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05 Apr 2011, 15:37
6
00:00

Difficulty:

25% (medium)

Question Stats:

80% (02:29) correct 20% (02:37) wrong based on 268 sessions

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A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was$1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? (A) 3/8 (B) 2/5 (C) 1/2 (D) 3/5 (E) 3/4 ##### Most Helpful Expert Reply Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 9138 Location: Pune, India Re: Rate problem [#permalink] ### Show Tags 05 Apr 2011, 18:26 5 5 Acer86 wrote: A total of$20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the$20.000 was invested at the higher rate?
(A) 3/8
(B) 2/5
(C) 1/2
(D) 3/5
(E) 3/4

You can use weighted average in this question. One amount is deposited at 6% and another at 8%. The overall interest rate is $$(\frac{1440}{20,000})*100 = 7.2%$$
$$\frac{w1}{w2}= \frac{(8 - 7.2)}{(7.2 - 6)} = \frac{2}{3}$$
So 2/5 of the 20,000 was invested at 6% and 3/5 was invested at 8%.

For explanation of the formula used above, see: http://www.veritasprep.com/blog/2011/03 ... -averages/
and
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/
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##### General Discussion
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Affiliations: ACCA
Joined: 17 Apr 2010
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Schools: IMD, Insead, LBS, IE, Cambridge, Oxford
Re: Rate problem  [#permalink]

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05 Apr 2011, 15:48
1
1
D
1440/20000*100%=7.2
7.2-6=1.2
8-6=2
1.2/2=3/5 D

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Intern
Affiliations: ACCA
Joined: 17 Apr 2010
Posts: 32
Schools: IMD, Insead, LBS, IE, Cambridge, Oxford
Re: Rate problem  [#permalink]

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05 Apr 2011, 15:48
D
1440/20000*100%=7.2
7.2-6=1.2
8-6=2
1.2/2=3/5 D

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Retired Moderator
Joined: 20 Dec 2010
Posts: 1784
Re: Rate problem  [#permalink]

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05 Apr 2011, 15:52
1
Acer86 wrote:
A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was$1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? (A) 3/8 (B) 2/5 (C) 1/2 (D) 3/5 (E) 3/4 Let "$x" be invested with the higher rate of 8%
Thus, "20000-x" must have been invested with lower rate of 6%

Simple Interest = Principal* Rate* Time

For the Amount invested at 8%
Principal = x
Rate = 0.08
Time = 1
Simple Interest = x* 0.08* 1= 0.08x

For the Amount invested at 6%
Principal = 20000-x
Rate = 0.06
Time = 1
Simple Interest = (20000-x)* 0.06* 1= 1200-0.06x

Total Interest = $1440 0.08x+1200-0.06x=1440 0.02x=240 x = 240/0.02=12000 Fraction of x per total amount = 12000/20000 = 12/20 = 3/5 Ans: "D" _________________ Manager Joined: 11 Dec 2010 Posts: 106 WE: Consulting (Consulting) Re: Rate problem [#permalink] ### Show Tags 05 Apr 2011, 18:32 1 VeritasPrepKarishma wrote: Known as Alligation technique... Attachments Pic016.gif [ 7.01 KiB | Viewed 5085 times ] Retired Moderator Joined: 16 Nov 2010 Posts: 1393 Location: United States (IN) Concentration: Strategy, Technology Re: Rate problem [#permalink] ### Show Tags 05 Apr 2011, 19:05 1 x * 6/100 * 1 + (20000 - x) * 8/100 * 1 = 1440 6x - 8x = 144000 - 160000 => -2x = -16000 => x = 8000 So 12000/20000 = 3/5 Answer - D _________________ Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership - big benefits and savings Manager Joined: 16 Mar 2011 Posts: 161 Re: Rate problem [#permalink] ### Show Tags 05 Apr 2011, 19:07 VeritasPrepKarishma wrote: Acer86 wrote: A total of$20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was $1,440 at the end of one year, what fractional part of the$20.000 was invested at the higher rate?
(A) 3/8
(B) 2/5
(C) 1/2
(D) 3/5
(E) 3/4

You can use weighted average in this question. One amount is deposited at 6% and another at 8%. The overall interest rate is $$(\frac{1440}{20,000})*100 = 7.2%$$
$$\frac{w1}{w2}= \frac{(8 - 7.2)}{(7.2 - 6)} = \frac{2}{3}$$
So 2/5 of the 20,000 was invested at 6% and 3/5 was invested at 8%.

For explanation of the formula used above, see: http://www.veritasprep.com/blog/2011/03 ... -averages/
and
http://www.veritasprep.com/blog/2011/04 ... ge-brutes/

i didnt know this technique... very good and efficient...
Manager
Joined: 09 Aug 2010
Posts: 89
Re: Rate problem  [#permalink]

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05 Apr 2011, 19:32
Acer86 wrote:

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01 Dec 2014, 08:10
Acer86 wrote:
A total of $20,000 was invested in two certificates of deposit at simple annual interest rates of 6 percent and 8 percent, respectively. If the total interest on the two certificates was$1,440 at the end of one year, what fractional part of the $20.000 was invested at the higher rate? (A) 3/8 (B) 2/5 (C) 1/2 (D) 3/5 (E) 3/4 Backsolving as option 1) take C to get that 1/2*20000=10000*8/100=800 and 1/2*20000=10000*6/100=600, so 800+600=1400 less than given. Eliminate A,B,C 2) go D to take 3/5*20000=12000*8/100=960 and 8000*6/100=480, so 960+480=1440. It is correct D SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1813 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: A total of$20,000 was invested in two certificates of depos  [#permalink]

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02 Dec 2014, 00:29
1
...................... 6% .................... 8% ............ Total

Principle ........ 20000-x ................ x .............. 20000

Interest ......... $$(20000-x)\frac{6}{100}$$ ..... $$\frac{8x}{100}$$ ....... 1440

$$\frac{(20000-x)6}{100} + \frac{8x}{100} = 1440$$

120000 - 6x + 8x = 144000

x = 72000-60000 = 12000

Fraction $$= \frac{12000}{24000} = \frac{3}{5}$$

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Re: A total of $20,000 was invested in two certificates of depos [#permalink] ### Show Tags 25 Jul 2017, 05:32 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Re: A total of$20,000 was invested in two certificates of depos   [#permalink] 25 Jul 2017, 05:32
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