When a certain tree was first planted, it was 4 feet tall and the heig

Question

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 6 year the tree was 1/5 taller then it was at the end of 4 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

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

Bunuel · Accepted Answer

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 6 year the tree was 1/5 taller then it was at the end of 4 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

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

Let the rate of increase be  x  feet per year.

At the end of the 4th year, the height was  4+4x . 
At the end of the 6th year, the height was  4+6x , which was "1/5 taller than at the end of the 4th year."

Therefore, we have  4+4x+\frac{1}{5}(4+4x)=4+6x . Simplifying, we get  \frac{1}{5}(4+4x)=2x , leading to  x=\frac{2}{3} .

Answer: D.

g106 · Answer

The tree grows by x feets per year
At d end of 4th year the height of tree =4x+4
Between 4 th and sixth year the tree grows by 2x feet=(1/5)(4+4x)

2x=1/5(4+4x)
2x=.8x+.8
1.2x=.8
X=2/3

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fozzzy · Answer

Year 1 = 4+x
Year 2 = 4+2x
Year 3 = 4+3x
year 4 = 4+4x
Year 5 = 4+5x
year 6 = 4 + 6x

4+6x = 4+4x ( \frac{1}{5} + 1)

When we solve this we get answer D

siddhans · Answer

Shouldnt this be 1/5 (4 + 4x) = 4 + 6x ?? why is it (4 + 4x) + 1/5 (4 + 4x) = 4 + 6x ? when the stmt says : " at the of the 6th year the height was 1/5 taller than it was at the end of the 4th year"

Asifpirlo · Answer

just like 10% increase = 100+10 here, tall=increase.
so,
1/5 taller means" original height + 1/5 of (original height) "
so, original height at 4 years = 4+4x
and at 6years = 4+6x
According to the question,
4+4x+ 1/5(4+4x) = 4+6x, or , x = 2/3

bb0214 · Answer

ok... English is not m native language is for this problem, i struggle is what it meant "1/5 taller than it was at the end of 4th year"

why is not the equation

a6 = a4+1/5 ??!!!!!

how is that different than saying John is 5 years old than tom?!!!! which is John = tom + 5?

HELP?!

Bunuel · Answer

It would be a6 = a4+1/5, if it were "at the end of 6 year the tree was 1/5   foot   taller then it was at the end of 4 year". In its current form 1/5 MUST refer to a fraction, not to the quantity.

Hope it's clear.

mcelroytutoring · Answer

Attached is a visual that should help. Notice that multiplying by 6/5 is an easier way to get to "1/5 greater than." In other words, (6/5)x = "1/5 greater than x"

EDIT, 2022 : Note that you can also simply try the answers using the backsolving method. Start with Choice C and adjust accordingly.

C) 4 -> 6 -> 7. Going from 6 to 7 is an increase of 1/6, not 1/5. Hence, 1/2 feet per year is too small. Move down to a larger answer.

D) 4 -> 20/3 -> 24/3. diff / orig = (4/3) / (20/3) = (4/3) x (3/20) = 4/20 = 1/5. Thus, going from 20/3 to 24/3 is an increase of exactly 1/5 — as is also true of going from 20 to 24. (Since the denominator is the same, you can ignore it.) Correct!

E) 4-> 44/5 -> 56/5. diff / orig = (11/5) / (44/5) = 1/4. Too big.

zoezhuyan · Answer

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ScottTargetTestPrep · Answer

We are given that 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 define this constant amount as 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 was 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 of 6/5, we can 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

Zosimus · Answer

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   was the answer with no difficulty.

PGTLrowanhand · Answer

Hi GMATters,

Check out my video explanation of the problem here:

0K8-fX6R8dI

Enjoy!

