How many zeros does 135^19 x 42^17 end with? : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 17 Jan 2017, 23:10

### 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

# How many zeros does 135^19 x 42^17 end with?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Jan 2011
Posts: 22
Followers: 1

Kudos [?]: 13 [0], given: 15

How many zeros does 135^19 x 42^17 end with? [#permalink]

### Show Tags

07 Sep 2013, 02:56
1
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

75% (01:57) correct 25% (01:17) wrong based on 75 sessions

### HideShow timer Statistics

How many zeros does 135^19 x 42^17 end with?

(a) 0
(b) 2
(c) 5
(d) 13
(e) 17
[Reveal] Spoiler: OA
Manager
Joined: 20 Jul 2012
Posts: 174
Location: India
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 28 [0], given: 559

Re: How many zeros does 135^19 x 42^17 end with? [#permalink]

### Show Tags

07 Sep 2013, 04:45
1
This post was
BOOKMARKED
salsal wrote:
How many zeros does 135^19 x 42^17 end with?

(a) 0
(b) 2
(c) 5
(d) 13
(e) 17

135=5x3^3 this implies
135^19=5^19x(3^3)^19..
similarly 42=2x3x7
42^17=2^17x3^17x7^17

we know to get zero we need 2 and 5... and we have 19 5's and 17 2's ...thus we can get 17 10's
_________________

Preparing for another shot...

Manager
Joined: 30 May 2013
Posts: 190
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 64 [0], given: 72

Re: How many zeros does 135^19 x 42^17 end with? [#permalink]

### Show Tags

07 Sep 2013, 05:18
salsal wrote:
How many zeros does 135^19 x 42^17 end with?

(a) 0
(b) 2
(c) 5
(d) 13
(e) 17

To know the zeros we need to know how many 10's are there for this need to find number of 2s and 5s ( 2 * 5 = 10)

135 = (5 x 3 ^3)^19 So Number of 5s are = 19
42 = (2x7x3)^17 so number of 2s = 17

So tot number of 10s in this number is (17-> 2s x 17-> 5s)

Senior Manager
Joined: 02 Dec 2014
Posts: 388
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
Followers: 0

Kudos [?]: 78 [0], given: 349

Re: How many zeros does 135^19 x 42^17 end with? [#permalink]

### Show Tags

16 Jul 2016, 06:28
5^19 always end on 5. 2^17 has a cycle of 4 (2,4,8,2 and again 2,4,8,2) Since 5 multiplied by each number from cycle of 2 has 0 in the end then the whole number will have 17s zero (since number of 2s is 17)
_________________

"Are you gangsters?" - "No we are Russians!"

Manager
Joined: 07 Jul 2016
Posts: 80
GPA: 4
Followers: 1

Kudos [?]: 17 [0], given: 51

How many zeros does 135^19 x 42^17 end with? [#permalink]

### Show Tags

03 Aug 2016, 12:30
salsal wrote:
How many zeros does $$135^{19} \times 42^{17}$$ end with?

Take the prime factorisations of the two numbers.

$$135 = 5 \times 3^3\\ 42 = 2 \times 3 \times 7$$

$$135^{19} = 5^{19} \times {(3^3)}^{19}\\ 42^{17} = 2^{17} \times 3^{17} \times 7^{17}$$

The prime factorisation of 10 is $$2 \times 5$$

$$135^{19} \times 42^{17} = \color{blue}{(2^{17} \times 5^{17})} \times 5^{2} \times {(3^3)}^{19} \times 3^{17} \times 7^{17} =\\ \color{blue}{10^{17}} \times 5^{2} \times {(3^3)}^{19} \times 3^{17} \times 7^{17}$$

[Reveal] Spoiler:
(e) 17

_________________

Please press +1 Kudos if this post helps.

How many zeros does 135^19 x 42^17 end with?   [#permalink] 03 Aug 2016, 12:30
Similar topics Replies Last post
Similar
Topics:
3 How many consecutive zeros will appear at the end of 43! if that numbe 4 02 Dec 2016, 13:09
2 How many zeroes are there at the end of the number N, if N = 100! + 20 4 08 Jun 2016, 09:50
14 If 73! has 16 zeroes at the end, how many zeroes will 80! 7 15 Feb 2013, 11:24
15 How many zeros are the end of ? 4 15 Nov 2012, 06:23
74 How many zeros does 100! end with? 20 07 Sep 2010, 12:41
Display posts from previous: Sort by

# How many zeros does 135^19 x 42^17 end with?

 Powered by phpBB © phpBB Group and phpBB SEO Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.