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Math Expert V
Joined: 02 Sep 2009
Posts: 55631

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Difficulty:   65% (hard)

Question Stats: 51% (02:27) correct 49% (02:34) wrong based on 37 sessions

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At the beginning of year 1, an investor puts $$p$$ dollars into an investment whose value increases at a variable rate of $$x_n%$$ per year, where $$n$$ is an integer ranging from 1 to 3 indicating the year. If $$85 \lt x_n \lt 110$$ for all $$n$$ between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between

A. $$$p$$ and$$$2p$$
B. $$$2p$$ and$$$5p$$
C. $$$5p$$ and$$$10p$$
D. $$$10p$$ and$$$25p$$
E. $$$25p$$ and$$$75p$$

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Math Expert V
Joined: 02 Sep 2009
Posts: 55631

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Official Solution:

At the beginning of year 1, an investor puts $$p$$ dollars into an investment whose value increases at a variable rate of $$x_n%$$ per year, where $$n$$ is an integer ranging from 1 to 3 indicating the year. If $$85 \lt x_n \lt 110$$ for all $$n$$ between 1 and 3, inclusive, then at the end of 3 years, the value of the investment must be between

A. $$$p$$ and$$$2p$$
B. $$$2p$$ and$$$5p$$
C. $$$5p$$ and$$$10p$$
D. $$$10p$$ and$$$25p$$
E. $$$25p$$ and$$$75p$$

The quick solution to this problem is to pick a convenient number in the allowed range of growth rates. If $$x_n$$ is always between 85 and 110, then the most convenient growth rate to pick is 100. An annual growth rate of 100% is exactly equivalent to doubling one's money. Doubling one's money three times is equivalent to multiplying one's investment by a factor of 8 ($$= 2^3$$). The only range that includes $$$8p$$ is the third range ($$$5p$$ to \$$$10p$$).

Computing the exact outer limits of the allowed range is much more cumbersome. We would have to cube 1.85 for the lower limit and 2.1 for the upper limit. The cube of 1.85 is 6.331625, and the cube of 2.1 is 9.261. These values fall between 5 and 10.

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Current Student B
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Joined: 16 May 2016
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Concentration: Operations, Strategy
GMAT 1: 710 Q50 V36 GPA: 3.4
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Hi There

I got little bit confused by the language . Growth rate of 85-100 ?

Is it normal to express growth rate as a mere number and not in percent/fraction ?

BR
Ashish
Intern  Joined: 24 Feb 2018
Posts: 4

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You're not alone on that.
Needs %
Manager  B
Joined: 12 Mar 2018
Posts: 124

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where is %?.. missing info
Intern  B
Joined: 11 Jun 2014
Posts: 2

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little bit confused about it belongs to simple or compound interest..
Intern  Joined: 08 Apr 2019
Posts: 2
Location: India

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Neither did I understand the language of the question nor did I understand the explanation.
Math Expert V
Joined: 02 Sep 2009
Posts: 55631

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namangambhir wrote:
Neither did I understand the language of the question nor did I understand the explanation.

Check more solutions here: https://gmatclub.com/forum/at-the-begin ... 88683.html Hope it helps.
_________________ Re: S97-18   [#permalink] 09 Apr 2019, 21:07
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