GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 17 Aug 2019, 07:59

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

The turnover of an organization named 'Coverage' was $640 crore per an

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

Hide Tags

Find Similar Topics 
Manager
Manager
User avatar
G
Joined: 15 Dec 2015
Posts: 114
GMAT 1: 680 Q49 V34
GPA: 4
WE: Information Technology (Computer Software)
The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post Updated on: 30 Jul 2017, 20:22
2
13
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

52% (03:00) correct 48% (02:49) wrong based on 159 sessions

HideShow timer Statistics

The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years

Originally posted by DHAR on 30 Jul 2017, 07:59.
Last edited by DHAR on 30 Jul 2017, 20:22, edited 2 times in total.
Most Helpful Community Reply
Intern
Intern
User avatar
B
Joined: 09 Dec 2014
Posts: 37
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 30 Jul 2017, 10:04
6
3
DH99 wrote:
The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years


Let x be the number of years after which turnovers of both the firms be equal.
For 'Miles' increase by 300% every year==> (100+300)/100 = 400/100 ==> 4 times every year
For 'Coverage' increase by 700% every two years ==> (100+700)/100 ==> 800/100 ==> 8 times every two years
We can write the equation by the given data as:

\(40*4^x=640*8^{x/2}\) (as for 'Coverage' the rise is every two years)
\(4^x=16*8^{x/2}\) ==> \(2^{2x}=2^4*(2^3)^{x/2}\)
\(2^{2x}=2^{(8+3x)/2}\) ==> 4x=8+3x ==> x=8
Answer: C
_________________
Thanks,
Ramya
General Discussion
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4565
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 30 Jul 2017, 09:01
1
DH99 wrote:
The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years
Attachment:
Capture.JPG
Capture.JPG [ 31.38 KiB | Viewed 3279 times ]

Answer will be (C) after 8 years...

_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Intern
Intern
avatar
B
Joined: 14 Dec 2015
Posts: 3
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 30 Jul 2017, 09:42
5
2
Apply the compound interest to solve it quickly. Assume that the turnover of both the companies becomes same at the end of "t" years.

for the organization named "Coverage" , the turnover in t years will be = 640 * ((1 + 7) ^ t/2)
(its t/2 because the turnover increases every 2 years)

for the organization named "Miles", the turnover in t years will be = 40 * ((1 + 3) ^ t)

The coverage will be same after "t" years, hence:
640 * ((1 + 7) ^ t/2) = 40 * ((1 + 3) ^ t)

Solve for "t" , and you will get t = 8 years
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57022
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 30 Jul 2017, 11:15
DH99 wrote:
The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years


Please name topics properly. Read rule 3 in our RULES OF POSTING. Thank you.
_________________
Intern
Intern
avatar
B
Joined: 18 Jul 2018
Posts: 18
The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 04 Nov 2018, 07:08
Hi,

I have a doubt..so if we use geometric progression here, n comes to 6 years. where am i going wrong?
Company coverage in 2001 has a turn over of 640 cr. In 2003 it will have 5120. Therefore, common ratio (r) is 8
Company Mike in 2001 has a turnover of 40 Cr. In 2001 it will have 160 Cr. Therefore common ratio (r) is 4

Company Coverage, x = 40(4)^(n-1)-----------1
Comany Mike, x = 640(8)^{(n/2)-1}-----------2

Equating 1 and 2, we get n = 6
Can you please help me figure where I am going wrong. Thankyou
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1258
The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 04 Nov 2018, 08:30
DHAR wrote:
The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years


pushpitkc chetan2u, Gladiator59 hello there!

formula for compound interest

\(A = p(1+\frac{r}{n})^{nt}\)

p - principal/ amount
r - annual rate of interest
t - number of years the amount is deposted
n - number of years the interest is compounded
a - money accumulated after n years


\(640(1+\frac{7}{2})^{2t} = 40(1+\frac{3}{1})^t\)

\(640(1+3.5)^{2t} = 40(1+3)^t\)

\(640(4.5)^{2t} = 40(4)^t\)

\(2880^{2t} = 160^t\) now what to do ? :? i got stuck here :? :)


for more information about compound formula click here :) https://qrc.depaul.edu/StudyGuide2009/N ... terest.htm
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1258
The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 05 Nov 2018, 10:03
cherryriya wrote:
Apply the compound interest to solve it quickly. Assume that the turnover of both the companies becomes same at the end of "t" years.

for the organization named "Coverage" , the turnover in t years will be = 640 * ((1 + 7) ^ t/2)
(its t/2 because the turnover increases every 2 years)

for the organization named "Miles", the turnover in t years will be = 40 * ((1 + 3) ^ t)

The coverage will be same after "t" years, hence:
640 * ((1 + 7) ^ t/2) = 40 * ((1 + 3) ^ t)

Solve for "t" , and you will get t = 8 years




can anyone solve for T after this 640 * ((1 + 7) ^ t/2) = 40 * ((1 + 3) ^ t)? need detailed algebraic solution Bunuel will you be my hero today ? :lol:
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 525
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 05 Nov 2018, 10:23
1
1
Hi dave13

640 * (1+7)^t/2 = 640 * (8)^t/2 = 640 * (2^3)^t/2 = 640 * 2^(3t/2)

The other hand is 40 * 4^t = 40 * 2^2t

Let 40 * 2^2t = 640 * 2^(3t/2) divide by 40 on both sides.

2^2t = 16 * 2^(3t/2)

2^2t = 2^4 * 2^(3t/2) Since all the base is equal we can equate the powers.

