It is currently 18 Jan 2018, 12:04

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

Hide Tags

Director
Joined: 29 Nov 2012
Posts: 861

Kudos [?]: 1535 [1], given: 543

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

Show Tags

22 Aug 2013, 06:05
1
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

75% (01:53) correct 25% (01:29) wrong based on 142 sessions

HideShow timer Statistics

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

_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Last edited by Bunuel on 22 Aug 2013, 06:10, edited 1 time in total.
Edited the question.

Kudos [?]: 1535 [1], given: 543

Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 624

Kudos [?]: 1436 [2], given: 136

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

Show Tags

22 Aug 2013, 06:11
2
KUDOS
1
This post was
BOOKMARKED
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.
_________________

Kudos [?]: 1436 [2], given: 136

Math Expert
Joined: 02 Sep 2009
Posts: 43323

Kudos [?]: 139428 [0], given: 12790

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

Show Tags

22 Aug 2013, 06:19
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.
_________________

Kudos [?]: 139428 [0], given: 12790

Director
Joined: 29 Nov 2012
Posts: 861

Kudos [?]: 1535 [0], given: 543

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

Show Tags

22 Aug 2013, 06:21
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?
_________________

Click +1 Kudos if my post helped...

Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/

GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html

Kudos [?]: 1535 [0], given: 543

Intern
Joined: 18 Aug 2013
Posts: 9

Kudos [?]: 1 [0], given: 7

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

Show Tags

24 Aug 2013, 15:20
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

Kudos [?]: 1 [0], given: 7

Intern
Joined: 20 Nov 2012
Posts: 18

Kudos [?]: 1 [0], given: 1

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

Show Tags

25 Aug 2013, 09:42
Hi Bunuel, I really do not understand how to solve the second part of data sufficiency. Can you please explain?

Kudos [?]: 1 [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 43323

Kudos [?]: 139428 [0], given: 12790

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

Show Tags

25 Aug 2013, 09:47
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.
_________________

Kudos [?]: 139428 [0], given: 12790

Intern
Joined: 18 Aug 2013
Posts: 9

Kudos [?]: 1 [0], given: 7

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

Show Tags

25 Aug 2013, 09:51
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.

Kudos [?]: 1 [0], given: 7

Math Expert
Joined: 02 Sep 2009
Posts: 43323

Kudos [?]: 139428 [1], given: 12790

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

Show Tags

25 Aug 2013, 09:53
1
KUDOS
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.
_________________

Kudos [?]: 139428 [1], given: 12790

Intern
Joined: 20 Nov 2012
Posts: 18

Kudos [?]: 1 [0], given: 1

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

Show Tags

25 Aug 2013, 22:00
Bunuel, thank you for your valuable feedback

Kudos [?]: 1 [0], given: 1

Intern
Joined: 05 Aug 2012
Posts: 17

Kudos [?]: 1 [0], given: 2

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

Show Tags

18 Sep 2013, 18:29
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

Kudos [?]: 1 [0], given: 2

EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 10696

Kudos [?]: 3776 [0], given: 173

Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Re: If n is an integer and k = 9.87 X 10^n, what is the value of [#permalink]

Show Tags

12 Dec 2017, 10:46
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

[Reveal] Spoiler:
D

GMAT assassins aren't born, they're made,
Rich
_________________

760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/

***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************

Kudos [?]: 3776 [0], given: 173

Re: If n is an integer and k = 9.87 X 10^n, what is the value of   [#permalink] 12 Dec 2017, 10:46
Display posts from previous: Sort by