Last visit was: 26 Jul 2024, 17:48 It is currently 26 Jul 2024, 17:48
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644161 [74]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   13 Aug 2023, 09:00
2
Kudos
72
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

58% (01:44) correct 42% (01:58) wrong based on 610 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
If k is an integer and \(10^{k-1} < 0.000125 < 10^k\), then k =

A. -6
B. -5
C. -4
D. -3
E. -2­


Show Spoiler
ShowHide Answer
Official Answer
D
Most Helpful Reply
User avatar
D
MartyMurray
Tutor
Joined: 11 Aug 2023
Posts: 1033
Own Kudos [?]: 2120 [12]
Given Kudos: 90
GMAT 1: 800 Q51 V51
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   13 Aug 2023, 09:27
9
Kudos
3
Bookmarks
Expert Reply
If k is an integer and \(10^{k-1} < 0.000125 < 10^k\), then k =

A. -6
B. -5
C. -4
D. -3
E. -2

We can quickly answer this question by using the answer choices.

Since \(0.000125 < 10^-3\) we can eliminate (E).

Since \(0.000125 > 10^-4\) we can eliminate (A), (B), and (C).

So, the correct answer is (D).
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3125
Own Kudos [?]: 5184 [9]
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   13 Aug 2023, 09:24
5
Kudos
4
Bookmarks
Bunuel wrote:
If k is an integer and \(10^{k-1} < 0.000125 < 10^k\), then k =

A. -6
B. -5
C. -4
D. -2
E. -1


\(10^{k-1} < 0.000125 < 10^k\)

\(10^{k-1} < 125*10^{-6} < 10^k\)

Dividing all sides by \(10^{-6}\)

\(10^{k-1+6} < 125 < 10^{k+6}\)

\(10^{k+5} < 125 < 10^{k+6}\)

Therefore \(k + 5 = 2\)

\(k = -3\)
General Discussion
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6633 [7]
Given Kudos: 1646
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   13 Aug 2023, 15:04
5
Kudos
2
Bookmarks
Expert Reply
Bunuel wrote:
If k is an integer and \(10^{k-1} < 0.000125 < 10^k\), then k =

A. -6
B. -5
C. -4
D. -3
E. -2


0.0001 < 0.000125 < 0.001

10ˉ⁴ < 0.000125 < 10ˉ³

k = -3

Answer: D
User avatar
B
Vineela.mk
Intern
Intern
Joined: 22 Apr 2017
Posts: 4
Own Kudos [?]: 4 [4]
Given Kudos: 5
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   03 Sep 2023, 04:39
4
Kudos
gmatophobia wrote:
Bunuel wrote:
If k is an integer and \(10^{k-1} < 0.000125 < 10^k\), then k =

A. -6
B. -5
C. -4
D. -2
E. -1


\(10^{k-1} < 0.000125 < 10^k\)

\(10^{k-1} < 125*10^{-6} < 10^k\)

Dividing all sides by \(10^{-6}\)

\(10^{k-1+6} < 125 < 10^{k+6}\)

\(10^{k+5} < 125 < 10^{k+6}\)

Therefore \(k + 5 = 2\)

\(k = -3\)



How did you deduce k + 5 = 2? What am I missing?
User avatar
S
Paras96
Senior Manager
Senior Manager
Joined: 11 Sep 2022
Posts: 497
Own Kudos [?]: 180 [4]
Given Kudos: 2
Location: India
Paras: Bhawsar
GMAT 1: 590 Q47 V24
GMAT 2: 580 Q49 V21
GMAT 3: 700 Q49 V35
GPA: 3.2
WE:Project Management (Other)
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   03 Sep 2023, 04:54
4
Kudos
10^(k−1)<0.000125<10^k
=>10^(k−1)<125*10^(-6)<10^k
=>10^(k−1)<125*10^(-6)<10^k
=>10^(k−1+6)<125<10^(k +6)
=>10^(k+5)<125<10^(k +6)

Since,
=> 100<125<1000
=>10^2<125<10^3

Therefore k+5=2
=>k=-3

Hence D
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3125
Own Kudos [?]: 5184 [7]
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   03 Sep 2023, 06:27
7
Kudos
Vineela.mk wrote:
How did you deduce k + 5 = 2? What am I missing?


