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

 It is currently 17 Jan 2019, 15:25

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

Events & Promotions

Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• The winning strategy for a high GRE score

January 17, 2019

January 17, 2019

08:00 AM PST

09:00 AM PST

Learn the winning strategy for a high GRE score — what do people who reach a high score do differently? We're going to share insights, tips and strategies from data we've collected from over 50,000 students who used examPAL.
• Free GMAT Strategy Webinar

January 19, 2019

January 19, 2019

07:00 AM PST

09:00 AM PST

Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT.

Bob invested one half of his savings in a bond that paid simple intere

Author Message
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 52231
Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

Show Tags

21 Apr 2015, 04:45
2
10
00:00

Difficulty:

75% (hard)

Question Stats:

58% (02:29) correct 42% (03:00) wrong based on 171 sessions

HideShow timer Statistics

Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received$605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.

_________________
Director
Joined: 07 Aug 2011
Posts: 533
GMAT 1: 630 Q49 V27
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

Show Tags

21 Apr 2015, 08:37
5
2
Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received$605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.

For the first year SimpleInterest and Compound interest will always be same if compounding is done annually.

To find the difference in interest gained, $330-$275= $55 increase in interest after the first year through compounding. From this information we can set up the equation$275 * X% = $55... 55/275=1/5=20% giving us answer choice E. _________________ Please pass me a +KUDOS if you liked my post! Thanks! Do not compare yourself to others, compare yourself to who you were yesterday. Math Expert Joined: 02 Sep 2009 Posts: 52231 Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] Show Tags 27 Apr 2015, 02:30 Bunuel wrote: Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received $605 as interest. What was the annual rate of interest? (A) 5% (B) 10% (C) 12% (D) 15% (E) 20% Kudos for a correct solution. CHECK VERITAS PREP OFFICIAL SOLUTION HERE: _________________ Senior Manager Joined: 15 Jan 2017 Posts: 355 Re: Bob invested one half of his savings in a bond that paid simple intere [#permalink] Show Tags 06 Dec 2017, 13:14 Used hit and trial. 605 - 550 = 55 dollars a) 5% of x is 25. So tried 10% (option B) --> it is$550

10% *550+500 = 605

Total interest = 10%+ 10%= 20 % interest
Senior Manager
Status: love the club...
Joined: 24 Mar 2015
Posts: 272
Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

Show Tags

28 Mar 2018, 07:38
in the first year interest earned from both bonds will remain the same, thus
interest earned from both bonds in the first year is

550 / 2 = 275

so, in the second year, interest earned from the bond that pays compounded interest will be (605 - 275) = 330

now, the extra amount (330 - 275) = 55 is the interest earned on the interest of previous year's interest

so, 55 = i * 275

=) i = 55 / 275

thus interest rate is 1/5 = 20 % = E the answer

thanks
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

Show Tags

09 Apr 2018, 15:30
Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received$605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Although we are not given the amount invested in either of the two bonds,, we know that the two amounts are equal. So we can let P = the amount invested in each bond. We can let r = the interest rate for each bond investment. We can create an equation for the amount of interest earned for the first bond, using the simple interest formula P x r x t = I. :

P x r x 2 = 550

We can also create an equation for the amount of interest earned for the second bond, using the compound interest formula: P(1 + r)^t - P = I:

P(1 + r)^2 - P = 605

Simplifying the first equation, we have P(2r) = 550 and simplifying the second equation, we have P[(1 + r)^2 - 1] = 605. Dividing the first equation by the second, we see that the P cancels out, and we have:
(2r)/[(1 + r)^2 - 1] = 550/605

605(2r) = 550[(1 + r)^2 - 1]

1210r = 550[1 + 2r + r^2 - 1]

1210r = 1100r + 550r^2

110r = 550r^2

Dividing both sides by 110r, (we can do that since r is nonzero), we have:

1 = 5r

r = 1/5 = 20%

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Intern
Joined: 01 Jan 2016
Posts: 21
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

Show Tags

07 May 2018, 18:07
JeffTargetTestPrep wrote:
Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received$605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Although we are not given the amount invested in either of the two bonds,, we know that the two amounts are equal. So we can let P = the amount invested in each bond. We can let r = the interest rate for each bond investment. We can create an equation for the amount of interest earned for the first bond, using the simple interest formula P x r x t = I. :

P x r x 2 = 550

We can also create an equation for the amount of interest earned for the second bond, using the compound interest formula: P(1 + r)^t - P = I:

P(1 + r)^2 - P = 605

Simplifying the first equation, we have P(2r) = 550 and simplifying the second equation, we have P[(1 + r)^2 - 1] = 605. Dividing the first equation by the second, we see that the P cancels out, and we have:
(2r)/[(1 + r)^2 - 1] = 550/605

605(2r) = 550[(1 + r)^2 - 1]

1210r = 550[1 + 2r + r^2 - 1]

1210r = 1100r + 550r^2

110r = 550r^2

Dividing both sides by 110r, (we can do that since r is nonzero), we have:

1 = 5r

r = 1/5 = 20%

QUESTION:

Why did you divide the first equation by the second?
Intern
Joined: 01 Jan 2016
Posts: 21
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

Show Tags

07 May 2018, 18:16
Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received$605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.

When it asks for the "annual rate of interest" I am under the assumption that there are two different bonds--(1) one that pays simple interest and (2) one that pays compound interest. How can there only be one annual rate of interest? Thank you.
Intern
Joined: 01 Jan 2016
Posts: 21
Re: Bob invested one half of his savings in a bond that paid simple intere  [#permalink]

Show Tags

07 May 2018, 18:23
Bunuel wrote:
Bob 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 (compounded annually) for the same 2 years at the same rate of interest and received$605 as interest. What was the annual rate of interest?

(A) 5%
(B) 10%
(C) 12%
(D) 15%
(E) 20%

Kudos for a correct solution.

Believe I may have answered my own question. One of the insights is to realize that though given two equations and two unknowns (P and r), the Ps cancel out leaving two equations and one unknown, therefore, one can solve for r, that annual rate of interest? Thanks.
Re: Bob invested one half of his savings in a bond that paid simple intere &nbs [#permalink] 07 May 2018, 18:23
Display posts from previous: Sort by