f(n) = the number of factors of n

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abhi332: Master | Next Rank: 500 Posts; Posts: 117; Joined: Wed Dec 30, 2009 1:57 pm; Location: India; Thanked: 4 times; Followed by:1 members

f(n) = the number of factors of n

by abhi332 » Wed Feb 24, 2010 11:46 am

The function f(n) = the number of factors of n. If p and q are positive integers and f(pq) = 4, what is the value of p?

(1) p + q is an odd integer

(2) q is less than p

[spoiler]OA : E[/spoiler]

What you think, you become.

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Source: Beat The GMAT — Data Sufficiency | Wed Feb 24, 2010 11:46 am

firdaus117: Master | Next Rank: 500 Posts; Posts: 102; Joined: Sat Feb 20, 2010 5:38 am; Location: IIM Ahmedabad; Thanked: 10 times

by firdaus117 » Wed Feb 24, 2010 12:25 pm

As 4=2*2 and 4*1,
pq=Product of two prime numbers or a*a^2 or 1 and a^3 where a is a prime number.
Condition 1.The set of p,q can be 2 and 5/7/11/13.....any prime number.Another possible set can be: 1 and 8.........Hence no unique value of p.Insufficient.
Condition 2.Here no restriction on p+q to be odd.We can have set of p,q as 2,4 or 5,25 or 7,49.Again,no unique p.Insuff.
Combining both,still no unique value for p.
Hence,Option E

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vineetbatra: Master | Next Rank: 500 Posts; Posts: 355; Joined: Thu Feb 19, 2009 12:42 pm; Thanked: 2 times; Followed by:1 members

by vineetbatra » Wed Feb 24, 2010 4:42 pm

firdaus117 wrote:As 4=2*2 and 4*1,
pq=Product of two prime numbers or a*a^2 or 1 and a^3 where a is a prime number.
,Option E

Why do you say that P and Q are Prime Numbers?

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sivareddy: Newbie | Next Rank: 10 Posts; Posts: 4; Joined: Sun Feb 21, 2010 8:40 pm; Location: Hyderabad

by sivareddy » Wed Feb 24, 2010 8:19 pm

this can be solved easily..

to get 4 factors.. u can have a cube term like 8 (2power 3) which has four factors like 1,2,4,8 or a 2*2 factors like a 6 which has 1,2,3,6 as factors..

first statement says sum is odd, true for both cases and second statement too is true for both cases and u cant decice..

So none of the statements is sufficient.. and together they are not sufficient too..