A certain sum was invested in a high-interest bond for which : GMAT Data Sufficiency (DS)
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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, 06:49
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75% (hard)

Question Stats:

38% (01:41) correct 62% (00:48) wrong based on 48 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 [?]: 28 [0], given: 31 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 16 Mar 2011, 08:24 thnx so much fluke regards GMAT Tutor Joined: 24 Jun 2008 Posts: 1183 Followers: 419 Kudos [?]: 1505 [0], given: 4 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 16 Mar 2011, 21:19 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 [?]: 183 [0], given: 5 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 17 Mar 2011, 06:10 Good point Ian, based on (2) I could easily say "initial investment is between$0 and $1372, approximately" Senior Manager Joined: 08 Nov 2010 Posts: 417 WE 1: Business Development Followers: 7 Kudos [?]: 105 [0], given: 161 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 18 Mar 2011, 09:37 Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. _________________ Math Forum Moderator Joined: 20 Dec 2010 Posts: 2021 Followers: 161 Kudos [?]: 1703 [0], given: 376 Re: A certain sum was invested in a high-interest bond for which [#permalink] ### Show Tags 18 Mar 2011, 10:00 144144 wrote: Fluke - how did u go from the 2nd stage to the 3rd?!?! 2. P(1+\frac{r}{12})^{(x+1)}=2744 P(1+\frac{r}{12})^x*(1+\frac{r}{12})=2744 2P*(1+\frac{r}{12})=2744 We still have two unknowns. Not Sufficient. From the stem, please see the [highlight]highlighted[/highlight] part. fluke wrote: Investment =$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, 19:05
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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can someone please have a look into this and let me know how to solve this?
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15 Nov 2011, 15:47
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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15 Nov 2011, 20:54
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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16 Nov 2011, 09:05
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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10 Sep 2013, 17:19
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, 02:42
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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19 Nov 2014, 10:32
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