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

It is currently 21 Nov 2019, 00:54

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

Edward invested five-ninths of his money at an annual rate of 2r% comp

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

Hide Tags

Find Similar Topics 
Director
Director
avatar
V
Joined: 18 Feb 2019
Posts: 591
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

Show Tags

New post 31 May 2019, 09:13
7
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

52% (03:10) correct 48% (02:59) wrong based on 63 sessions

HideShow timer Statistics

Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?


A. 10%
B. 15%
C. 20%
D. 25%
E. 33%
VP
VP
User avatar
D
Joined: 19 Oct 2018
Posts: 1080
Location: India
Premium Member CAT Tests
Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

Show Tags

New post 31 May 2019, 15:01
2
There are 2 approaches to solve this question

1. Alligation Method
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, his total interest would be slightly above 2r%.
We can use allegation method which would give us approximate answer.

2r...................r
.....100/3.........
5....................4

\(\frac{6r-100}{100-3r}\)=4/5
42r=900
r=21 which is closest to 20



2. General Approach
Let principal amount = P

a. 5P/9 is invested at annual 2r% compounded semi-annually
Interest= [5P/9{1+(r/100)}^2] -5P/9
b. 4P/9 is invested at an annual rate of r% compounded annually
Interest= [4P/9{1+(r/100)}]- 4P/9

Total interest=[5P/9{1+(r/100)}^2]-5P/9 + [4P/9{1+(r/100)}]- 4P/9= P/3

Solving above equation, we will get r=20

This approach is a bit lengthy though.






kiran120680 wrote:
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?


A. 10%
B. 15%
C. 20%
D. 25%
E. 33%
Director
Director
avatar
P
Joined: 24 Nov 2016
Posts: 809
Location: United States
Re: Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

Show Tags

New post 30 Sep 2019, 08:31
kiran120680 wrote:
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?

A. 10%
B. 15%
C. 20%
D. 25%
E. 33%


\((5x/9)(1+2r/2)^2+(4x/9)(1+r)=(1+1/3)x\)
\((5x/9)(1+r)^2+(4x/9)(1+r)=(1+1/3)x\)
\((1+r)[(5x/9)(1+r)+(4x/9)]=(1+1/3)x\)
\((1+r)[(5x+5xr+4x)/9]=(1+1/3)x\)
\((1+r)(9x+5xr)=(1+1/3)x(9)\)
\(9x+5xr+9xr+5xr^2=(1+1/3)(9)(x)\)
\(9+14r+5r^2=1.333(9)\)
\(5r^2+14r+9(1-1.333)=0\)
\(5r^2+14r+9(-0.333)=0\)
\(5r^2+14r-3=0\)
\((5r-1)(r+3)=0\)
\(r=(1/5,-3)>0=1/5=0.20\)

Answer (C)
Intern
Intern
avatar
B
Joined: 12 Aug 2019
Posts: 14
Re: Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

Show Tags

New post 30 Sep 2019, 19:36
nick1816 wrote:
There are 2 approaches to solve this question

1. Alligation Method
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, his total interest would be slightly above 2r%.
We can use allegation method which would give us approximate answer.

2r...................r
.....100/3.........
5....................4

\(\frac{6r-100}{100-3r}\)=4/5
42r=900
r=21 which is closest to 20



2. General Approach
Let principal amount = P

a. 5P/9 is invested at annual 2r% compounded semi-annually
Interest= [5P/9{1+(r/100)}^2] -5P/9
b. 4P/9 is invested at an annual rate of r% compounded annually
Interest= [4P/9{1+(r/100)}]- 4P/9

Total interest=[5P/9{1+(r/100)}^2]-5P/9 + [4P/9{1+(r/100)}]- 4P/9= P/3

Solving above equation, we will get r=20

This approach is a bit lengthy though.






kiran120680 wrote:
Edward invested five-ninths of his money at an annual rate of 2r% compounded semi-annually, and the remaining money at an annual rate of r% compounded annually. If after one year, Edward’s money had grown by one-thirds, the value of r is equal to which of the following?


A. 10%
B. 15%
C. 20%
D. 25%
E. 33%


Can you please explain your first approach in greater detail?
Intern
Intern
avatar
B
Joined: 01 Jun 2019
Posts: 9
Re: Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

Show Tags

New post 03 Oct 2019, 13:18
1
1
Took me about 4 minutes to solve it, but this is how I did it. (Pardon the poor quality of the scan).
Attachments

699E843E-9331-4EFD-A9EF-846A8F23D6D1.JPG
699E843E-9331-4EFD-A9EF-846A8F23D6D1.JPG [ 1009.8 KiB | Viewed 283 times ]

GMAT Club Bot
Re: Edward invested five-ninths of his money at an annual rate of 2r% comp   [#permalink] 03 Oct 2019, 13:18
Display posts from previous: Sort by

Edward invested five-ninths of his money at an annual rate of 2r% comp

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





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