NP prob: If n is a multiple of 5 and n=(p^2)q, where p and q

[catennacio]

catennacio --

your logic is pretty much ok, except for the part at the end about symmetry.
on the other hand, your post suggests that you may not be thinking enough -- maybe not at all, in fact -- about testing cases.

for instance, you can kill answer choice (a) pretty quickly with p = 2, q = 5; you can kill answer choice (b) quickly by reversing those values. and either of those pairs of values, in fact, is good enough to knock out choice (c).

testing cases is a bedrock skill in data sufficiency -- in fact, it may be the single most central principle in DS. you should employ it more often than it seems you currently do.

symmetricity (not sure if this is written right, I'm not a native speaker)

should be "symmetry"

of numbers. Since 25 = 5*5, the pair of factors must be symmetric. If any answer choice is asymmetric, we can guess that it is wrong.

nope.

the point of the problem has nothing to do with symmetry; the point of the problem is that either p or q -- but we don't know which -- is 5.
so, any expression in which the powers of p and q are each 2 or more will suffice. for instance, (p^2)(q^2) is a correct answer to this problem, but so are all of the following:
(p^2)(q^3)
(p^6)(q^2)
(p^9)(q^9)
(p^161109)(q^1000000)
etc.

Thanks for your answer... Spot on my lack of testing.. I tend to convert every problem to algebra to solve as a momentum. I really need to change my mindset to try test cases first. My only problem is that many times I failed to choose the right numbers to test on. In your example, how did you come up with 2 and 5 and not other numbers? Can you give me any hint?

You're right about the symmetry thing, as another shortcoming of mine is that I tend to generalize pattern to quickly and prematurely. This can be helpful sometimes, but I guess it costs more damage in GMAT than it brings benefits. I think this depends on experience and is hard to correct thou, as each of us tends to make usual assumptions in our daily life right?

[RonPurewal]

Thanks for your answer... Spot on my lack of testing.. I tend to convert every problem to algebra to solve as a momentum. I really need to change my mindset to try test cases first.

i like what you wrote here -- except for the word "first".

you don't need to rank the different methods, and it's not optimal to think of some of them as "primary" and others as "secondary". instead, there is only one key, and it's a pretty simple mentality: have as many approaches as possible, and be able to QUIT and SWITCH when one approach isn't working.

what i mean is that, if you are doing algebra and it makes total sense -- with no uncertainty -- that you should just keep doing the algebra. no need to fix what isn't broken.
on the other hand, in any situation where you are less than 100% sure -- even if it's 99% -- you should go ahead and switch methods, and see if you can get anything more concrete.

My only problem is that many times I failed to choose the right numbers to test on. In your example, how did you come up with 2 and 5 and not other numbers? Can you give me any hint?

the point was to pick 5 and basically any other prime number.
you probably don't need any help seeing why you should choose 5 -- this whole problem is awash in 5's. the 2 was actually a completely random choice.

You're right about the symmetry thing, as another shortcoming of mine is that I tend to generalize pattern to quickly and prematurely. This can be helpful sometimes, but I guess it costs more damage in GMAT than it brings benefits. I think this depends on experience and is hard to correct thou, as each of us tends to make usual assumptions in our daily life right?

the problem here is not the mindset, it's the scope of that mindset.
you should absolutely, positively, recognize patterns and generalize them in analyzing individual problems. for instance, if you are working some problem about odds and evens and the first few cases you try all wind up even, then you should totally jump to the conclusion of "always even".
in fact, no exaggeration, this is probably the single most useful skill you can have for the entire gmat quant section.
the trouble starts when you extend this mentality to the problems in general. the problems are meant to feature individual patterns that can be discovered -- hence the success of that kind of mentality on individual problems -- but they are NOT meant to work like each other! in fact, this is the entire point of the gmat: new problems don't work like old problems, so that the test is impossible to beat with pure memorization.