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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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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!

Originally posted by fozzzy on 22 Aug 2013, 07:05.
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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New post 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.

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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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New post 22 Aug 2013, 07:19
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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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New post 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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Re: If n is an integer and k = 9.87 X 10^n, what is the value of  [#permalink]

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New post 24 Aug 2013, 16:20
mau5 wrote:


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

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[/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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New post 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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New post 25 Aug 2013, 10:47
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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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New post 25 Aug 2013, 10:51
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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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New post 25 Aug 2013, 10:53
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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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New post 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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New post 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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New post 12 Dec 2017, 11:46
Hi All,

This question is essentially about 'decimal' shifts. Since N is an integer, we know that K will the same digits (just shifted depending on the decimal). For example:

N = 1... K = 98.7
N = 2... K = 987
N = 3... K = 9870

We're NOT told that N is necessarily positive though, so we have to consider other options...

N = 0... K = 9.87
N = -1... K = 0.987
N = -2... K = 0.0987
N = -3... K = 0.00987
Etc.

We're asked for the value of N.

1) 10^-4 < K < 10^-3

With this range, we know that K is between 1/10,000 and 1/1,000. There's only one value that fits this range: K = 0.000987, so N must be -4.
Fact 1 is SUFFICIENT

2) 10^3 < K^-1 < 10^4

You might find it helpful to rewrite this range as:
10^3 < 1/K < 10^4

In that way, K would have to be between 1/1,000 and 1/10,000 (the same information we were given in Fact 1).
Fact 2 is SUFFICIENT

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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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Re: If n is an integer and k = 9.87 X 10^n, what is the value of   [#permalink] 18 Jan 2019, 03:02
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