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

It is currently 17 Aug 2019, 13:54

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

The simple interest on a certain sum of money for 3 yrs is $225 and th

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

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 57025
The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post 29 Jan 2019, 01:58
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

54% (03:04) correct 46% (02:57) wrong based on 35 sessions

HideShow timer Statistics

GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 4464
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post Updated on: 30 Jan 2019, 04:06
2
Bunuel wrote:
The simple interest on a certain sum of money for 3 yrs is $225 and the compound interest on the same sum at the same rate for 2yrs is $153. What is the principal invested?

A. $1500

B. $1875

C. $2250

D. $2500

E. $2750


SI=p*r*t/100
225=p*r*3/100
r/100= 75/p

CI= P * ( 1+r/100) ^t

Compounded amount in 2 years = P(1+r100)2P(1+r100)2

interest earned = Compounded amount in 2 years - Invested amount = P(1+r100)^2 - P

153=P*(1+r/100)^2-P
153=P*(1+75/P)^2-P
solve for P
3P=75*75
p= 75*25
p= 1875
IMOB
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.

Originally posted by Archit3110 on 29 Jan 2019, 02:18.
Last edited by Archit3110 on 30 Jan 2019, 04:06, edited 2 times in total.
NUS School Moderator
avatar
V
Joined: 18 Jul 2018
Posts: 1026
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge CAT Tests
The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post 29 Jan 2019, 02:54
As simple interest is the same for each year. SI per year = 225/3 = 75$.
SI = PTR/100
225 = PR*3/100
PR = 7500

Also, \(CI_2-SI_2 = \frac{PR^2}{100^2}\) = 153-150 = 7500*R/10000

\(CI_2\) and \(SI_2\) are compound and simple interest for 2 years.
R = 4%
75 = P*4*1/100
P = 1875

B is the answer.
_________________
Press +1 Kudos If my post helps!
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3019
Re: The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post 29 Jan 2019, 03:26
1
1

Solution


Given:
    • The simple interest on a certain sum of money for 3 years = $225
    • The compound interest on the same sum at the same rate for 2 years = $153

To find:
    • The principal amount invested

Approach and Working:
Let the principal amount invested = $P
    • Simple interest earned for 3 years =\(P * 3 * \frac{r}{100} = $225\)
      o Implies, \(\frac{r}{100}= \frac{75}{P}\)

    • Compound interest earned for 2 years = P(1 + r/100)^2 – P = $153
      o Implies, \(P(1 + \frac{75}{P})^2 – P = $153\)
      o \((P + 75)^2 – P^2 = 153P\)
      o \(150P + 75^2 = 153P\)
      o \(3P = 75^2\)
    • Therefore, P = 25 * 75 = 1875

Hence, the correct answer is Option B

Answer: B

Image

_________________
GMAT Club Legend
GMAT Club Legend
User avatar
D
Joined: 18 Aug 2017
Posts: 4464
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post 29 Jan 2019, 03:32
EgmatQuantExpert wrote:

Solution


Given:
    • The simple interest on a certain sum of money for 3 years = $225
    • The compound interest on the same sum at the same rate for 2 years = $153

To find:
    • The principal amount invested

Approach and Working:
Let the principal amount invested = $P
    • Simple interest earned for 3 years =\(P * 3 * \frac{r}{100} = $225\)
      o Implies, \(\frac{r}{100}= \frac{75}{P}\)

    • Compound interest earned for 2 years = P(1 + r/100)^2 – P = $153
      o Implies, \(P(1 + \frac{75}{P})^2 – P = $153\)
      o \((P + 75)^2 – P^2 = 153P\)
      o \(150P + 75^2 = 153P\)
      o \(3P = 75^2\)
    • Therefore, P = 25 * 75 = 1875

Hence, the correct answer is Option B

Answer: B

Image



EgmatQuantExpert
could you please explain the highlighted part , how did you get that? why is CI subtracted with P?
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
e-GMAT Representative
User avatar
V
Joined: 04 Jan 2015
Posts: 3019
Re: The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post 29 Jan 2019, 03:37
1
Archit3110 wrote:
EgmatQuantExpert
could you please explain the highlighted part , how did you get that? why is CI subtracted with P?


Hi Archit3110,

Compounded amount in 2 years = \(P(1 + \frac{r}{100})^2\)

Now, the interest earned = Compounded amount in 2 years - Invested amount = \(P(1 + \frac{r}{100})^2\) - P

Regards,
_________________
CEO
CEO
User avatar
D
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2966
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Reviews Badge
The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post 29 Jan 2019, 03:53
2
Bunuel wrote:
The simple interest on a certain sum of money for 3 yrs is $225 and the compound interest on the same sum at the same rate for 2yrs is $153. What is the principal invested?

A. $1500

B. $1875

C. $2250

D. $2500

E. $2750


Simple interest for 3 yrs is $225

i.e. Simple Interest for 1 year = 225/3 = $75 (Simple interest on a fixed sum remains same every year as the principle sum remains static)

i.e. Compound interest for first year = 75 (For first compounding Simple interest and compound interests are same... they start differing from second compounding)
Compound interest for Second year = 153 - 75 = 78

i.e. Coumpound interest for second year is 78-75 = $3 more which is interest charged on interest earned in previous compounding

i.e. Interest earned on $75 = $3

i.e. interest rate = (3/75)*100 = 4%

i.e. interest at Principle P for 1 year @4% = $75

i.e. (4/100)*P = 75

i.e. P = $1875


Answer: Option B
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Senior Manager
Senior Manager
avatar
G
Joined: 24 Nov 2016
Posts: 308
Location: United States
CAT Tests
Re: The simple interest on a certain sum of money for 3 yrs is $225 and th  [#permalink]

Show Tags

New post 07 Aug 2019, 13:11
Bunuel wrote:
The simple interest on a certain sum of money for 3 yrs is $225 and the compound interest on the same sum at the same rate for 2yrs is $153. What is the principal invested?

A. $1500
B. $1875
C. $2250
D. $2500
E. $2750


simple interest: principal • rate • years - principal = interest
compound interest: principal • (1+rate)^years - principal = interest

given: p(1+r/100)(3)-p=225 and p(1+r/100)^2-p=153;
isolate (r/100): p(1+r/100)(3)-p=225 is the same as p(r/100)(3)=225,…(r/100)=(75/p)
substitue (r/100): p(1+r/100)^2-p=153,… p(1+(75/p))^2-p=153,…p=1875

Answer (B).
GMAT Club Bot
Re: The simple interest on a certain sum of money for 3 yrs is $225 and th   [#permalink] 07 Aug 2019, 13:11
Display posts from previous: Sort by

The simple interest on a certain sum of money for 3 yrs is $225 and th

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





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