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

 It is currently 09 Dec 2018, 19:01

### 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 December
PrevNext
SuMoTuWeThFrSa
2526272829301
2345678
9101112131415
16171819202122
23242526272829
303112345
Open Detailed Calendar
• ### Free GMAT Algebra Webinar

December 09, 2018

December 09, 2018

07:00 AM PST

09:00 AM PST

Attend this Free Algebra Webinar and learn how to master Inequalities and Absolute Value problems on GMAT.
• ### Free lesson on number properties

December 10, 2018

December 10, 2018

10:00 PM PST

11:00 PM PST

Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

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

Author Message
TAGS:

### Hide Tags

Intern
Joined: 28 Jan 2011
Posts: 22
How many zeros does 135^19 x 42^17 end with?  [#permalink]

### Show Tags

07 Sep 2013, 02:56
3
00:00

Difficulty:

25% (medium)

Question Stats:

68% (01:15) correct 32% (01:39) wrong based on 120 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
Manager
Joined: 20 Jul 2012
Posts: 128
Location: India
WE: Information Technology (Computer Software)
Re: How many zeros does 135^19 x 42^17 end with?  [#permalink]

### Show Tags

07 Sep 2013, 04:45
2
1
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: 159
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
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: 376
Location: Russian Federation
Concentration: General Management, Economics
GMAT 1: 640 Q44 V33
WE: Sales (Telecommunications)
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: 78
GPA: 4
How many zeros does 135^19 x 42^17 end with?  [#permalink]

### Show Tags

03 Aug 2016, 12:30
1
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 $$2 \times 5$$

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

(e) 17

_________________

Please press +1 Kudos if this post helps.

Manager
Joined: 18 Jun 2018
Posts: 247
Re: How many zeros does 135^19 x 42^17 end with?  [#permalink]

### Show Tags

05 Sep 2018, 11:49
OA:E

$$135^{19} * 42^{17} = 3^{3*19}*5^{19}*2^{17}*3^{17}*7^{17}=2^{17}*3^{74}*5^{19}*7^{17}=10^{17}*3^{74}*5^2*7^{17}$$

$$10^{17}$$ will lead to $$17$$ zeros
Re: How many zeros does 135^19 x 42^17 end with? &nbs [#permalink] 05 Sep 2018, 11:49
Display posts from previous: Sort by