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# 6( 10) n > 60,006

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6( 10) n > 60,006 [#permalink]  20 Oct 2018, 08:51
Expert's post
00:00

Question Stats:

67% (00:28) correct 32% (00:31) wrong based on 34 sessions
$$6( 10)^n > 60,006$$

 Quantity A Quantity B n 6

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

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Re: 6( 10) n > 60,006 [#permalink]  21 Oct 2018, 05:59
$$10^4$$ = 10000
$$6*10^4$$ = 60000
We know for sure that n >4 so n can be 5,6,7 and so on.
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This is my response to the question and may be incorrect. Feel free to rectify any mistakes

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Re: 6( 10) n > 60,006 [#permalink]  23 Oct 2018, 03:08
Expert's post
Carcass wrote:
$$6( 10)^n > 60,006$$

 Quantity A Quantity B n 6

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

$$6( 10)^n > 60,006.....10^n>10,001....10^n>10^4+1$$
So n>4
If n is 5, B>A
If n is 6, B=A
If n is >6, B<A

So data Insufficient

D
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Some useful Theory.
1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressions-arithmetic-geometric-and-harmonic-11574.html#p27048
2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effects-of-arithmetic-operations-on-fractions-11573.html?sid=d570445335a783891cd4d48a17db9825
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4. Number properties : https://greprepclub.com/forum/number-property-all-you-require-11518.html
5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolute-modulus-a-better-understanding-11281.html

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Re: 6( 10) n > 60,006 [#permalink]  23 Oct 2018, 20:35
This is basically a simple problem where they want to see if you get tripped up by forgetting that, since there is an inequality, n will be ANY number greater than or equal to the first n value that puts the left side above the right. n=4 gives 60,000. n=5 gives 600,000 (the first value above 60,006). Therefore the MINIMUM value for n is 5 while the greatest is "infinite answers." Since B is 6, n=5 gives A<B, n=6 gives A=B, and n=7+ gives A>B...all being possible answers. The answer is therefore clearly D.
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Re: 6( 10) n > 60,006 [#permalink]  24 Oct 2018, 06:12
I didn't understand the concept.
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Re: 6( 10) n > 60,006 [#permalink]  28 Nov 2018, 12:57
6* (10^n) > 60,006

60,006 = 60,000 + 6 = 6 *(10,000) + 6 = 6* (10^4) + 6

6* (10^n) > 6* (10^4) + 6 n>4 or n>=5
So n should be at least 5, it can be 5, 6, ….
So the answer is D because it might be 5 and less than 6, equal to 6 or even more than 6.
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Re: 6( 10) n > 60,006   [#permalink] 28 Nov 2018, 12:57
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