned about the increase per year -- this equals 12/5.

Why is this wrong? If it's a constant increase, it's increasing by the SAME amount each year correct. It's NOT compounding from the previous year. Am I correct? By that theory, shouldn't my method work?

On another note -- if the above was an increase to the previous year, meaning, compounded, how would the equation change?

Re: When a certain tree was first planted, it was 4 feet tall, [#permalink]

Show Tags

10 Apr 2017, 07:56

I was surprised to see that everyone has taken an algebraic approach. The problem isn't that complicated and can be solved with no algebra at all.

We will simply run two scenarios based on answer choices (B) and (D). If either of them turns out to be the answer, then we're golden. This will happen 40% of the time. Otherwise, we should be able to see whether the answer lies between (B) and (D) or whether it is an outlier.

To make the scenario easier, I will reclassify the original height for answer choice (B) as 20/5 and for answer choice (D) as 12/3, although I will not write the denominator each time for added speed and simplicity.

Scenario (B)

Year 0—20/5 Year 1—22 Year 2—24 Year 3—26 Year 4—28 Year 5—30 Year 6—32

Since 1/5 of 28 (year 4) is 5 and change, we can see that one fifth more will be 33 and change. So (B) is not the answer—it's too small.

Scenario (D) Year 0—12/3 Year 1—14 Year 2—16 Year 3—18 Year 4—20 Year 5—22 Year 6—24

Since 1/5 of 20 (year 4) is 4, (D) is the answer. Had (D) not been the answer, we would have been able to determine which of the other three [(A), (C), or (E)] was the answer with no difficulty.
_________________

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 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 increase each year?

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

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. Since we know that the growth is by a constant amount, we have a linear growth problem. Thus, we can let x = the yearly growth amount in feet:

Starting height = 4

Height after year one = 4 + x

Height after year two = 4 + 2x

Height after year three = 4 + 3x

Height after year four = 4 + 4x

Height after year five = 4 + 5x

Height after year six = 4 + 6x

We are also given that at the end of the 6th year the tree was 1/5 taller than it was at the end of the 4th year. This means the height of the tree at the end of the 6th year is 6/5 times as tall as its height at the end of the 4th year. Thus, we can create the following equation:

(6/5)(4 + 4x) = 4 + 6x

To eliminate the fraction 6/5, we multiply the entire equation by 5:

6(4 + 4x) = 20 + 30x

24 + 24x = 20 + 30x

6x = 4

x = 4/6 = 2/3 feet

Answer: D
_________________

Jeffery Miller Head of GMAT Instruction

GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions