It is currently 21 Feb 2018, 17:15

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Each year for 4 years, a farmer increased the number of trees in a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
D
Joined: 02 Aug 2009
Posts: 5660
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 19 Jan 2016, 00:25
Sunil01 wrote:
Each year for 4 years, a farmer increased the number
of trees in a certain orchard by 1/4 of the number of
trees in the orchard the preceding year. If all of the
trees thrived and there were 6,250 trees in the
orchard at the end of the 4-year period, how many
trees were in the orchard at the beginning of the
4-year period?
(A) 1,250
(B) 1,563
(C) 2,250
(D) 2,560
(E) 2,752

I am going wrong somewhere.
Could someone help me, is something wrong with my method to solve this question.
Not getting the correct answer.
Please help.

My Approach:
Let number of trees at the beginning of the year be x.
2nd year no. of trees = x+x/4
3rd year no. of trees = (x+x/4) +1/4(x+x/4) 1.e. x + x/4 + x/4 + x/16 = x +x/2 + x/16
4th year no of trees = x + x/2 + x/16 + 1/4(x + x/2 + x/16)
6250 = x + x/2 + x/16 + x/4 + x/8 + x/64
6250 = (64x + 32x + 4x + 16x + 8x + x)/64
6250 = 125x/64
x = 3200
...


Hi,
you have gone wrong in that you have calculated only for three years..
each year it increases by 1/4, so calculate for the end of the year,...
in this case the first year end would be x+x/4, which you have shown for second year..
By your approach you should check for % year begining to get the answer..

the answer you have got is at teh end of one year..
if it was y in begining, it will become5y/4..
so here 5y/4=3200...
or y=3200*4/5=4*640=2560..

Hope it helps you..
you have missed out on one year..
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


BANGALORE/-

Director
Director
avatar
G
Joined: 07 Dec 2014
Posts: 906
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 18 Apr 2016, 13:53
let t=# of original trees
(t)(5/4)^4=6250
t=6250/(5/4)^4
t=2560 trees
Manager
Manager
avatar
Joined: 20 Mar 2015
Posts: 62
GMAT ToolKit User
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 29 Jun 2016, 01:59
isn't this a GP and the 6250 is sum of the GP?

Can't we use S=\(\frac{a(1-r^n)}{1-r}\)

where r=1/4
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7944
Location: Pune, India
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 29 Jun 2016, 20:49
1
This post received
KUDOS
Expert's post
bimalr9 wrote:
isn't this a GP and the 6250 is sum of the GP?

Can't we use S=\(\frac{a(1-r^n)}{1-r}\)

where r=1/4


Yes, there is a GP but r = 5/4. Also, 6250 is the last term, not sum of the GP.

a*(5/4), a*(5/4)*(5/4), ...

Every previous term is multiplied by 5/4 to get the next term. The 4th term is 6250.

\(6250 = a * (5/4)^4\)

\(a = 10 * 4^4\)

\(a = 2560\)

Answer (D)



a ( r^n - 1)/(r - 1) = a ((5/4)^4 - 1)/(5/4 - 1)

6250 = a * (5^4 - 4^4)/4^3

2 * 5^4 * 4^3 = a * 369
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
User avatar
Joined: 11 Apr 2015
Posts: 36
Location: Germany
Concentration: General Management, Entrepreneurship
GPA: 3.1
WE: Project Management (Energy and Utilities)
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 05 Jul 2016, 11:05
converting 6250 into prime factorization form (625*10 = 5*5*5*5*5*2) can save some time in solving this question, as many 5's will cancel out nicely
_________________

"I fear not the man who has practiced 10,000 kicks once, but I fear the man who has practiced one kick 10,000 times." Bruce Lee

"I hated every minute of training, but I said, "Don’t quit. Suffer now and live the rest of your life as a champion."" Muhammad Ali

Intern
Intern
avatar
B
Joined: 16 Nov 2016
Posts: 31
Location: India
Concentration: Finance, International Business
GPA: 3.78
WE: Accounting (Accounting)
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 29 Jan 2017, 22:57
What's wrong if we add up 1/4 for each year. Please help me understand this in detail.

