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# A certain sum was invested in a high-interest bond for which

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A certain sum was invested in a high-interest bond for which [#permalink]

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16 Mar 2011, 07:49
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Difficulty:

75% (hard)

Question Stats:

32% (01:47) correct 68% (00:51) wrong based on 36 sessions

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A certain sum was invested in a high-interest bond for which the interest is compounded monthly. The bond was sold x number of months later, where x is an integer. If the value of the original investment doubled during this period, what was the approximate amount of the original investment in dollars?

(1) The interest rate during the period of investment was greater than 39 percent but less than 45 percent.

Investment = $P time: x months = x/12 years Periods = n = 12 Return after application of the compound Interest for x months; $$P(1+\frac{r}{n})^{nt}$$ $$P(1+\frac{r}{12})^{12*x/12}$$ $$P(1+\frac{r}{12})^x$$ It is given that the investment doubles after x months; $$P(1+\frac{r}{12})^x=2P$$ $$(1+\frac{r}{12})^x=2$$ r and x are unknown 1. 0.4<=r<=0.44 $$(1+\frac{0.4}{12})^x=(1.033)^x = 2$$ to $$(1+\frac{0.44}{12})^x=(1.036)^x=2$$ x can be found; but we don't know P. Not Sufficient. 2. $$P(1+\frac{r}{12})^{(x+1)}=2744$$ $$P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744$$ $$2P*(1+\frac{r}{12})=2744$$ We still have two unknowns. Not Sufficient. Combining both; r= 0.4 $$2P*(1+\frac{0.4}{12})=2744$$ Now, we can get approx value of P. Ans: "C" _________________ Intern Joined: 08 Mar 2011 Posts: 23 Followers: 0 Kudos [?]: 25 [0], given: 31 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 16 Mar 2011, 09:24 thnx so much fluke regards GMAT Tutor Joined: 24 Jun 2008 Posts: 1183 Followers: 381 Kudos [?]: 1315 [0], given: 4 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 16 Mar 2011, 22:19 Expert's post Where is this question from? It makes no sense, in DS, to ask for the 'approximate value' of something -- how could you possibly know what information would be sufficient? If I ask the following question: What is the approximate value of x? 1. 3 < x < 5 2. 4 < x < 4.5 Is Statement 1 sufficient? Statement 2? You can't possibly know. It's a nonsensical question to ask in DS, so I wouldn't use other questions from the same source. _________________ GMAT Tutor in Toronto If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com Senior Manager Joined: 17 Mar 2011 Posts: 452 Location: United States (DC) Concentration: General Management, Technology GMAT 1: 760 Q49 V45 GPA: 3.37 WE: Information Technology (Consulting) Followers: 11 Kudos [?]: 181 [0], given: 5 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 17 Mar 2011, 07:10 Good point Ian, based on (2) I could easily say "initial investment is between$0 and $1372, approximately" Senior Manager Joined: 08 Nov 2010 Posts: 417 WE 1: Business Development Followers: 7 Kudos [?]: 87 [0], given: 161 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 18 Mar 2011, 10:37 Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. _________________ Math Forum Moderator Joined: 20 Dec 2010 Posts: 2021 Followers: 156 Kudos [?]: 1518 [0], given: 376 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 18 Mar 2011, 11:00 144144 wrote: Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. From the stem, please see the [highlight]highlighted[/highlight] part. fluke wrote: Investment =$P
time: x months = x/12 years
Periods = n = 12

Return after application of the compound Interest for x months;

$$P(1+\frac{r}{n})^{nt}$$
$$P(1+\frac{r}{12})^{12*x/12}$$
$$P(1+\frac{r}{12})^x$$
It is given that the investment doubles after x months;
$$P(1+\frac{r}{12})^x=2P$$ [highlight]--------------A[/highlight]
$$(1+\frac{r}{12})^x=2$$

r and x are unknown

1. 0.4<=r<=0.44
$$(1+\frac{0.4}{12})^x=(1.033)^x = 2$$
to
$$(1+\frac{0.44}{12})^x=(1.036)^x=2$$

x can be found; but we don't know P.
Not Sufficient.

2.
$$P(1+\frac{r}{12})^{(x+1)}=2744$$
$$P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744$$
[highlight]Substitute from equation A[/highlight]
$$2P*(1+\frac{r}{12})=2744$$
We still have two unknowns.
Not Sufficient.

Combining both;

r= 0.4
$$2P*(1+\frac{0.4}{12})=2744$$

Now, we can get approx value of P.

