how many different prime numbers are factors of the expressi

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bhumika.k.shah: Legendary Member; Posts: 941; Joined: Sun Dec 27, 2009 12:28 amFollowed by: 1 member; Thanked: 20 times

by bhumika.k.shah » Sat Jan 30, 2010 3:00 am

If K is a positive integer, how many different prime numbers are factors of the expression K^2?

Three different prime numbers are factors of 4K^4.
Three different prime numbers are factors of 4K.

How to even approach these kinda sums ???

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Source: Beat The GMAT — Data Sufficiency | Sat Jan 30, 2010 3:00 am

thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jan 30, 2010 5:39 am

is it D

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sars72: Master | Next Rank: 500 Posts; Posts: 241; Joined: Wed Jan 27, 2010 10:10 pmFollowed by: 2 members; Location: Chennai; Thanked: 23 times; GMAT Score:690

by sars72 » Sat Jan 30, 2010 5:50 am

The statements just say that "3 different primes are factors of ...." since the statements don't say that there are only 3 prime factors, can we say insufficient?

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jan 30, 2010 6:04 am

sars72 wrote:The statements just say that "3 different primes are factors of ...." since the statements don't say that there are only 3 prime factors, can we say insufficient?

even then also i think we can find out

for the s1) let k=2*3*5*7*6=1260

k^2 will have same numbers of prime factors
as k^4
if k=3*5*2*2
then 4*k^4 will have 3 prime factors
and k^2 will also have 3 prime factors

so in that way think we can find out
what does OA says

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Jan 30, 2010 6:23 am

bhumika.k.shah wrote:If K is a positive integer, how many different prime numbers are factors of the expression K^2?

Three different prime numbers are factors of 4K^4.
Three different prime numbers are factors of 4K.

How to even approach these kinda sums ???

K as well as K^2 has same no of prime factors

4K^4 has same no factors as 2K and 4K Which can be one less than the number of factors K has if K is even and equal to bo of factors k has if k is odd

For an example say k =15 = 3*5

4K^4 has 3 prime factors 3,5 and 2
4K has 3 prime factors 3 5 and 2

K has 2 prime factors
K^2 has 2 prime factors

on the other hand say if K=30 = 3*5*2

4K^4 has 3 prime factors
4K has 3 prime factors

K has 3 prime factors
K^2 has 3 prime factors

Hence E

Last edited by ajith on Sat Jan 30, 2010 12:46 pm, edited 1 time in total.

Always borrow money from a pessimist, he doesn't expect to be paid back.

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thephoenix: Legendary Member; Posts: 1560; Joined: Tue Nov 17, 2009 2:38 amFollowed by: 5 members; Thanked: 137 times

by thephoenix » Sat Jan 30, 2010 7:38 am

ajith wrote:
bhumika.k.shah wrote:If K is a positive integer, how many different prime numbers are factors of the expression K^2?

Three different prime numbers are factors of 4K^4.
Three different prime numbers are factors of 4K.

How to even approach these kinda sums ???
K as well as K^2 has same no of prime factors

4K^4 has same no factors as 2K and 4K Which can be one less than the number of factors K has if K is even and equal to bo of factors k has if k is odd

For an example say k =15 = 3*5

4K^4 has 3 prime factors 3,5 and 2
4K has 3 prime factors 3 5 and 2

K has 2 prime factors
K^2 has 2 prime factors

on the other hand say if K=30 = 3*5*2

4K^4 has 3 prime factors
4K has 4 prime factors

K has 3 prime factors
K^2 has 3 prime factors

Hence E

yes you are correct thanks for soln.....

just check the bold part is there a mistake

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

by ajith » Sat Jan 30, 2010 12:47 pm

thephoenix wrote: yes you are correct thanks for soln.....

just check the bold part is there a mistake

Thanks Phoenix,
Original post edited to correct the solution

Always borrow money from a pessimist, he doesn't expect to be paid back.

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