First year begin: x------------- ending 5x/4
2nd year begin: 5x/4----------ending 3x/2(5x/4+x/4)
3year begin: 3x/2--------------ending 7x/4
4 year begin : 7x/4-----------ending 2x
I dont get the answer and iam not understanding what is wrong with this approch ... please help
Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2192
Location: United States (CA)
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 01 Feb 2017, 08:21
1
This post received
KUDOS
Expert's post
imhimanshu wrote:
Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752


This problem is testing us on exponential growth. We are given that the number of trees increased by ¼ each year. To determine the number of trees in a certain year, we multiply the number of trees from the previous year by 1.25, or 5/4. Let’s let x equal the number of trees at the beginning (of the first year) of the 4-year period.

Start of year 1 = x

End of year 1 = x(5/4)

End of year 2 = x(5/4)(5/4)

End of year 3 = x(5/4)(5/4)(5/4)

End of year 4 = x(5/4)(5/4)(5/4)(5/4) = (625/256)x

We are given that there were 6,250 trees at the end of year 4, so we can set up the following equation:

(625/256)x = 6,250

625x = 6,250(256)

x = 10(256) = 2,560

Thus, there were 2,560 trees at the beginning of the 4-year period.

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
G
Joined: 16 Oct 2010
Posts: 7944
Location: Pune, India
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 02 Feb 2017, 03:58
1
This post received
KUDOS
Expert's post
muthappashivani wrote:
What's wrong if we add up 1/4 for each year. Please help me understand this in detail.

First year begin: x------------- ending 5x/4
2nd year begin: 5x/4----------ending 3x/2(5x/4+x/4)
3year begin: 3x/2--------------ending 7x/4
4 year begin : 7x/4-----------ending 2x
I dont get the answer and iam not understanding what is wrong with this approch ... please help


This is what the question says:

"Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year"

He increases the trees by 1/4 of the number in the preceding year. So in 3rd year, he increases the trees by a fourth of the number of trees in the 2nd year, not one fourth of those in the 1st year.
Hence, 2nd year end/3rd year beg, the number of trees will be 5x/4 + (1/4)*(5x/4)
and so on...
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 28 Mar 2017
Posts: 1
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 21 Apr 2017, 04:18
All the above responses have been around trying to solve this algebraically. But we can do plug and play with the answer choices. We know what the end result trees are and we know what the annual increase. Given that the annual increase is 1/4 --> we know that the answer choices must be a factor of 4. So (B) is eliminated automatically since its an odd number.

The rest of the answers choices with the exception of D are not factors of 4. so we can eliminate that way.

Now if we had two answers that were divisible by 4, then we can easily do another step and recalculate.

Personally I find this much easier then having to the algebra formula but both can be done under 2 min easily.
1 KUDOS received
Intern
Intern
avatar
B
Joined: 24 May 2016
Posts: 19
Location: Germany
Concentration: International Business, General Management
GMAT ToolKit User
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 04 Jun 2017, 01:26
1
This post received
KUDOS
1
This post was
BOOKMARKED
Another approach would be test the answers:
Normally, starting with B or D, I have chosen D as it is a cleaner number.
Assuming the farmer had at the beginning 2,560 trees he will have one year later (2,560 *1,25) or calculate 1/4 of it and add it.
--> After 1 year: 3200 trees
--> 2. Year: 3200*1,25= 4000 trees
--> 3. Year: 4000*1,25= 5000 trees
--> 4. Year: 5000*1,25= 6250 trees - Bingo!
As we arrived to the desired value Answer D is correct! The hint was that after the first year the numbers cleaned up very nicely and the calculations involved less work.
Manager
Manager
User avatar
B
Joined: 23 May 2017
Posts: 201
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
CAT Tests
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 10 Jul 2017, 22:25
IMHO I think we can skip the calculation part in this question.

my reasoning behind solving this question was : since the number of trees are increasing in a fashion of 1/4 .
so by end of 4th year we will have a number which is of form X/64....( we are adding 1/4 three times in the initial number) Total number of trees in the orchard after 4 years = 6250, factor of which does not have 64 : so we must have a initial number which will have a factor of 64 or we can say the number must be divisible by 64.

Let's scan the numbers : let's start finding the number which is divisible by 8

A. 1250
B. 1563
C. 2250
D. 2560 --> divisible by 8
E. 2752 --> divisible by 8

so we have only two options to check for further divisibility: as we further divide the number by another 8 we will see only D fits our requirement
_________________

If you like the post, please award me Kudos!! It motivates me

Intern
Intern
User avatar
B
Joined: 27 Oct 2017
Posts: 4
Location: Brazil
Concentration: Strategy, Operations
GMAT 1: 600 Q46 V28
GMAT 2: 650 Q46 V34
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 10 Nov 2017, 16:28
I arrived to the answer through an easier way (at least in my opinion), but one thing almost got me troubled in the end.