Ans: "C"

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Re: A certain sum was invested in a high-interest bond for which [#permalink]

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18 Mar 2011, 20:05
Expert's post
This question reminds me:

Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest.

i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years.
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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews CEO Status: Nothing comes easy: neither do I want. Joined: 12 Oct 2009 Posts: 2797 Location: Malaysia Concentration: Technology, Entrepreneurship Schools: ISB '15 (M) GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35 Followers: 219 Kudos [?]: 1470 [0], given: 235 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 19 Mar 2011, 11:54 Not a Gmat question. Do not waste your time. _________________ Fight for your dreams :For all those who fear from Verbal- lets give it a fight Money Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership - big benefits and savings Gmat test review : http://gmatclub.com/forum/670-to-710-a-long-journey-without-destination-still-happy-141642.html Director Status: Finally Done. Admitted in Kellogg for 2015 intake Joined: 25 Jun 2011 Posts: 538 Location: United Kingdom Concentration: International Business, Strategy GMAT 1: 730 Q49 V45 GPA: 2.9 WE: Information Technology (Consulting) Followers: 65 Kudos [?]: 2364 [0], given: 217 A certain sum was invested in a high-interest bond for which the inter [#permalink] ### Show Tags 15 Nov 2011, 15:44 1 This post was BOOKMARKED A certain sum was invested in a high-interest bond for which the interest is compounded monthly. The bond was sold x number of months later, where x is an integer. If the value of the original investment doubled during this period, what was the approximate amount of the original investment in dollars? (1) The interest rate during the period of investment was greater than 39 percent but less than 45 percent. (2) If the period of investment had been one month longer, the final sale value of the bond would have been approximately$2,744.

can someone please have a look into this and let me know how to solve this?
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Re: A certain sum was invested in a high-interest bond for which the inter [#permalink]

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15 Nov 2011, 16:47
So we now there was an investment in a bond that compounds monthly for X months. X is a whole number so no fractional months, and that the value of the bond doubled in our X months of investment.

Statement 1 - gives us not info about value - granted we can back into a range of X but a dollar amount is impossible - insuff.
Statement 2- gives us a value at X+1, but its impossible to determine the starting value as we do not know either the interest rate or the starting value - insuff.

Together you have a range of rates and a X-1 ending value. Since the starting value doesn't have to be an integer and the interest rate doesn't have to be an integer either their are a number of possible answers for this.

I would say it should be E.
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Re: A certain sum was invested in a high-interest bond for which the inter [#permalink]

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15 Nov 2011, 21:54
1
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You can find a good explanation here: http://www.urch.com/forums/gmat-math/20537-interest-rates.html
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Re: A certain sum was invested in a high-interest bond for which the inter [#permalink]

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16 Nov 2011, 10:05
I decided on C after three mins, but it was more of a guess off of what I know rather than confirmation. Just hope you don't get one of these on the test
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Re: A certain sum was invested in a high-interest bond for which [#permalink]

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10 Sep 2013, 18:19
VeritasPrepKarishma wrote:
This question reminds me:

Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest.

i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years.

Couldn't the following give multiple values of x (may be with a minor difference each)? So, we wouldn't have a single answer to the question & hence 1 & 2 aren't sufficient together. SO, the answer shd be E. Please correct me if I'm wrong. Thank you.
**********************************
(1+\frac{0.4}{12})^x=(1.033)^x = 2
to
(1+\frac{0.44}{12})^x=(1.036)^x=2

x can be found; but we don't know P.
**********************************
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Re: A certain sum was invested in a high-interest bond for which [#permalink]

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11 Sep 2013, 03:42
Expert's post
divineacclivity wrote:
VeritasPrepKarishma wrote:
This question reminds me:

Sometimes, it's useful to know that in compound interest, the principal doubles approximately every 72/r years where r is the rate of interest.

i.e. if rate of interest is 10, the principal doubles in approximately 72/10 = 7.2 years.

Couldn't the following give multiple values of x (may be with a minor difference each)? So, we wouldn't have a single answer to the question & hence 1 & 2 aren't sufficient together. SO, the answer shd be E. Please correct me if I'm wrong. Thank you.
**********************************
(1+\frac{0.4}{12})^x=(1.033)^x = 2
to
(1+\frac{0.44}{12})^x=(1.036)^x=2

x can be found; but we don't know P.
**********************************

This is a poor quality question. Check here: a-certain-sum-was-invested-in-a-high-interest-bond-for-which-110991.html#p893606
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Re: A certain sum was invested in a high-interest bond for which the inter [#permalink]

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19 Nov 2014, 11:32
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Re: A certain sum was invested in a high-interest bond for which the inter   [#permalink] 19 Nov 2014, 11:32
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