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
Can someone solve this?
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rookieingmat
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szapiszapo
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Answer is D
at t=0 year, height = 4 feet
at t=1 year, height = 4 feet + x (x being the constant yearly amount)
at t=2 years, height = 4 feet + 2x
at t=3, ....
...
at t=6, height = 4 + 6x
We know that at the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
therefore it translates into 4 + 6x = (1+1/5) * (4 + 4x)
resolving this equation gives x = 2/3
at t=0 year, height = 4 feet
at t=1 year, height = 4 feet + x (x being the constant yearly amount)
at t=2 years, height = 4 feet + 2x
at t=3, ....
...
at t=6, height = 4 + 6x
We know that at the end of the 6th year, the tree was 1/5 taller than it was at the end of the 4th year
therefore it translates into 4 + 6x = (1+1/5) * (4 + 4x)
resolving this equation gives x = 2/3
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FrozenFire757
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I understand everything else but I can't seem to figure out where the "1" in "(1+1/5)" comes from. Can someone explain?
Let's say A is the height at the end of year 6, and B is the height at the end of year 4FrozenFire757 wrote:I understand everything else but I can't seem to figure out where the "1" in "(1+1/5)" comes from. Can someone explain?
If A is 1/5 taller than B, that means it's as tall as B (which is 5/5) + 1/5 of B, so that's 6/5.
A is equal to 6/5 of B.
I Agree, I don't think the 1 is needed there. all we need is the following.FrozenFire757 wrote:I understand everything else but I can't seem to figure out where the "1" in "(1+1/5)" comes from. Can someone explain?
4 + 6x = (1/5) (4 + 4x) + (4 + 4x)
=> x = 2/3
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Stuart@KaplanGMAT
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You could solve for an answer in terms of H, but you couldn't answer with a definitive number.monge1980 wrote:Guys I have a question: could we arrive to the same solution without the information about the initial height? Let's assume the initial height was the unknown "H".
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mindful
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Sounds a little silly, but I am having a bit of an 'English' moment here.
When the tree increases by a constant amount every year, I wasn't sure whether this means it increases arithmetically or geometrically. I am not sure if I am using the right terms. In simple language, I wasn't if 'increasing' by a 'constant' amount means this: Original Length + x + Original Length + x + x
+ Original Length + x + x + x and so on...
or if it means Original Length + Original Length*x + Original Length + (Original Length + Original Length*x) * x and so on.
Finally, when at the end of the 6th year the tree is 1/5 taller than what it was after 4th year, then is it this:
Tree end of 6th year = Tree end of 4th year + 1/5 * (Tree end of 4th year)
Well I guess this end of 6th year, 4th year is clear to me. I don't know what else it could be. But with the first part why did I get confused. Sorry if I confused anyone further. Would love someone to shed some light on this.
When the tree increases by a constant amount every year, I wasn't sure whether this means it increases arithmetically or geometrically. I am not sure if I am using the right terms. In simple language, I wasn't if 'increasing' by a 'constant' amount means this: Original Length + x + Original Length + x + x
+ Original Length + x + x + x and so on...
or if it means Original Length + Original Length*x + Original Length + (Original Length + Original Length*x) * x and so on.
Finally, when at the end of the 6th year the tree is 1/5 taller than what it was after 4th year, then is it this:
Tree end of 6th year = Tree end of 4th year + 1/5 * (Tree end of 4th year)
Well I guess this end of 6th year, 4th year is clear to me. I don't know what else it could be. But with the first part why did I get confused. Sorry if I confused anyone further. Would love someone to shed some light on this.
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The questions says "the height of the tree increased by a constant amount each year."mindful wrote:Sounds a little silly, but I am having a bit of an 'English' moment here.
When the tree increases by a constant amount every year, I wasn't sure whether this means it increases arithmetically or geometrically. I am not sure if I am using the right terms. In simple language, I wasn't if 'increasing' by a 'constant' amount means this: Original Length + x + Original Length + x + x
+ Original Length + x + x + x and so on...
or if it means Original Length + Original Length*x + Original Length + (Original Length + Original Length*x) * x and so on.
Think about it. The height increased by a constant amount. The question does not say that height increased by a constant multiple of the previous height or something along those lines.
A constant amount is the same every year. So given what the question says you have the following.
Start: Original Height
After 1 Year: Original Height + x
After 2 Years: Original Height + 2x
After 3 Years: Original Height + 3x
and so on.
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[email protected]
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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.
If we start with Answer C (1/2 foot growth per year), here's what we'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 (since E is SO much bigger), 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.
If we start with Answer C (1/2 foot growth per year), here's what we'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 (since E is SO much bigger), 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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Don't feel bad for missing this: it must be one of the top ten most asked questions from the GMATPrep software, or at least close to that.
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Turksonaaron
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I'm a little bit confused here. How did you calculate 7 to 6 as 1/6 greater[email protected] wrote: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.
If we start with Answer C (1/2 foot growth per year), here's what we'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 (since E is SO much bigger), 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