1. I started considering 6250 it was the number of trees in 3rd year + a fifth of this number.
2. So, I divided 6250 by 5 and multiplied the result by 4, to get the number of trees in the 3rd year = 5000.
3. Then, I did the same process with 5000 and arrived to the number of trees on 2nd year = 4000.
4. Did it once again and arrived to the number of trees in the 1st year, 3200.

I stopped here and fortunatelly there was no choice with that number, otherwise I would have gone for it. :suspect
The tricky thing is that the author doesn't ask you the number of trees in the first year, but how many trees there were prior to that.

So, I picked the 3200 and did it all once again: (3200/5)*4 and finally got the letter (D) 2560. I think this approach is more straight to the point and doesn't require almost any algebra.
Intern
Intern
User avatar
Joined: 16 Jan 2014
Posts: 1
Concentration: Other, Marketing
GPA: 3.65
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 24 Nov 2017, 18:02
My solution was quick and simple. Each of the answer choices would need to be multiplied by 125% the first year and than that answer multiplied by 125% for the 2nd year, and so on until the 4th year equaled 6250.

I looked at each of the answer choices, and given that I wanted to find what 25% of each answer choice was, and then I would add that to one of the answer choices (which would give me 25% +100% = 125%). However, since 25% is 1/4 of 100% I looked at which answer choice could be divisible by 4. The only one was answer D.

Choice A:
100% of 1250 = 1250
25% of 1250 = 312.50 (Farmer isn't going to plant half a tree in the 2nd year so this answer is wrong. Thus all decimal answers are wrong.)

Choice B:
25% of 1563 = 390.75 (Farmer isn't going to plant 3/4ths of a tree in 2nd year so this is wrong.)

Choice C:
etc. etc...

To save time, I then divided all answer choices by 4. (All you need to do is look at the last 2 digits of each big number, if the last two digits are divisible by 4, then the overall big number is divisible by 4.) The only answer choice that was divisible by 4 was D. (The last two digits of answer choice D. are 60, which is divisible by 4).
Manager
Manager
avatar
Joined: 09 Jun 2015
Posts: 102
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 22 Dec 2017, 22:23
imhimanshu wrote:
Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752

Can someone walk me through the logic behind this question. I am able to solve this by using options as well as by assuming the number of trees = x. However, had the question been, "If all of the trees thrived and there were 6250 trees in the orchard at the end of 15 year period, how many trees were in the orchard at the beginning of the 4 year period". then it would have been difficult to solve.

Thanks

The ratio of FV and PV is 5/4. In 4 years, the ratio will be (5/4)^4=625/256. The FV is given as 6250; the PV will be 2560.
1 KUDOS received
Intern
Intern
avatar
Joined: 23 Dec 2017
Posts: 3
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 25 Dec 2017, 20:32
1
This post received
KUDOS
VeritasPrepKarishma wrote:
aeglorre wrote:
Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752



Isn't the question quite ambiguous, though? I mean the first scentence could be interpreted as "for the first year we have (4/4)x and for the second year (5/4)x and for the third..." etc.. With that reasoning one would have (5/4)^3 * x + x and then your approach doesnt work.

Obviously, I understand that this was a flaw in my reasoning but I cannot understand how they - with that wording - will assume that we totally understand that at the end of year one he has (5/4)x..

Is there a straightforward "word translation" way in knowing how to interpret wordings like this?


Actually, it is not ambiguous. Read the statement:
Each year a farmer increased the number of trees by 1/4. He did this for 4 years. (In GMAT Verbal and Quant are integrated. You need Verbal skills (slash and burn) in Quant and Quant skills (Data Interpretation) in Verbal.

So in the first year, he increased it by 1/4
The next year, he again increased it by 1/4 (of preceding year)
Next year, again the same.
Next year, again the same.
So he did it for a total of 4 years.

So if initially the number of trees was x, in the first year he made them (5/4)x


Correct me if I am wrong, but it seems to me that there is a flaw in this GMAT problem. If you read the statement:
"by 1/4 of the number of trees in the orchard of the preceding year"
So you cannot increase the number of trees the first year as you do not know the number of tree of the year preceding that first year.
And the only way to increase the number of trees of the preceding year is to be in the second year, and then you know what is the number of trees of the preceding year.

