Last visit was: 17 May 2026, 21:46 It is currently 17 May 2026, 21:46
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 17 May 2026
Posts: 110,529
Own Kudos:
815,442
 [13]
Given Kudos: 106,285
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 110,529
Kudos: 815,442
 [13]
Edward invested five-ninths of his money at an annual rate of 2r% comp 05 Oct 2023, 01:30
1
Kudos
Add Kudos
12
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

60% (02:54) correct 40% (03:04) wrong based on 131 sessions

History

Date
Time
Result
Not Attempted Yet
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%


ShowHide Answer
Official Answer
C
User avatar
AryaSwagat
User avatar
Joined: 08 Nov 2021
Last visit: 02 Aug 2025
Posts: 81
Own Kudos:
116
 [2]
Given Kudos: 105
Location: India
Concentration: General Management, Strategy
GPA: 8.7
WE:Engineering (Technology)
Posts: 81
Kudos: 116
 [2]
Edward invested five-ninths of his money at an annual rate of 2r% comp 07 Oct 2023, 19:12
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Taking the principal 1, at 2r % rate 5/9th of it compounds semiannually.
After one year the return would be \(5/9 * (1+\frac{2r}{2*100})^2 \) as it compounds semiannually, so the rate is halved and the period is doubled.
4/9 th of it compounds at r% annually. After one year the return is \(4/9 * (1+\frac{r}{100})\).
Now putting the given values in the formula and test one by one.
1) r= 10%
So 5/9* (1.1)^2 + 4/9 * (1.1) = 5/9* 1.21+ 4/9*1.1= 1.1655....
3) 20%
So 5/9* (1.2)^2 + 4/9 *( 1.2) = 0.8+ 0.533 = 1.333 ......so here increase over 1 is 33.33% ie. 1/3rd .

So C

* In this way the problem seems calculation heavy, kindly suggest any other methods.
User avatar
stne
User avatar
Joined: 27 May 2012
Last visit: 16 May 2026
Posts: 1,814
Own Kudos:
2,107
Given Kudos: 687
Posts: 1,814
Kudos: 2,107
Edward invested five-ninths of his money at an annual rate of 2r% comp 07 Oct 2023, 23:56
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AryaSwagat
Taking the principal 1, at 2r % rate 5/9th of it compounds semiannually.
After one year the return would be \(5/9 * (1+\frac{2r}{2*100})^2 \) as it compounds semiannually, so the rate is halved and the period is doubled.
4/9 th of it compounds at r% annually. After one year the return is \(4/9 * (1+\frac{r}{100})\).
Now putting the given values in the formula and test one by one.
1) r= 10%
So 5/9* (1.1)^2 + 4/9 * (1.1) = 5/9* 1.21+ 4/9*1.1= 1.1655....
3) 20%
So 5/9* (1.2)^2 + 4/9 *( 1.2) = 0.8+ 0.533 = 1.333 ......so here increase over 1 is 33.33% ie. 1/3rd .

So C

* In this way the problem seems calculation heavy, kindly suggest any other methods.
Show more

Did you get C = 20% or E =33%?
User avatar
AryaSwagat
User avatar
Joined: 08 Nov 2021
Last visit: 02 Aug 2025
Posts: 81
Own Kudos:
116
Given Kudos: 105
Location: India
Concentration: General Management, Strategy
GPA: 8.7
WE:Engineering (Technology)
Posts: 81
Kudos: 116
Edward invested five-ninths of his money at an annual rate of 2r% comp 08 Oct 2023, 00:22
Kudos
Add Kudos
Bookmarks
Bookmark this Post
stne
AryaSwagat
Taking the principal 1, at 2r % rate 5/9th of it compounds semiannually.
After one year the return would be \(5/9 * (1+\frac{2r}{2*100})^2 \) as it compounds semiannually, so the rate is halved and the period is doubled.
4/9 th of it compounds at r% annually. After one year the return is \(4/9 * (1+\frac{r}{100})\).
Now putting the given values in the formula and test one by one.
1) r= 10%
So 5/9* (1.1)^2 + 4/9 * (1.1) = 5/9* 1.21+ 4/9*1.1= 1.1655....
3) 20%
So 5/9* (1.2)^2 + 4/9 *( 1.2) = 0.8+ 0.533 = 1.333 ......so here increase over 1 is 33.33% ie. 1/3rd .