2t = 4 + 3t/2

0.5t = 4

t = 8

Hope this helps :D
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 525
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 05 Nov 2018, 10:29
1
yashna36 wrote:
Hi,

I have a doubt..so if we use geometric progression here, n comes to 6 years. where am i going wrong?
Company coverage in 2001 has a turn over of 640 cr. In 2003 it will have 5120. Therefore, common ratio (r) is 8
Company Mike in 2001 has a turnover of 40 Cr. In 2001 it will have 160 Cr. Therefore common ratio (r) is 4

Company Coverage, x = 40(4)^(n-1)-----------1
Comany Mike, x = 640(8)^{(n/2)-1}-----------2

Equating 1 and 2, we get n = 6
Can you please help me figure where I am going wrong. Thankyou


Hi yashna36

If we look at it from this perspective for Company with 40$ per annum the increase is 300% per year correct?

so it is 40 * (1 + 300%) = 40 * (1+3) = 40 * 4 (per year)

So every year it will increase by 4. This way 40*4 for first year and 40*4*4 for 2nd year etc.. which can be replaced by the compound interest equation.

where 40 is the principal amount 40* (1+3)^x because it goes per year.

The other equation is 640 * (1+7)^(x/2) the reason we are dividing by 2 is because the increase happens every 2 years.

I hope this helps.
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1258
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 05 Nov 2018, 10:35
Salsanousi wrote:
Hi dave13

640 * (1+7)^t/2 = 640 * (8)^t/2 = 640 * (2^3)^t/2 = 640 * 2^(3t/2)

The other hand is 40 * 4^t = 40 * 2^2t

Let 40 * 2^2t = 640 * 2^(3t/2) divide by 40 on both sides.

2^2t = 16 * 2^(3t/2)

2^2t = 2^4 * 2^(3t/2) Since all the base is equal we can equate the powers.

2t = 4 + 3t/2

0.5t = 4

t = 8

Hope this helps :D



Salsanousi mashallah :) thank you. i forgot to divide both sides by 40 :) that is why was getting very very wrong answer :lol:
Director
Director
avatar
G
Joined: 19 Oct 2013
Posts: 525
Location: Kuwait
GPA: 3.2
WE: Engineering (Real Estate)
GMAT ToolKit User
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 05 Nov 2018, 10:44
1
I tried approaching the question with backsolving

I tried with 6 first so 40 * 4^6 = 40 * 2^12 and tried to make it equal to the other side of 640 * 8^3 (because every 2 years it happens)

40 * 2^12 = 640 * 2^9

2^12 = 16 * 2^9

2^12 = 2^4 * 2^9 which is not true. 2^12 < 2^13

I tried with C

40 * 4^8 = 640 * 8^4

2^16 = 2^4 * 2^12

2^16 = 2^16
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 7367
Location: United States (CA)
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 07 Nov 2018, 18:57
1
DHAR wrote:
The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years


For Miles, when the turnover increased by 300% each year, it means that there was a fourfold increase per year. Let n be a positive integer. In 2n years (after 2001), Miles’ turnover is 40 x 4^(2n). For Coverage, when the turnover increased by 700% every two years, it means that there was an eightfold increase every two years, and so Coverage’s turnover is 640 x 8^n. Since we are interested in determining the number of years since 2001 it took for their turnovers to be the same, we equate the two growth expressions in the following equation:

40 x 4^(2n) = 640 x 8^n

40 x 16^n = 640 x 8^n

16^n/8^n = 640/40

2^n = 16

n = 4

Therefore, in 2 x 4 = 8 years, the two turnovers will be the same.

Answer: C
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Intern
Intern
avatar
B
Joined: 08 May 2019
Posts: 5
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 24 Jul 2019, 18:39
Abhishek009 wrote:
DH99 wrote:
The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years
Attachment:
Capture.JPG

Answer will be (C) after 8 years...



Year-Coverage-Miles
2001-640-40
2002-640-160
2003-5120-640
2004-5120-2560
2005-40960-10240
2006-40960-40960

I am getting same value in 6th year itself.
Coverage growth is once in 2 years while miles have every year.
Coverage will be 8 times in every 2 years while miles would be 4 times from previous year.

Need to what I am doing wrong.
Intern
Intern
avatar
B
Status: Writing the GMAT this month
Joined: 12 Apr 2019
Posts: 10
Location: India
GPA: 2.9
WE: Marketing (Retail)
Re: The turnover of an organization named 'Coverage' was $640 crore per an  [#permalink]

Show Tags

New post 08 Aug 2019, 05:00
Abhishek009 wrote:
DH99 wrote:
The turnover of an organization named 'Coverage' was $640 crore per annum in 2001.In the same year another organization named 'Miles', established just a few years back, had the turnover of $40 crore per annum.The turnover of 'Miles' increased by 300% every year whereas Coverage's turnover increased by 700% every two years.After how many years will both the companies have the same turnover?

A. 4 years
B. 6 years
C. 8 years
D. 10 years
E. 12 years
Attachment:
Capture.JPG

Answer will be (C) after 8 years...


Hi Abhishek,

Unable to understand how you got the above figures. Could you elaborate, please?
GMAT Club Bot
Re: The turnover of an organization named 'Coverage' was $640 crore per an   [#permalink] 08 Aug 2019, 05:00
Display posts from previous: Sort by

The turnover of an organization named 'Coverage' was $640 crore per an

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





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