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GMAT Prep: Number Properties

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by rookieingmat » Sun Jun 29, 2008 4:51 pm
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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by szapiszapo » Tue Jul 01, 2008 12:54 pm
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
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by FrozenFire757 » Sat Jan 02, 2010 2:45 pm
I understand everything else but I can't seem to figure out where the "1" in "(1+1/5)" comes from. Can someone explain?
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by cameronwu » Sat Jan 02, 2010 3:41 pm
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?
Let's say A is the height at the end of year 6, and B is the height at the end of year 4

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.
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by amirp » Wed Sep 29, 2010 2:25 pm
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?
I Agree, I don't think the 1 is needed there. all we need is the following.

4 + 6x = (1/5) (4 + 4x) + (4 + 4x)

=> x = 2/3
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by monge1980 » Tue Apr 05, 2011 12:50 pm
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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by Stuart@KaplanGMAT » Tue Apr 05, 2011 1:59 pm
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".
You could solve for an answer in terms of H, but you couldn't answer with a definitive number.
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by force5 » Wed Apr 06, 2011 12:26 am
yes correct actually doesnt matter what you assume.
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by monge1980 » Wed Apr 06, 2011 1:04 am
I Agree with Stuart, we cannot answer with a definitive number. In fact, If I assume H=0, the yearly increase semms to be "0".

I ended up with yearly increase rate x=H/6.

Thanks
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by mindful » Sat May 07, 2016 2:41 am
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.
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by MartyMurray » Sat May 07, 2016 5:30 am
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.
The questions says "the height of the tree increased by a constant amount each year."

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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by mindful » Sat May 07, 2016 6:45 am
Thanks. Makes total sense. Not sure why I got confused. Maybe under test conditions...encountered it on a practice test.
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by [email protected] » Sat May 07, 2016 8:50 am
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

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by Matt@VeritasPrep » Thu May 12, 2016 12:35 am
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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by Turksonaaron » Fri Jun 23, 2017 11:15 am
[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
I'm a little bit confused here. How did you calculate 7 to 6 as 1/6 greater
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