So either you are assuming that the number of trees before that first year is = n, but this is not provided by the statement, or you are taking into account the fourth increase that happened actually at the beginning of the fifth year, and this is wrong as the number 6250 is the number of trees at the end of the 4-year period.

(And you cannot be between the first and the second year, either you are in the first year or in the second year)
Attachments

GMAT flaw.png
GMAT flaw.png [ 125.63 KiB | Viewed 228 times ]

Senior Manager
Senior Manager
avatar
S
Joined: 02 Apr 2014
Posts: 403
Re: Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 11 Feb 2018, 01:14
Let there be 256x(purposefully chosen, 256 as it as \(4^4\)) tree at the beginning of 4 years.

First year: (5/4) * 256x = 320x
second year: (5/4)* 320x = 400x
thrid year: (5/4)*400x = 500x
fourth year: (5/4) * 500x = 625x = 6250 => x = 10
So first year, number of trees 256x = 2560
Intern
Intern
avatar
Joined: 01 Feb 2018
Posts: 1
Each year for 4 years, a farmer increased the number of trees in a [#permalink]

Show Tags

New post 11 Feb 2018, 04:53
aeglorre wrote:
Bunuel wrote:
imhimanshu wrote:
Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year. If all of the trees thrived and there were 6250 trees in the orchard at the end of 4 year period, how many trees were in the orchard at the beginning of the 4 year period.

A. 1250
B. 1563
C. 2250
D. 2560
E. 2752

Can someone walk me through the logic behind this question. I am able to solve this by using options as well as by assuming the number of trees = x. However, had the question been, "If all of the trees thrived and there were 6250 trees in the orchard at the end of 15 year period, how many trees were in the orchard at the beginning of the 4 year period". then it would have been difficult to solve.

Thanks


Say the number of trees at the beginning of the 4 year period was x, then:
At the end of the 1st year the number of trees would be \(x+\frac{1}{4}x=\frac{5}{4}*x\);
At the end of the 2nd year the number of trees would be \((\frac{5}{4})^2*x\);
At the end of the 3rd year the number of trees would be \((\frac{5}{4})^3*x\);
At the end of the 4th year the number of trees would be \((\frac{5}{4})^4*x\);
At the end of the \(n_{th}\) year the number of trees would be \((\frac{5}{4})^n*x\);

So, we have that \((\frac{5}{4})^4*x=6,250\) --> \(\frac{5^4}{4^4}*x=5^4*10\) --> \(x=4^4*10=2,560\).

Answer: D.

If the question were "if all of the trees thrived and there were 6250 trees in the orchard at the end of 15 year period, how many trees were in the orchard at the beginning of the 4 year period", then we would have that: \((\frac{5}{4})^{15}*x=6,250\) --> \(x\neq{integer}\), so it would be a flawed question.

Hope it's clear.



Isn't the question quite ambiguous, though? I mean the first scentence could be interpreted as "for the first year we have (4/4)x and for the second year (5/4)x and for the third..." etc.. With that reasoning one would have (5/4)^3 * x + x and then your approach doesnt work.

Obviously, I understand that this was a flaw in my reasoning but I cannot understand how they - with that wording - will assume that we totally understand that at the end of year one he has (5/4)x..

Is there a straightforward "word translation" way in knowing how to interpret wordings like this?


I agree with this interpretation of the question, mostly because this is how I read it as well.
So, when I read : "Each year for 4 years, a farmer increased the number of trees in a certain orchard by 1/4 of the number of trees in the orchard of the preceding year" I assume Year 1 starts with x trees. At the start of year 2 the farmer plants 1/4 x more than year 1, so the trees at the start of the 2nd year is 5x/4.
Then,
Year 0 (before the question): (4/5)x
Year 1: x
Year 2: (5/4)x
Year 3: (5/4)^2x
Year 4: (5/4)^3x
From the question I'm not sure if the increase happens during the year or at the start of it...
Can someone help me understand why this interpretation is entirely incorrect?


Edit: Never mind, I got it...Took me a while :/
Each year for 4 years, a farmer increased the number of trees in a   [#permalink] 11 Feb 2018, 04:53

Go to page   Previous    1   2   [ 37 posts ] 

Display posts from previous: Sort by

Each year for 4 years, a farmer increased the number of trees in a

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.