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# Comapre two exponentials 950^2000 and 10^6000

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GRE Prep Club Legend
Joined: 07 Jun 2014
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Comapre two exponentials 950^2000 and 10^6000 [#permalink]  26 Jan 2016, 00:53
Expert's post
00:00

Question Stats:

70% (00:46) correct 29% (00:58) wrong based on 57 sessions
 Quantity A Quantity B $$950^{2,000}$$ $$10^{6,000}$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 3
Page: 465
Difficulty: hard
[Reveal] Spoiler: OA

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GRE Prep Club Legend
Joined: 07 Jun 2014
Posts: 4810
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 117

Kudos [?]: 1895 [1] , given: 397

Re: Comapre two exponentials 950^2000 and 10^6000 [#permalink]  26 Jan 2016, 00:58
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Solution

Note that 950 is close to, but a little less than, 1,000, or $$10^3$$. So

$$950 <1000$$

or $$950^2^0^0^0 <1000^2^0^0^0$$

or $$950^2^0^0^0 <(10^3)^2^0^0^0$$

or $$950^2^0^0^0 < 10^6^0^0^0$$

Hence Choice B is the correct option.
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Re: Comapre two exponentials 950^2000 and 10^6000 [#permalink]  27 Jan 2016, 15:59
Expert's post
Another way to solve the question is to get rid of the exponents

$$950^2*10^3$$ and $$10^6*10^3$$. You can disregard $$10^3$$ so we have $$10^6$$ and $$950^2.$$ The latter is far less inferior than the first one value $$10^6$$

So the answer is B
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Re: Comapre two exponentials 950^2000 and 10^6000 [#permalink]  26 Apr 2016, 04:11
well, to compare two exponent, we can convert (10)6000 into (1000)^2000. so clearly answer is (B)
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Re: Comapre two exponentials 950^2000 and 10^6000 [#permalink]  27 May 2016, 18:21
sandy wrote:
 Quantity A Quantity B $$950^{2,000}$$ $$10^6^0^0^0$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Practice Questions
Question: 3
Page: 465
Difficulty: hard

950^2000 && 10^6000

950^(6000/3) && 10^6000

(950^(1/3))^6000 && 10^6000

As 9^3=729 < 950 < 10^3
Therefore, 950^(1/3) = 9.something

So, (9.something)^ 6000 < 10^6000 as (9.something) < 10
Ans B
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Re: Comapre two exponentials 950^2000 and 10^6000 [#permalink]  01 Jun 2016, 14:45
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Expert's post
sandy wrote:
 Quantity A Quantity B $$950^{2,000}$$ $$10^6^0^0^0$$

A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.

Given:
Quantity A: 950^2000
Quantity B: 10^6000

Rewrite quantity B as follows:
Quantity A: 950^2000
Quantity B: (10^3)^2000

Simplify quantity B as follows:
Quantity A: 950^2000
Quantity B: 1000^2000

[Reveal] Spoiler:
B

RELATED RESOURCE (video)
- https://www.greenlighttestprep.com/modu ... video/1026

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Brent
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Joined: 22 Feb 2018
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Re: Comapre two exponentials 950^2000 and 10^6000 [#permalink]  16 Mar 2018, 13:08
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correct: B
In this kind of questions we should do some changes to make the different options look same in some way in order to simply compare them.
950 ^ 2000 = (9.5 * 10 * 10) ^ 2000 = 9.5^2000 * 10^2000 * 10^2000 < 10^2000 * 10^2000 * 10^2000 which the right side equals to (10^2000)^3 = 10^(2000*3) = 10^6000

So 950 ^2000 is less than 10^ 6000 and B is correct.

Another approach is starting with 10^ 6000 which equals (10^3)^2000. now power of 950^2000 and (10^3)^2000 are same. and we know 950 is less than 1000=10^3

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Re: Comapre two exponentials 950^2000 and 10^6000   [#permalink] 16 Mar 2018, 13:08
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# Comapre two exponentials 950^2000 and 10^6000

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