Rowan

BrentGMATPrepNow · Answer

Height of tree on day 0 = 4
Let d = the height increase each year 
Height of tree at the end of the 1st year = 4+d
Height of tree at the end of the 2nd year = 4+d+d = 4 + 2d
Height of tree at the end of the 3rd year = 4+d+d+d = 4 + 3d
Height of tree at the end of the 4th year = 4+d+d+d+d =  4 + 4d 
Height of tree at the end of the 5th year = 4+d+d+d+d+d = 4 + 5d
Height of tree at the  end of the 6th year  = 4+d+d+d+d+d+d =  4 + 6d

At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year  
In other words, 6th year height = 4th year height + 1/5(4th year height)
Or we can write  4 + 6d  = ( 4 + 4d ) + 1/5( 4 + 4d )
Simplify: 4 + 6d = 6/5(4 + 4d)
Multiply both sides by 5 to get: 5(4 + 6d) = 6(4 + 4d)
Expand: 20 + 30d = 24 + 24d
Simplify: 6d = 4
d = 4/6 = 2/3 = D

Cheers,
Brent

EMPOWERgmatRichC · Answer

Hi All,

TESTing the ANSWERS is a great way to tackle this question. The "fast" way to solve a problem can still sometimes take time, but regardless of how you approach a prompt, you still need to take notes and stay organized.

From the screen capture, you chose answer C (1/2). If you jot down some quick notes, here's what you'd have:

Start = 4 ft 
Yr. 1 = 4 1/2 
Yr. 2 = 5 
Yr. 3 = 5 1/2 
Yr. 4 = 6 
Yr. 5 = 6 1/2 
Yr. 6 = 7

It doesn't make much time/effort to take these notes. Now, compare Year 6 to Year 4….Is it 1/5 greater? 7 to 6 is 1/6 greater, so answer C is not what we're looking for. It also gives us a "nudge" in the right direction. We need a 1/5 increase, but we only have a 1/6 increase right now….so we need a bigger increase…..so we need a bigger absolute increase each year. The correct answer has to be D or E.

Looking at all 5 choices as a group, I'm pretty sure the answer is D, but we can certainly prove it…

Start = 4 ft 
Yr. 1 = 4 2/3 
Yr. 2 = 5 1/3 
Yr. 3 = 6 
Yr. 4 = 6 2/3 
Yr. 5 = 7 1/3 
Yr. 6 = 8

This comparison requires a bit more math, but isn't "crazy" by any definition.

6 2/3 = 20/3 
8 = 24/3

Ignore the denominators….24 to 20….. 1/5 of 20 = 4…..24 IS 1/5 greater than 20.

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

LoneSurvivor · Answer

At the end of 6 year the tree was 1/5 taller then it was at the end of 4 year

This wording is very confusing

bndrnk · Answer

Hi,

Why does nobody care that it might be (4/5)*(6x+4) = 4x+4?  " At the end of the 6th year , the tree was  1/5 taller "  sounds like you have to take 1/5 of the 6th year tree, not the 4th year tree

EMPOWERgmatRichC · Answer

Hi bndrnk,

The word "taller" implies a comparison: taller than what....? If the prompt included no additional language, then there would be other ways to interpret what "At the end of the 6th year, the tree was 1/5 taller" means. However, the rest of that sentences tells you EXACTLY what the comparison is: "...1/5 taller than it (re: the tree) was at the end of the 4th year."

In addition, you have to be careful about how you apply the math concepts that are implied by the prompt. Multiplying the height in the 6th year by 4/5 is NOT the same as multiplying the height in the 4th year by 1.2 (which is the equivalent of "1/5 taller than").

GMAT assassins aren't born, they're made, 
Rich

robinbjoern · Answer

Is there a rule for when to use the compounded or the normal interest formular? I thought that when it increases every year we take the increase from the already bigger tree so i messed around with the compounded interest formular and abviously got it wrong

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EMPOWERgmatRichC · Answer

Hi robinbjoern,

The Compound Interest Formula is essentially about multiplication, since we're increasing by the same PERCENTAGE time period after time period. For example, if you invested $500 at 10% interest compounded annually for 3 years, you would have:

($500)(1.10)^3 = 
($500)(1.10)(1.10)(1.10) =
($500)(1.331)

However, in this prompt, the tree is NOT increasing by the same PERCENTAGE each year; it's increasing by a FIXED AMOUNT (in feet) each year. This ultimately means that we're dealing with addition, so the Compound Interest Formula doesn't apply.
 
GMAT assassins aren't born, they're made,
Rich

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