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

It is currently 20 Aug 2018, 08:08

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

Shawn invested one half of his savings in a bond that paid s

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

Hide Tags

Director
Director
avatar
Joined: 02 Mar 2006
Posts: 568
Location: France
Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post Updated on: 10 Nov 2013, 04:24
2
35
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

61% (04:11) correct 39% (03:14) wrong based on 436 sessions

HideShow timer Statistics

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000

Originally posted by karlfurt on 25 Oct 2006, 08:22.
Last edited by Bunuel on 10 Nov 2013, 04:24, edited 1 time in total.
Edited the question and added the OA.
Most Helpful Community Reply
Senior Manager
Senior Manager
User avatar
Joined: 01 Sep 2006
Posts: 301
Location: Phoenix, AZ, USA
Answer D  [#permalink]

Show Tags

New post 25 Oct 2006, 08:35
10
8
CI means SI for 1st year + SI for 2nd Year + SI on (SI for 2nd year)

SI for 1st year = 550/2=275

275+275+SI on (275)=605==> SI on 275=55==>
SI on 275 = 275*R*1/100=55
R=20%

Now using SI for 2 years on T/2 of the money

(T/2)*20*2/100=550
T=550*5= 2750
General Discussion
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 615
Premium Member
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 20 Nov 2013, 10:47
1
2
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

Thus, if the rate be r, then \(r*x*(1+r)=330\).

Again, we know that\(2r*x = 550\),

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

Replacing this in the second equation, we get \(2x = \frac{550}{r} = 550*5 = 2750\)

A.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 200
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 20 Nov 2013, 17:59
mau5 wrote:
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

Thus, if the rate be r, then \(r*x*(1+r)=330\).

Again, we know that\(2r*x = 550\),

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

Replacing this in the second equation, we get \(2x = \frac{550}{r} = 550*5 = 2750\)

A.


wait how did you know that \((1+r) = \frac{6}{5}\)


also where do you get \(2x = \frac{550}{r} = 550*5 = 2750\) from? Is there a lot of work you did in your head?

Because if you sub in 1/5 for R, then you end up with 2x=550/(1/5) and then 2x=2750, and x=1375, not 2750...
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 615
Premium Member
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 20 Nov 2013, 22:43
1
AccipiterQ wrote:

wait how did you know that \((1+r) = \frac{6}{5}\)


\(r*x*(1+r)=330\).

Again, we know that\(2r*x = 550\),

Replace the value of r*x from the second equation in the first.

AccipiterQ wrote:
also where do you get \(2x = \frac{550}{r} = 550*5 = 2750\) from? Is there a lot of work you did in your head?

Because if you sub in 1/5 for R, then you end up with 2x=550/(1/5) and then 2x=2750, and x=1375, not 2750...


I have assumed the initial amount to be 2x, not x.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
avatar
B
Joined: 27 Jul 2011
Posts: 58
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 20 Nov 2013, 23:57
Please explain:
Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

I do not understand the the underlined statement; how to get it? please explain. Thanks.
Simple interest formula: I = PRt
550 = PR2
550/2P = R

Compound interest formula: P + I = P(1+R)^t
P + 605 = P(1+R)^2
P + 605 = P(1 + 2(550/2P) + (550/2P)^2)
P + 605 = P + 550/2 + (550)^2/ 4P
55 = (550)^2/4P
P = 2750
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 615
Premium Member
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 21 Nov 2013, 00:05
1
smartyman wrote:
Please explain:
Let the total amount invested be 2x. Now, we know that from half of it, he got 275$ per year for 2 years, and from the other half he got a total of 605$ over 2 years as Cumulative interest. Now, the amount of interest he got from the second year of cumulative interest : 605-275 = 330$

I do not understand the the underlined statement; how to get it? please explain. Thanks.


Say you have 200 $. Half of it is getting you simple interest per year at 10% rate.Thus, the interest you earn for the first year : \(\frac{10}{100}*100 = 10 $\)

Now, the other half is getting you compound interest at 10%, where interest is again compounded annually.Thus, the interest from the first year : \(\frac{10}{100}*100 = 10 $\)

Now, suppose I told you that the total CI you got from the other half for 2 years was 40 $, then the interest you earned from the second year is nothing but : 40-10 = 30$

The same has been done above. Note that as the rate of interest and the time is the same for both CI and SI, the interest earned for the first year will be exactly same in either case.

Hope this helps
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Intern
Intern
avatar
Joined: 06 Jan 2014
Posts: 41
GMAT ToolKit User
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 09 Jan 2014, 06:30
1
1
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Tough problem omg!

I understand that the interest paid per year from the simple interest was $275 (i.e. 550/2) and that the second years payment for the second year of the compound interest is $330 (i.e. 605 - 275) and thus the rate is 20% because (330/275=1.2)

but

after that....I AM LOST!!!!

HELP HELP HELP
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48061
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 09 Jan 2014, 07:19
3
1
TroyfontaineMacon wrote:
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Tough problem omg!

I understand that the interest paid per year from the simple interest was $275 (i.e. 550/2) and that the second years payment for the second year of the compound interest is $330 (i.e. 605 - 275) and thus the rate is 20% because (330/275=1.2)

but

after that....I AM LOST!!!!

HELP HELP HELP


So, we know that Shawn received 20% of the amount he invested in a year. We also know that in one year Shawn received $275, thud 0.2x = $275 --> x = $1,375.

Since, he invested equal sums in his 2 bonds, then his total savings before investing was 2*$1,375 = $2,700.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
User avatar
G
Joined: 14 Dec 2017
Posts: 457
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 24 Jun 2018, 01:02
karlfurt wrote:
Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received $550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received $605 as interest. What was the value of his total savings before investing in these two bonds?

(A) $2,750
(B) $5,500
(C) $11,000
(D) $22,000
(E) $44,000


Let Shawn's Total Savings = 2X

He invests X amount at simple interest for 2 years at "r" rate of interest & receives $550 as interest.

550 = X * 2 * r

Xr = 275..........................(i)

He invests X amount at compound interest for 2 years at same "r" rate of interest & receives $605 as interest.

In year one,

Interest on amount X = Xr

In year two,

Interest on amount X + Xr = (X + Xr) * r = Xr + Xr^2

Total interest for 2 years = Xr + Xr + Xr^2 = 2Xr + Xr^2


Hence we have, 2Xr + Xr^2 = 605

2*275 + 275*r = 605

Solving we get, r = 1/5

Hence X = 275 * 5 = 1375

Therefore the Total Savings = 2X = 2*1375 = 2750

Answer A.


Thanks,
GyM
Intern
Intern
avatar
B
Joined: 12 Mar 2018
Posts: 7
CAT Tests
Re: Shawn invested one half of his savings in a bond that paid s  [#permalink]

Show Tags

New post 05 Aug 2018, 11:20
karlfurt: You should have added an option 1375$, people would have chosen that. It would have been more difficult.
Re: Shawn invested one half of his savings in a bond that paid s &nbs [#permalink] 05 Aug 2018, 11:20
Display posts from previous: Sort by

Shawn invested one half of his savings in a bond that paid s

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

Events & Promotions

PREV
NEXT


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®.