Last visit was: 20 Nov 2025, 00:59 It is currently 20 Nov 2025, 00:59
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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
Back to Forum
Create Topic
505-555 Level|   Arithmetic|   Exponents|      
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,784
Own Kudos:
12,807
 [11]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,784
Kudos: 12,807
 [11]
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what Updated on: 03 Feb 2024, 09:40
Originally posted by EMPOWERgmatRichC on 19 Nov 2015, 17:51.
Last edited by Bunuel on 03 Feb 2024, 09:40, edited 2 times in total.
1
Kudos
Add Kudos
10
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

15% (low)

Question Stats:

86% (01:59) correct 14% (02:22) wrong based on 274 sessions

History

Date
Time
Result
Not Attempted Yet
If \((2^{N}) (3^{K})(5^{8})\) is equal to one percent of \(60^{10}\), then what is the value of N – K?

A) 7
B) 8
C) 12
D) 14
E) 15

Show Spoiler
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^8)...

48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation
ShowHide Answer
Official Answer
B
User avatar
peachfuzz
User avatar
Joined: 28 Feb 2014
Last visit: 27 Jan 2018
Posts: 269
Own Kudos:
360
 [1]
Given Kudos: 132
Location: United States
Concentration: Strategy, General Management
Products:
My Reviews
Posts: 269
Kudos: 360
 [1]
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 19 Nov 2015, 18:19
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
If (\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) is equal to one percent of \(60^{10}\) , then what is the value of N – K?

A) 7
B) 8
C) 12
D) 14
E) 15

60=(2^2)*3*5

(\(1/100\))*(\((2^2)*3*5\))^100= (\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\))
(\(2^{20}\))*(\(3^{10}\))*(\(5^{10}\))= (\(2^{N+2}\)) (\(3^{K}\)) (\(5^{10}\))

N+2=20
N=18

K=10

18-10=8

Answer: B
User avatar
ENGRTOMBA2018
User avatar
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,325
Own Kudos:
3,837
 [1]
Given Kudos: 816
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
My Reviews
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
Posts: 2,325
Kudos: 3,837
 [1]
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 23 Nov 2015, 09:28
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^12)...

If (\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) is equal to one percent of \(60^{10}\) , then what is the value of N – K?

A) 7
B) 8
C) 12
D) 14
E) 15


48 Hour Window Answer & Explanation Window
Earn KUDOS! Post your answer and explanation.
OA, and explanation will be posted after the 48 hour window closes.

This question is part of the Quant 4-Pack series

Scroll Down For Official Explanation
Show more


Given, (\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) = 1% of \(60^{10}\)= \(60^8\)

---> (\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) = \(60^8\) =\([(2^2)*(3)*5]^8\) = \([(2^{16})*(3^8)*5^8]\)---> n=16 and m=8 , giving n-k=8. B is the correct answer.
avatar
bschool3
avatar
Joined: 28 Jul 2014
Last visit: 04 May 2017
Posts: 8
Own Kudos:
11
 [1]
Given Kudos: 17
Posts: 8
Kudos: 11
 [1]
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 23 Nov 2015, 09:45
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
(2^N) * (3^K)*(5^8) = (10^-2)*(60^10)
RHS = (2*5)^-2 * (2^2*3*5)^10 = (2^-2)*(5^-2)*(2^20)*(3^10)*(5^10) = (2^18)*(3^10)*(5^8)
N = 18, K = 10; N-K = 8
=>B
User avatar
Abhishek009
User avatar
Board of Directors
Joined: 11 Jun 2011
Last visit: 18 Jul 2025
Posts: 5,934
Own Kudos:
5,329
 [1]
Given Kudos: 463
Status:QA & VA Forum Moderator
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Posts: 5,934
Kudos: 5,329
 [1]
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 23 Nov 2015, 12:05
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^12)...

If (\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) is equal to one percent of \(60^{10}\) , then what is the value of N – K?

