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# If it is well known that (1.0001)^100

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If it is well known that (1.0001)^100  [#permalink]

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24 Apr 2016, 09:03
6
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Difficulty:

65% (hard)

Question Stats:

58% (02:34) correct 42% (02:25) wrong based on 145 sessions

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If it is well known that (1.0001)^100 is approximately 1.01 and (1.01)^100 is approximately 2.7, what is the value of ((1.0001)^200)^200 approximately?
A. 43 B. 47 C. 53 D. 61 E. 64

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Re: If it is well known that (1.0001)^100  [#permalink]

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24 Apr 2016, 11:06
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smartguy595 wrote:
If it is well known that (1.0001)^100 is approximately 1.01 and (1.01)^100 is approximately 2.7, what is the value of ((1.0001)^200)^200 approximately?
A. 43 B. 47 C. 53 D. 61 E. 64

((1.0001)^200)^200 = ((1.0001)^100)^400 = ((1.01)^400) = (2.7)^4 = between 50 and 60
ans 53
C
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Re: If it is well known that (1.0001)^100  [#permalink]

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07 Jun 2016, 05:48
chetan2u wrote:
smartguy595 wrote:
If it is well known that (1.0001)^100 is approximately 1.01 and (1.01)^100 is approximately 2.7, what is the value of ((1.0001)^200)^200 approximately?
A. 43 B. 47 C. 53 D. 61 E. 64

((1.0001)^200)^200 = ((1.0001)^100)^400 = ((1.01)^400) = (2.7)^4 = between 50 and 60
ans 53
C

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Re: If it is well known that (1.0001)^100  [#permalink]

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07 Jun 2016, 08:10
smartguy595 wrote:
If it is well known that (1.0001)^100 is approximately 1.01 and (1.01)^100 is approximately 2.7, what is the value of ((1.0001)^200)^200 approximately?
A. 43 B. 47 C. 53 D. 61 E. 64

((1.0001)^200)^200
((1.0001)^100 * (1.0001)^100)^200

(1.01*1.01)^200

(1.01)^400

2.7^4= 53 (approx)
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Re: If it is well known that (1.0001)^100  [#permalink]

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02 Jan 2019, 19:22

Hi Experts,
I was wondering could you please go over my solution and see where I made a mistake as I got a completely different answer from the given options.

(1.0001^200)^200
((1.001^100)*(1.001^100))^200
((1.01)(1.01))^200
(1.01^100)*(1.01^100)
2.7*2.7=7.29

Thank you!
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Re: If it is well known that (1.0001)^100  [#permalink]

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02 Jan 2019, 19:31
csaluja wrote:

Hi Experts,
I was wondering could you please go over my solution and see where I made a mistake as I got a completely different answer from the given options.

(1.0001^200)^200
((1.001^100)*(1.001^100))^200
((1.01)(1.01))^200
(1.01^100)*(1.01^100)
2.7*2.7=7.29

Thank you!

You are wrong in this ..
(1.01)(1.01))^200
(1.01^100)*(1.01^100)

It will be 1.01^200*1.01^200

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Re: If it is well known that (1.0001)^100  [#permalink]

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03 Jan 2019, 05:10
((1.0001)^200)^200 = (1.0001)^40000 = (1.01)^400 = (2.7)^4 = (7.29)^2 = approx. greater than and closest to 7^2 i.e. 49.
Ans C (53)
Re: If it is well known that (1.0001)^100   [#permalink] 03 Jan 2019, 05:10
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