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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:

67% (00:49) correct
32% (00:54) wrong based on 46 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

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 \(10^6\)

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

Re: Comapre two exponentials 950^2000 and 10^6000 [#permalink]
01 Jun 2016, 14:45

1

This post received KUDOS

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

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

1

This post received KUDOS

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