So C

* In this way the problem seems calculation heavy, kindly suggest any other methods.

Did you get C = 20% or E =33%?
Show more

Overall investment increases by one third, that is 1.33 times of principal investment. The interest rate is 20%.
Answer is C = 20%

Posted from my mobile device
User avatar
stne
User avatar
Joined: 27 May 2012
Last visit: 16 May 2026
Posts: 1,814
Own Kudos:
2,107
 [1]
Given Kudos: 687
Posts: 1,814
Kudos: 2,107
 [1]
Edward invested five-ninths of his money at an annual rate of 2r% comp 08 Oct 2023, 00:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
AryaSwagat
Taking the principal 1, at 2r % rate 5/9th of it compounds semiannually.
After one year the return would be \(5/9 * (1+\frac{2r}{2*100})^2 \) as it compounds semiannually, so the rate is halved and the period is doubled.
4/9 th of it compounds at r% annually. After one year the return is \(4/9 * (1+\frac{r}{100})\).
Now putting the given values in the formula and test one by one.
1) r= 10%
So 5/9* (1.1)^2 + 4/9 * (1.1) = 5/9* 1.21+ 4/9*1.1= 1.1655....
3) 20%
So 5/9* (1.2)^2 + 4/9 *( 1.2) = 0.8+ 0.533 = 1.333 ......so here increase over 1 is 33.33% ie. 1/3rd .

So C

* In this way the problem seems calculation heavy, kindly suggest any other methods.
Show more

Another way:

Let the principal be \(= 90\)

\(50(1+ \frac{2r}{2*100})^2 + 40(1+ \frac{r}{100}) = 120\)

\(50x^2 +40x-120 = 0 \)... Putting (\(1+\frac{r}{100} =x\))

\(5x^2 +4x-12 = 0\)

\((x+2)(5x-6)=0 \)

\(x \neq -2 \) as \(x\) is positive

\(x= \frac{6}{5}\)

Thus \(1+\frac{r}{100} = \frac{6}{5}\)

\(r =20\%\)

Ans C

Hope it helps.
User avatar
rushimehta
User avatar
Joined: 28 Sep 2023
Last visit: 15 May 2026
Posts: 51
Own Kudos:
4
Given Kudos: 70
Location: India
Schools: Tuck '27 Ross '27 Fuqua '27
GPA: 3.78
Schools: Tuck '27 Ross '27 Fuqua '27
Posts: 51
Kudos: 4
Edward invested five-ninths of his money at an annual rate of 2r% comp 05 Jan 2025, 00:53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Another way to solve, can be simply taking numbers.

Let's say, total investment to be made is 9.
5@2r% compounded for 1 year semi-annually, 4@r% compounded for 1 year annually...
So the final amount with interest after 1 year is 1.33 of the initial amount... which becomes 12.

You can start with the middle option, r=20%
So 5@40% compounded for 1 year semi-annually --> so every 6 months it will grow by 20%...
after 6 months = 6
after 12 months = 7.2

and 4@20% compounded for 1 year annually --> so every 12 months it will grow by 20%...
after 12 months = 4.8

7.2+4.8 = 12... thus option C is the correct answer.

In case using option C, you get the final answer < 12... then you can move on to try option D and E... if you get >12%... you can try out option A and B

Might take a bit longer, but I feel better than going the algebric way... algebra usually confuses me... :)
Moderators:
Bunuel
Math Expert
110523 posts
Krunaal
Tuck School Moderator
852 posts