GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 26 Aug 2019, 00:21 ### 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. ### Request Expert Reply # How many factors of the number 2^9 * 3^6 * 5^5 * 10^4 are multiples of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Director  P
Joined: 20 Jul 2017
Posts: 636
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
How many factors of the number 2^9 * 3^6 * 5^5 * 10^4 are multiples of  [#permalink]

### Show Tags

1 00:00

Difficulty:   45% (medium)

Question Stats: 56% (02:19) correct 44% (02:18) wrong based on 18 sessions

### HideShow timer Statistics

How many factors of the number $$2^9*3^6*5^5*10^4$$ are multiples of 60?

A. 594
B. 648
C. 980
D. 1200
E. 2100
##### Most Helpful Community Reply
Manager  G
Joined: 10 Jan 2017
Posts: 204
Location: India
Re: How many factors of the number 2^9 * 3^6 * 5^5 * 10^4 are multiples of  [#permalink]

### Show Tags

5
Dillesh4096 wrote:
How many factors of the number $$2^9*3^6*5^5*10^4$$ are multiples of 60?

A. 594
B. 648
C. 980
D. 1200
E. 2100

Lets have 10^4 as 2^4*5^4

so combined we have the number as 2^13*3^6*5^9

prime factorization of 60 we have = 2^2*5*3

so, number of factors of the above number when it is a multiple of 60 is if we calculate the number of factors when we have taken out the exponents of prime factors of 60 from them, basically dividing it!!

now we have - 2^11*3^5*5^8

no. of factors of the above number is (11+1)*(5+1)*(8+1) = 648

Hence, answer is B
_________________
Your limitation—it's only your imagination.
Please hit +1 Kudos if you like my Post.
##### General Discussion
Intern  B
Joined: 11 Jun 2019
Posts: 23
Location: India
How many factors of the number 2^9 * 3^6 * 5^5 * 10^4 are multiples of  [#permalink]

### Show Tags

1
My approach-
2^9 x 3^6 x 5^5 x 10^4 can be written as 2^13 x 3^6 x 5^9.
60= 2^2 x 3^1 x 5^1

Now to find number of multiples of 60 in given number, 2 can have any number of powers between 2 to 13. Hence 2 can be raised to 12 numbers (2,3,4,5,6,7,8,9,10,11,12,13)= 12
Similarly, 3 can be raised to any number between 1 to 6 (1,2,3,4,5,6)=6
and 5 can be raised to any number between 1 to 9 (1,2,3,4,5,6,7,8,9)= 9

Hence total possible numbers are- 12 X 6 X 9 = 648
Hence (B) How many factors of the number 2^9 * 3^6 * 5^5 * 10^4 are multiples of   [#permalink] 09 Aug 2019, 09:42
Display posts from previous: Sort by

# How many factors of the number 2^9 * 3^6 * 5^5 * 10^4 are multiples of

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

#### MBA Resources  