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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!
[Reveal] Spoiler: OA

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

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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 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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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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.

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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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
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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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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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
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, 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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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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