number system

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon May 27, 2013 9:09 pm

If m is divisible by 3, how many prime factors does m have?
1). m/3 is divisible by 3.
2). m/3 has two different prime factors

Ans is C but my take E

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Mon May 27, 2013 9:35 pm

m can be 3,6,9,12,15,18 ...

St1: m/3 is divisible by 3
So m can be: 9 or 18 and corresponding m/3 would be 3 and 6 (div. by 3)
# prime factors of 9 = 1 {3}
# prime factors of 18 = 2 {2,3}
Not sufficient

St2: m/3 has 2 different prime factors
if m/3 = 10 {prime factors 2 and 5}, then m = 30 and # prime factors of 30 = 3 {2,3,5}
if m/3 = 6 {prime factors 2 and 3}, then m = 18 and # prime factors of 18 = 2 {2,3}
Insufficient

Together: m/3 is divisible by 3 and m/3 has 2 prime factors
if m = 18, # prime factors of 18 = 2 {2,3}
if m = 36, # prime factors of 36 = 2 {2,3}
Sufficient

Ans C

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon May 27, 2013 9:50 pm

Thanks I considered that before but my query remains same

qustion asking: If m is divisible by 3, how many prime factors does m have?
Note that NOT differant prime factors

here in your solution 18 have 3 (2x3x3) total factors and 2 differant factors
and 36 have 4 total factors (2x2x3x3) and 2 differant prime factors

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srcc25anu: Master | Next Rank: 500 Posts; Posts: 423; Joined: Fri Jun 11, 2010 7:59 amFollowed by: 2 members; Location: Seattle, WA; Thanked: 86 times

by srcc25anu » Mon May 27, 2013 10:19 pm

18 = {1,2,3,6,9,18}
Total # of factors = 6
# prime factors = 2 {2 and 3} = # Distinct prime factors

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon May 27, 2013 10:56 pm

18 -Total no of prime factors 2x3x3 = 3; distinct prime factors = 2
36 - Total no of prime factors 2x2x3x3 = 4 ; distinct prime factors = 2

Qustion asking total no of prime factors not distinct prime factors ;since 3 not equal to 4 hence my ans remain same E

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Mon May 27, 2013 11:08 pm

vipulgoyal wrote:18 -Total no of prime factors 2x3x3 = 3; distinct prime factors = 2
36 - Total no of prime factors 2x2x3x3 = 4 ; distinct prime factors = 2

Qustion asking total no of prime factors not distinct prime factors ;since 3 not equal to 4 hence my ans remain same E

I think we need to check the definition of prime factor.
From the top of my head we dont distinguish between distinct prime factors and prime factors i.e. we dont count them twice.

I ll have to agree with srcc25anu

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon May 27, 2013 11:21 pm

I am sure experts might have come across couple of qustions where Total number of prime factors and dictinct no of prime factors didnt mean same, but my query still dangling

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faraz_jeddah: Master | Next Rank: 500 Posts; Posts: 358; Joined: Thu Apr 18, 2013 9:46 amFollowed by: 7 members; Location: Jeddah, Saudi Arabia; Thanked: 42 times; GMAT Score:730

by faraz_jeddah » Tue May 28, 2013 3:43 am

Yup expert reply would be great!

*tick tock tick tock*

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue May 28, 2013 4:24 am

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