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# S is the product of a list of consecutive integers from 1 to

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Manager
Joined: 23 Jan 2006
Posts: 192
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Kudos [?]: 10 [0], given: 0

S is the product of a list of consecutive integers from 1 to [#permalink]  31 May 2006, 05:40
S is the product of a list of consecutive integers from 1 to 24, and 10 k is a factor of S. What greatest value of k?
A: 1
B: 2
C: 3
D: 4
E: 5
Manager
Joined: 29 Sep 2005
Posts: 125
Followers: 1

Kudos [?]: 2 [0], given: 0

S is the product of a list of consecutive integers from 1 to 24, and 10 k is a factor of S. What greatest value of k?
A: 1
B: 2
C: 3
D: 4
E: 5

**********************************************

Is it E)--5?

Since this is a product of consecutive integers and 10K is a factor of S so,

A: 10*1 is a factor
B: 10*2 is a factor
C: 10*3 is a factor
D: 10*4 is a factor
E: 10*5 is a factor -----> Greatest value of K is 5
Manager
Joined: 23 Jan 2006
Posts: 192
Followers: 1

Kudos [?]: 10 [0], given: 0

Argh.
I was originally puzzled by this question. It was written wrong. Should be:

S is the product of a list of consecutive integers from 1 to 24, and 10^k is a factor of S. What greatest value of k?
A: 1
B: 2
C: 3
D: 4
E: 5

got it now....
Manager
Joined: 29 Sep 2005
Posts: 125
Followers: 1

Kudos [?]: 2 [0], given: 0

In that case is the answer 3?

I am not sure if this is the right approach though

I broke up each of the choices or powers of 10 into the primes:

10^1 = 5*2 --->divsible since both 2 and 5 are in the series
10^2 = 5*2*2--->divisible since both 4 and 4 are in the series
10^3 = (5*2)(5*2*2)*5 = 10*20*5-->divisible since all nos are in the series.
Fails for the rest of the choices
Manager
Joined: 29 Sep 2005
Posts: 125
Followers: 1

Kudos [?]: 2 [0], given: 0

Professor what was the approach you took to arrive at 4? Can you pls explain?
Senior Manager
Joined: 08 Jun 2004
Posts: 499
Location: Europe
Followers: 1

Kudos [?]: 20 [0], given: 0

tapan22 wrote:
Professor what was the approach you took to arrive at 4? Can you pls explain?

D it is, 4.

There are just 4 10s.
2*5 = 10
10 by itself
4*15 =60 = 10*6
20 = 10 *2

No digits left that give us zero at the end.
Senior Manager
Joined: 19 Feb 2005
Posts: 487
Location: Milan Italy
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yeah D it is

because 24/5=4 -> 4 multiples of 5
and 24/2=12 -> more than 4 multiples of 5
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Manager
Joined: 29 Sep 2005
Posts: 125
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Kudos [?]: 2 [0], given: 0

Thanks M8 and thearch very elegant and simple explanations.
VP
Joined: 29 Dec 2005
Posts: 1349
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Kudos [?]: 30 [0], given: 0

tapan22 wrote:
Professor what was the approach you took to arrive at 4? Can you pls explain?

there are at least four 5's and 2's. so that makes 10^4.

1. 25/5 -1 = 4 (four) 5's
2. 24/2 = 12 (twelve) 2's.

so that makes 4 (four) 10's.
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