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

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

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Source: GMAT Paper Tests

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 years the tree was 1/5 taller then it was at the end of 4 years. 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

The OA is D

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GMAT/MBA Expert

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BTGmoderatorLU wrote:
Source: GMAT Paper Tests

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 years the tree was 1/5 taller then it was at the end of 4 years. 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
Let x = the yearly increase.
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.

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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GMAT/MBA Expert

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BTGmoderatorLU wrote:
Source: GMAT Paper Tests

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 years the tree was 1/5 taller then it was at the end of 4 years. 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

The OA is D
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

Answer: D

Cheers,
Brent

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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

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Contact Rich at Rich.C@empowergmat.com

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