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

It is currently 21 Apr 2019, 09:24

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

A sum of money invested under simple interest, amounts to $1200 in

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54376
A sum of money invested under simple interest, amounts to $1200 in  [#permalink]

Show Tags

New post 02 Jul 2017, 02:23
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

77% (02:39) correct 23% (02:45) wrong based on 70 sessions

HideShow timer Statistics

Director
Director
User avatar
V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
GMAT ToolKit User
A sum of money invested under simple interest, amounts to $1200 in  [#permalink]

Show Tags

New post 02 Jul 2017, 03:15
Bunuel wrote:
A sum of money invested under simple interest, amounts to $1200 in three years and $1500 in five years. What is the rate at which the sum of money was invested?

(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 45%


Principal, Rate is same for \(3\) years and \(5\) years.

\(Amount = P + SI\) ------------ (\(SI =\) Simple interest. \(SI = \frac{Principle * Rate * Time}{100}\))

\(1200 = P + SI_3 => P = 1200 - SI_3\) --------- (i) ---------- (\(SI_3 = SI\) for \(3\) years)

\(1500 = P + SI_5 => P = 1500 - SI_5\) ---------- (ii) ---------- (\(SI_5 = SI\) for \(5\) years)

Equating (i) and (ii), we get;

\(1200 - SI_3 = 1500 - SI_5\)

\(1200 - \frac{PR*3}{100} = 1500 - \frac{PR*5}{100}\)

\(120000 - PR*3 = 150000 - PR*5\)

\(PR*5 - PR*3 = 150000 - 120000\)

\(PR(5 - 3) = 30000\)

\(PR = \frac{30000}{2} = 15000\)

Substituting value of \(PR\) in \(SI_3\), we get;

\(1200 = P + \frac{PR*3}{100}\)

\(1200 = P + \frac{15000*3}{100} = P + 450\)

\(P = 1200 - 45 = $750\)

\(SI\) for amount \(1200\) for \(3\) years \(= $450\)

\(450 = \frac{PR*3}{100}\)

\(R = \frac{450 * 100}{3*750} = 20\)%.

Answer (C)...
Manager
Manager
avatar
B
Joined: 03 Feb 2017
Posts: 74
Location: Australia
GMAT 1: 720 Q48 V40
Re: A sum of money invested under simple interest, amounts to $1200 in  [#permalink]

Show Tags

New post 02 Jul 2017, 03:44
1
1
The amount at the end of 5 years is 1500 and at the end of 3 years is 1200
Total interest earned in these 2 years = 1500-1200 = 300
Interest earned per year = \(\frac{300}{2}\) = 150

The original amount invested at the beginning of year 1 = 1200-3*(150) = 1200-450 = 750
Annual rate of interest = \(\frac{150}{750}\) = \(\frac{1}{5}\) = 20%

Answer C
VP
VP
User avatar
D
Status: Learning
Joined: 20 Dec 2015
Posts: 1018
Location: India
Concentration: Operations, Marketing
GMAT 1: 670 Q48 V36
GRE 1: Q157 V157
GPA: 3.4
WE: Engineering (Manufacturing)
Reviews Badge CAT Tests
Re: A sum of money invested under simple interest, amounts to $1200 in  [#permalink]

Show Tags

New post 02 Jul 2017, 04:34
1
Rate of SI =p*r*t according to the question we have
1200=p(1+r*3/100).......(1)
1500=P(1+r*5/100).......(2)
Divide 1 by 2 we have
4/5=(100+3r)/(100+5r) solving we get r=20%
Thus C
_________________
Please give kudos if you found my answers useful
Current Student
avatar
B
Joined: 06 Nov 2016
Posts: 103
Location: India
GMAT 1: 710 Q50 V36
GPA: 2.8
Reviews Badge
Re: A sum of money invested under simple interest, amounts to $1200 in  [#permalink]

Show Tags

New post 03 Jul 2017, 11:42
It is given that:
3PR/100 + P = 1200 ------- (1)

PR = 100 (1200 - P)/3 ------- (2)

Also given:
5PR/100 + P = 1500 -----(3)

substituting equation 2 into 3,
500/300*(1200-P) + P = 1500

or P = 750 ----(4)

further substituting (4) into (2)

R is 20%
Retired Moderator
User avatar
P
Joined: 19 Mar 2014
Posts: 931
Location: India
Concentration: Finance, Entrepreneurship
GPA: 3.5
GMAT ToolKit User
Re: A sum of money invested under simple interest, amounts to $1200 in  [#permalink]

Show Tags

New post 03 Jul 2017, 12:29
Bunuel wrote:
A sum of money invested under simple interest, amounts to $1200 in three years and $1500 in five years. What is the rate at which the sum of money was invested?

(A) 10%
(B) 15%
(C) 20%
(D) 25%
(E) 45%


I got the answer of C - 20% however my method was a bit longer one. Some really good solutions out there.
_________________
"Nothing in this world can take the place of persistence. Talent will not: nothing is more common than unsuccessful men with talent. Genius will not; unrewarded genius is almost a proverb. Education will not: the world is full of educated derelicts. Persistence and determination alone are omnipotent."

Best AWA Template: https://gmatclub.com/forum/how-to-get-6-0-awa-my-guide-64327.html#p470475
GMAT Club Bot
Re: A sum of money invested under simple interest, amounts to $1200 in   [#permalink] 03 Jul 2017, 12:29
Display posts from previous: Sort by

A sum of money invested under simple interest, amounts to $1200 in

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.