factors of n

[neoreaves]

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 < p

[thephoenix]

IMO E

[neoreaves]

IMO E

I wonder how you arrived at your "IMO"

[thephoenix]

if pq means p*q
then my soln is
if p and q are 2 and 3 then s1) that is 2+3=odd is satisfied and q stem p*q=6 has 4 factors and thus satisfied
same is true for p and q are 2 and 5 respectievly
insuff

s2) not of much help

combining p can be 3 or 5 as seen above not suff

am i wrong

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PostPosted: Thu Apr 08, 2010 7:47 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

Only even +odd=odd
so p,q can have a number of possibilities
f(pq)=4, where pq =25,34,49,....
p cannot be determined, (2) is insufficient

(2) q < p
f(pq)=4 , where pq can be 21,10...
so insufficient

(1) and (2) together gives number like 65,74,85... where p+q=odd and q<p

so E is the answer

[pops]

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 < p

f(n) = number of factors on n
f(pq) = 4
now one factor of pq is 1 and second is pq
this implies only other 2 factors are p and q themselves.. that means p and q are prime !

statement 1: p+q is odd
sum of two primes is odd => one prime is 2
so either of p or q is 2

statement 2: q<p
now, for sure the smaller number is 2 hence q=2.. so we get no info about p

hence E..

important here is to arrive at p,q being prime..
if info was asked about q then aswer would have been C

[neoreaves]

OA is E

[eaakbari]

I think one should quickly jump to the conclusion that the answer is E. Since they are asking us for a value and none of the statements give us any value, just number of factors, it is clearly insufficient.

E

[Brian@VeritasPrep]

Great question here, guys - and, pops, you nailed the explanation:

The question tells us that the product pq has 4 factors. We know that every positive integer is divisible by itself and 1, so two of those factors are:

1
pq

And if p and q are positive integers, they're also factors, so the whole list is:

1
p
q
pq

p and q must be prime, because, if they weren't, then their factors would also be factors of pq, and there would be more than 4 factors.

(NOTE: I'm just paraphrasing pops - forgive me for taking any credit away from you!)

The really important point here, though, is the last one that pops makes. Because statement 1 tells us that the sum of p and q is odd, we know that one of them MUST BE 2, but we don't know which one. If we combine that with statement 2, which tells us that p is greater than q, then we know that q is 2: 2 is the only even prime number, and the lowest prime number, so p must be greater than 2.

So, if statement 2 were reversed to:

p < q

then we'd know the value of p as 2, and the answer would be C.

This is a great example of a couple of principles related to Data Sufficiency:

1) Often times on problems that seem very abstract like this one, you know a lot more than you think you do if you break the problem down further. Never just assume the answer is E because it looks hopeless at first glance.

2) If the answer is E, it's almost always just one step away from being C - the statements aren't sufficient, but only for one tiny factor like we saw above. Before you select E, try to identify that missing piece of evidence that you'd need, as it's highly unlikely that the GMAT will reward you for just saying "nope...too tough...can't do it".

[akhpad]

I think one should quickly jump to the conclusion that the answer is E. Since they are asking us for a value and none of the statements give us any value, just number of factors, it is clearly insufficient.

E

No, We cannot do that

Statement 1:
p + q is an odd integer

(p, q) = (2, 3) or (3, 2)
(p, q) = (2, 5) or (5, 2)
(p, q) = (2, 7) or (7, 2)
(p, q) = (2, 11) or (11, 2)
(p, q) = (2, 13) or (13, 2)

Not Sufficient.

Statement 2:
q < p
Not Sufficient.

Statement 1 and 2
q = 2 and p = 3, 5, 7, 11, 13, 17 etc
Not Sufficient

Answer: E

However, if p<p, then p = 2.