A) 7
B) 8
C) 12
D) 14
E) 15
Show more

(\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) = \(10\)% of \(60^{10}\)

(\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) = \(60^{8}\)

To make the highlighted part a factor of 60, we must have -

(\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) = \(60^{8}\)

(\(2^{16}\)) (\(3^{8}\)) (\(5^{8}\)) = \(60^{8}\) since - Since 60 = \(2^{2}\) ( \(3\))( \(5\))

Now we get N = 16 and K = 8

So, N - K = 8
User avatar
EMPOWERgmatRichC
User avatar
Major Poster
Joined: 19 Dec 2014
Last visit: 31 Dec 2023
Posts: 21,784
Own Kudos:
12,807
 [1]
Given Kudos: 450
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Expert
Expert reply
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Posts: 21,784
Kudos: 12,807
 [1]
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 24 Nov 2015, 01:26
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
EMPOWERgmatRichC
QUANT 4-PACK SERIES Problem Solving Pack 4 Question 4 If (2^n)(3^k)(5^8)...

If (\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) is equal to one percent of \(60^{10}\) , then what is the value of N – K?

A) 7
B) 8
C) 12
D) 14
E) 15
Show more

Hi All,

This question is based on the concept of Prime Factorization (the idea that every positive integer greater than 1 is either a prime number OR the product of prime numbers).

To start, we're told that (\(2^{N}\)) (\(3^{K}\)) (\(5)^{8}\)) = \(60^{10}\) / 100

The 'right side' of the equation can be rewritten as...

\((2x2x3x5)^{10}\)/ (2x2x5x5) =
\((2)^{18}\) \((3)^{10}\) \((5^{8}\)

When this calculation is substituted into the larger equation, we have...

(\(2^{N}\)) (\(3^{K}\)) (\(5^{8}\)) = \((2)^{18}\) \((3)^{10}\) \((5)^{8}\)

'Canceling out' the common terms leaves us....

N = 18 and K = 10

Thus, N - K = 18 - 10 = 8

Final Answer:
Show Spoiler
B

GMAT assassins aren't born, they're made,
Rich
User avatar
fahdman
User avatar
Joined: 23 Nov 2023
Last visit: 07 Mar 2024
Posts: 14
Own Kudos:
1
Given Kudos: 55
Posts: 14
Kudos: 1
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 03 Feb 2024, 08:49
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello,
please, how to get 60 exponent 8 ? iis there a formula used? Thank you
@bunnuel
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,408
Own Kudos:
778,423
 [1]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,408
Kudos: 778,423
 [1]
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 03 Feb 2024, 09:53
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
fahdman
If \((2^{N}) (3^{K})(5^{8})\) is equal to one percent of \(60^{10}\), then what is the value of N – K?

A) 7
B) 8
C) 12
D) 14
E) 15


Hello,
please, how to get 60 exponent 8 ? iis there a formula used? Thank you
@bunnuel
Show more

Firstly, the question must specify that N and K are integers; otherwise, option B wouldn't necessarily be correct.

    \(60^{10}=(2^2*3*5)^{10} = 2^{20}*3^{10}*5^{10}\)

One percent of \(60^{10}\), is 1/100 of \(60^{10}\), so it's:

    \(\frac{60^{10}}{100} = \)

    \(=\frac{2^{20}*3^{10}*5^{10}}{10^2}=\)

    \(=\frac{2^{20}*3^{10}*5^{10}}{2^25^2}=\)

    \(=2^{18}*3^{10}*5^{8}\)

Hence, \((2^{N}) (3^{K})(5^{8})=2^{18}*3^{10}*5^{8}\). Since N and K must be integers, N = 18 and K = 10. Therefore, N - K = 18 - 10 = 8.

Answer: B.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,593
Own Kudos:
1,079
Posts: 38,593
Kudos: 1,079
If (2^n)(3^k)(5^12) is equal to one percent of 60^10, then what 17 Feb 2025, 10:47
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Moderators:
Bunuel
Math Expert
105408 posts
Krunaal
Tuck School Moderator
805 posts