When a certain tree was first planted, it was 4 ft 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
Ans: D
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Can't get through this...please assist!!
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asherkunal
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Let x = the yearly increase.When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain 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
Height after 4 years = 4 + 4x.
Height after 6 years = 4 + 6x.
At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year.
The phrase in red implies the following:
The height in the 6th year was 6/5 of the height in the 4th year.
An equivalent statement:
At the end of the 6th year, the tree was 20% taller than it was at the end of the 4th year.
Here, the phrase in red implies the following:
The height in the 6th year was 120% of the height in the 4th year.
Since the height in the 6th year was 6/5 of the height in the 4th year, we get:
(4 + 6x) = (6/5)(4 + 4x)
20 + 30x = 24 + 24x
6x = 4
x = 4/6 = 2/3.
The correct answer is D.
An alternate approach is to plug in the answers, which represent the increase each year.
When the correct answer choice is plugged in, (6th-year height)/(4th-year height) = 6/5.
Answer choice D: 2/3
Height after 4 years = 4 + 4(2/3) = 20/3.
Height after 2 more years = 20/3 + 2(2/3) = 24/3.
(6th-year height)/(4th-year height) = (24/3) / (20/3) = 24/20 = 6/5.
Success!
The correct answer is D.
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asherkunal
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Why can we not use 1/5 in our equation?GMATGuruNY wrote:Let x = the yearly increase.When a certain tree was first planted, it was 4 feet tall, and the height of the tree increased by a certain 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
Height after 4 years = 4 + 4x.
Height after 6 years = 4 + 6x.
At the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year.
The phrase in red implies the following:
The height in the 6th year was 6/5 of the height in the 4th year.
An equivalent statement:
At the end of the 6th year, the tree was 20% taller than it was at the end of the 4th year.
Here, the phrase in red implies the following:
The height in the 6th year was 120% of the height in the 4th year.
Since the height in the 6th year was 6/5 of the height in the 4th year, we get:
(4 + 6x) = (6/5)(4 + 4x)
20 + 30x = 24 + 24x
6x = 4
x = 4/6 = 2/3.
The correct answer is D.
An alternate approach is to plug in the answers, which represent the increase each year.
When the correct answer choice is plugged in, (6th-year height)/(4th-year height) = 6/5.
Answer choice D: 2/3
Height after 4 years = 4 + 4(2/3) = 20/3.
Height after 2 more years = 20/3 + 2(2/3) = 24/3.
(6th-year height)/(4th-year height) = (24/3) / (20/3) = 24/20 = 6/5.
Success!
The correct answer is D.
I know it would yield a negative result, but isn't there way to use it as it is?
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To clarify:Why can we not use 1/5 in our equation?
The prompt does not state that the tree was 1/5 foot taller.
Rather, it states that the tree was 1/5 TALLER.
1/5 taller means 20% taller.
In other words, the 6th-year height was 6/5 -- or 120% -- of the 4th-year height.
To increase x by 1/2 implies the following:isn't there way to use it as it is?
x + (1/2)x = (3/2)x.
To increase x by 1/3 implies the following:
x + (1/3)x = (4/3)x.
To increase x by 1/5 implies the following:
x + (1/5)x = (6/5)x.
Since the height after 4 years (4+4x) increases by 1/5 to yield the height after 6 years (4+6x), we get:
(4+4x) + (1/5)(4+4x) = 4+6x
(6/5)(4+4x) = 4+6x
24 + 24x = 20 + 30x
4 = 6x
x = 4/6 = 2/3.
Last edited by GMATGuruNY on Wed Apr 12, 2017 5:18 am, edited 1 time in total.
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Brent@GMATPrepNow
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Height of tree on day 0 = 4When 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 6th year, the tree was 1/5 taller than it was at the end of 4th year. By how many feet the height of the tree increase each year?
1) 3/10
2) 2/5
3) 1/2
4) 2/3
5) 6/5
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 = [spoiler]2/3[/spoiler] = D
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Hi asherkunal,
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
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
