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

 It is currently 20 Nov 2019, 18:12 ### 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

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

Author Message
TAGS:

### Hide Tags

Director  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

7 00:00

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  D
Joined: 19 Oct 2018
Posts: 1080
Location: India
Edward invested five-ninths of his money at an annual rate of 2r% comp  [#permalink]

### Show Tags

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  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

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%

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

Intern  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

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%

Intern  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

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 [ 1009.8 KiB | Viewed 280 times ] 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  