number

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sun Nov 13, 2011 4:25 pm

If N is the product of all multiples of 3 between 1 and 100, what is the greatest integer m for which is an integer?

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(1)3

(2)

6

(3)

7

(4)

8

(5)

10

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Source: Beat The GMAT — Quantitative Reasoning | Sun Nov 13, 2011 4:25 pm

neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sun Nov 13, 2011 4:28 pm

Hi rupsk, I am sure that this is not the complete question. Can you please check and edit the post with the correct question?

what is the greatest integer m for which ____ is an integer

Anil Gandham
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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sun Nov 13, 2011 5:19 pm

sorry my mistake it says what is the greatest integer m for which N/10^m is an integer?

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Sun Nov 13, 2011 5:37 pm

rupsk wrote:sorry my mistake it says what is the greatest integer m for which N/10^m is an integer?

N/10^m = Integer

N =3*9*12*15*...30*..45*..60*..75*..90. So N contains 5^7 and 2^n where n > 7

N/10^m = X*5^7*2^n/10^m

The maximum value of m = 7

IMO C

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
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rooster: Senior | Next Rank: 100 Posts; Posts: 44; Joined: Wed Aug 25, 2010 12:23 am; Thanked: 6 times

by rooster » Sun Nov 13, 2011 6:59 pm

neelgandham wrote:
rupsk wrote:sorry my mistake it says what is the greatest integer m for which N/10^m is an integer?
N/10^m = Integer

N =3*9*12*15*...30*..45*..60*..75*..90. So N contains 5^7 and 2^n where n > 7

N/10^m = X*5^7*2^n/10^m

The maximum value of m = 7

IMO C

Right approach, but I don't see how you get 7 5's

Basically, you need to know how many 10s are in the product of all the multiples of 3.

From what we know, the only 10s that can be factored out are 30, 60 and 90

BUT

We also have 15, 45, and 75, which all have 5s in them and there are enough 2s in the problem to multiply and create 10s.

So, from this we get 6 10s, which means that the product of all multiples of 3 that are less than 100 equal to 10^6

therefore the choice should be B

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rupsk: Master | Next Rank: 500 Posts; Posts: 123; Joined: Mon Feb 07, 2011 12:11 pmFollowed by: 1 member

by rupsk » Sun Nov 13, 2011 7:14 pm

even if I try to find number of 5 I get value as 6. Please explain how you get 5^7?

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shankar.ashwin: Legendary Member; Posts: 966; Joined: Sat Jan 02, 2010 8:06 amFollowed by: 21 members; Thanked: 230 times

by shankar.ashwin » Sun Nov 13, 2011 9:28 pm

N = 3*6*9*12*15*18*..... * 99.

For N to be divisible by 10^m, we need to find number of 0's N has.

Number of 0's can be found by finding number of factors of 5 in the series.

Factors of 5;

15 - 5*3 - 1
30 - 5*6 - 1
45 - 5*9 - 1
60 - 5*12 - 1
75 - 5*15 = 5*5*3 - 2
90 - 5*18 - 1

Adding we have 7 factors of 5. So 'm' would be 7 here. C

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neelgandham: Community Manager; Posts: 1060; Joined: Fri May 13, 2011 6:46 amFollowed by: 52 members; Location: Utrecht, The Netherlands; Thanked: 318 times

by neelgandham » Mon Nov 14, 2011 12:18 am

rupsk wrote:even if I try to find number of 5 I get value as 6. Please explain how you get 5^7?

As Shankar already explained

N = 3*...*15*...30*...45*....60*....75(5*5*3)*...90*...99, So, the highest power of 3 is 7

Anil Gandham
Welcome to BEATtheGMAT | Photography | Getting Started | BTG Community rules | MBA Watch
Check out GMAT Prep Now's online course at https://www.gmatprepnow.com/

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