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# 0.3^20 or 0.03^50

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Joined: 10 Sep 2018
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0.3^20 or 0.03^50 [#permalink]  12 Sep 2018, 00:25
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Question Stats:

81% (00:28) correct 18% (00:52) wrong based on 27 sessions
 Quantity A Quantity B $$(0.3)^{20}$$ $$(0.03)^{50}$$

A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
[Reveal] Spoiler: OA

Last edited by Carcass on 12 Sep 2018, 04:33, edited 2 times in total.
Edited by Carcass
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Kudos [?]: 1113 [1] , given: 5130

Re: 0.3^20 or 0.03^50 [#permalink]  12 Sep 2018, 08:04
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Expert's post
No need for any calculation.

0.3 is > 0.03 on the number line.

So when you raise 0.03 to a power you get a long list of zeroes > of when 0.3 is raised. As such. 0.03 getting smaller and smaller than 0.3.

A is the answer.

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Re: 0.3^20 or 0.03^50 [#permalink]  13 Sep 2018, 07:44
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saifee wrote:
 Quantity A Quantity B $$(0.3)^{20}$$ $$(0.03)^{50}$$

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

Another approach is to apply a nice rule that says: (xy)^n = (x^n)(y^n)
So, 0.3 = (0.03)(10)

So, (0.3)^20 = [(0.03)(10)]^20
= (0.03^20)(10^20) [as per the rule above]

So we get:
Quantity A: (0.03^20)(10^20)
Quantity B: (0.03)^50

Divide both quantities by 0.03^20 to get:
Quantity A: (10^20)
Quantity B: (0.03)^30

At this point, we can see that Quantity A will be a HUGE number (1 followed by 20 zeros), whereas Quantity B will evaluate to be a number less than 1

Answer: A

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Re: 0.3^20 or 0.03^50   [#permalink] 13 Sep 2018, 07:44
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# 0.3^20 or 0.03^50

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