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# If n is an integer and k = 9.87 X 10^n, what is the value of

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If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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22 Aug 2013, 07:05
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If n is an integer and $$k = 9.87 * 10^n$$, what is the value of n?

(1) $$10^{-4} < K < 10^{-3}$$
(2) $$10^3 < K^{-1} < 10^4$$

Can someone please provide detailed explanations. Thanks!
[Reveal] Spoiler: OA

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Last edited by Bunuel on 22 Aug 2013, 07:10, edited 1 time in total.
Edited the question.

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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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22 Aug 2013, 07:11
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fozzzy wrote:
If n is an integer and k = $$9.87 * 10^n$$, what is the value of n?

$$1) 10^{-4} < K < 10^{-3}$$
$$2) 10^3 < K^{-1} < 10^4$$

Can someone please provide detailed explanations. Thanks!

Firstly, for any value of n, K will always be a positive entity.

From F.S 1, we have $$10^{-4} < K < 10^{-3}$$ , multiply across by $$10^4 \to$$ $$10^{-4+4} < K *10^4< 10^{-3+4}$$$$\to$$ $$1< 9.87*10^{n+4} < 10$$$$\to$$ Thus, the only value which n can assume is n =-4.Sufficient.

F.S 2 can be re-written as the same as F.S 1, Thus Sufficient.

D.
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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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22 Aug 2013, 07:19
fozzzy wrote:
If n is an integer and $$k = 9.87 * 10^n$$, what is the value of n?

(1) $$10^{-4} < K < 10^{-3}$$
(2) $$10^3 < K^{-1} < 10^4$$

Can someone please provide detailed explanations. Thanks!

Similar question to practice: if-k-is-a-positive-integer-and-n-7-049-10-k-what-is-the-val-131649.html

Hope it helps.
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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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22 Aug 2013, 07:21
Great Method... I would have never thought of that to multiply $$10^4$$ that step made the problem really easy... would there be any other alternative?
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Intern
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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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24 Aug 2013, 16:20
mau5 wrote:

F.S 2 can be re-written as the same as F.S 1, Thus Sufficient.

D.
[/quote]

can someone please show me this step? thanks

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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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25 Aug 2013, 10:42
Hi Bunuel, I really do not understand how to solve the second part of data sufficiency. Can you please explain?

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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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25 Aug 2013, 10:47
bluecatie1 wrote:
Hi Bunel, I really do not understand how to solve the second part of data sufficiency. Can you please explain?

Consider this: 10<20<100 can be rewritten as 1/100<1/20<1/10.

The same way: 10^3<1/k<10^4 can be rewritten as 1/10^4<k<1/10^3 --> the same equation as in the first statement.

Hope it's clear.
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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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25 Aug 2013, 10:51
Bunuel wrote:
bluecatie1 wrote:
Hi Bunel, I really do not understand how to solve the second part of data sufficiency. Can you please explain?

Consider this: 10<20<100 can be rewritten as 1/100<1/20<1/10.

The same way: 10^3<1/k<10^4 can be rewritten as 1/10^4<k<1/10^3 --> the same equation as in the first statement.

Hope it's clear.

thank you, but why is there a change in the order of the inequality. I though u only change the algebraic sign if you multiply with a negative number. but here u merely multiply with a fraction.

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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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25 Aug 2013, 10:53
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Expert's post
SKTRain wrote:
Bunuel wrote:
bluecatie1 wrote:
Hi Bunel, I really do not understand how to solve the second part of data sufficiency. Can you please explain?

Consider this: 10<20<100 can be rewritten as 1/100<1/20<1/10.

The same way: 10^3<1/k<10^4 can be rewritten as 1/10^4<k<1/10^3 --> the same equation as in the first statement.

Hope it's clear.

thank you, but why is there a change in the order of the inequality. I though u only change the algebraic sign if you multiply with a negative number. but here u merely multiply with a fraction.

Simplest way to understand to consider an example: 2<3<4 --> 1/4<1/3<1/2.
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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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25 Aug 2013, 23:00
Bunuel, thank you for your valuable feedback

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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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18 Sep 2013, 19:29
Hi Bunuel,
Even I was stuck in the second part, can you please explain me with some examples especially if there are negative numbers involved ( since the sign flips )

Thank You

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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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09 Oct 2014, 09:43
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Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

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20 Sep 2016, 17:08
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Re: If n is an integer and k = 9.87 X 10^n, what is the value of   [#permalink] 20 Sep 2016, 17:08
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