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Director  Joined: 29 Nov 2012
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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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Difficulty:   25% (medium)

Question Stats: 78% (01:46) correct 22% (02:09) wrong based on 195 sessions

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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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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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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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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?
Intern  Joined: 18 Aug 2013
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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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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
Intern  Joined: 20 Nov 2012
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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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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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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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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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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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Bunuel, thank you for your valuable feedback Intern  Joined: 05 Aug 2012
Posts: 15
Re: If n is an integer and k = 9.87 X 10^n, what is the value of  [#permalink]

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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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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If n is an integer and k = 9.87 X 10^n, what is the value of  [#permalink]

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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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