Vineela.mk -

Quote:
\(10^{k+5} < 125 < 10^{k+6}\)


Let's take one part at a time -

\(10^{k+5} < 125 \)

We know k is an integer and that \(10^{k+5} < 125 \). The value, \(10^{k+5}\) is a power of 10. The closest power of 10 which is less than 125 is 100. Therefore we can write the expression as

\(10^{k+5} \leq 100 \)

\(10^{k+5} \leq 10^2 \)

Comparing the powers

\(k + 5 \leq 2\)

\(k \leq -3\)

\(125 < 10^{k+6} \)

The closest power of 10 which is greater than 125 is 1000. Therefore we can write the expression as

\(1000 \leq 10^{k+6} \)

\(10^3 \leq 10^{k+6} \)

Comparing the powers

\(3 \leq k+6 \)

\(-3 \leq k \)

The common value of \(k\) from both ⇒ \(k = -3\)

Hope this helps.
User avatar
D
Hoozan
Director
Director
Joined: 28 Sep 2018
Posts: 710
Own Kudos [?]: 574 [0]
Given Kudos: 248
GMAT 1: 660 Q48 V33 (Online)
GMAT 2: 700 Q49 V37
Send PM
Reviews Badge
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   06 Sep 2023, 03:12
gmatophobia wrote:
Bunuel wrote:
If k is an integer and \(10^{k-1} < 0.000125 < 10^k\), then k =

A. -6
B. -5
C. -4
D. -2
E. -1


\(10^{k-1} < 0.000125 < 10^k\)

\(10^{k-1} < 125*10^{-6} < 10^k\)

Dividing all sides by \(10^{-6}\)

\(10^{k-1+6} < 125 < 10^{k+6}\)

\(10^{k+5} < 125 < 10^{k+6}\)

Therefore \(k + 5 = 2\)

\(k = -3\)


After arriving at \(10^{k+5} < 125 < 10^{k+6}\) how did you conclude that \(k + 5 = 2\) ??
User avatar
L
gmatophobia
Quant Chat Moderator
Joined: 22 Dec 2016
Posts: 3125
Own Kudos [?]: 5184 [0]
Given Kudos: 1859
Location: India
Concentration: Strategy, Leadership
Send PM
CAT Tests Forum Quiz Mode
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   12 Sep 2023, 11:15
Hoozan wrote:
After arriving at \(10^{k+5} < 125 < 10^{k+6}\) how did you conclude that \(k + 5 = 2\) ??


Hi Hoozan

Checking if you got a chance to refer to this post -

https://gmatclub.com/forum/if-k-is-an-i ... l#p3262194

Let me know if you still have any question.
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 15159
Own Kudos [?]: 66908 [4]
Given Kudos: 436
Location: Pune, India
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   08 Apr 2024, 09:14
2
Kudos
2
Bookmarks
Expert Reply
 
Bunuel wrote:
If k is an integer and \(10^{k-1} < 0.000125 < 10^k\), then k =

A. -6
B. -5
C. -4
D. -3
E. -2

­\(10^{k-1} < 0.000125 < 10^k\)

First notice that all options are negative so let's take powers of 10 to the denominator.

\(10^{k-1} < \frac{125}{10^6} < 10^k\)
\(10^{k-1} < \frac{1.25*10^2}{10^6} < 10^k\)
\(10^{k-1} < \frac{ 1.25}{10^4} < 10^k\)

We know that 
\(\frac{1}{10^4} <  \frac{ 1.25}{10^4} < \frac{10}{10^4}\)

\(10^{-4} <  \frac{ 1.25}{10^4} < 10^{-3}\)

k = -3­

Answer (D)
User avatar
B
colfer
Intern
Intern
Joined: 16 Mar 2024
Posts: 15
Own Kudos [?]: 4 [0]
Given Kudos: 1
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   23 Apr 2024, 05:18
­10^(k-1) < 1.25* 10^-4 < 10^-k 

­10^(k-1) <10^-4 < 10^-k 
User avatar
S
DanTheGMATMan
Tutor
Joined: 02 Oct 2015
Posts: 263
Own Kudos [?]: 41 [0]
Given Kudos: 8
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   17 May 2024, 09:59
Expert Reply
­Approximate that middle term a bit. No sweat:

User avatar
B
aryamannm750+
Intern
Intern
Joined: 03 Jun 2023
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 8
Send PM
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   20 Jun 2024, 03:55
Bunuel please attach more questions like these!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 94619
Own Kudos [?]: 644161 [1]
Given Kudos: 86770
Send PM
CAT Tests Forum Quiz Mode
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink] If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k =   20 Jun 2024, 05:19
1
Bookmarks
Expert Reply
aryamannm750+ wrote:
Bunuel please attach more questions like these!

­
Check Exponents and Inequalities Questions.
GMAT Club Bot
gmatclubot
Re: If k is an integer and 10^(k - 1) < 0.000125 < 10^k, then k = [#permalink]
20 Jun 2024, 05:19
Moderator:
Bunuel
Math Expert
94619 posts