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

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

Kudos [?]: 9 [0], given: 15

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

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New post 07 Sep 2013, 03:56
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Difficulty:

  25% (medium)

Question Stats:

69% (01:46) correct 31% (00:57) wrong based on 36 sessions

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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
Manager
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Joined: 20 Jul 2012
Posts: 170
Location: India
WE: Information Technology (Computer Software)
Followers: 1

Kudos [?]: 18 [0], given: 524

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

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New post 07 Sep 2013, 05:45
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
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Manager
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Joined: 30 May 2013
Posts: 190
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.82
Followers: 0

Kudos [?]: 50 [0], given: 72

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

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New post 07 Sep 2013, 06:18
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)

So answer is 17
Re: How many zeros does 135^19 x 42^17 end with?   [#permalink] 07 Sep 2013, 06:18
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How many zeros does 135^19 x 42^17 end with?

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