Data Sufficiency

From OG11 page 336 ex 146
Is n an integer?
(I) n^2 is an integer
(II) sqr root of n is an integer.

I understand the explanation OG11 gives to the statement (II), but I can’t understand (or it seems a bit confusing to me) the way he explains the statement (I). OG says the following:

“…If n is an integer, then n^2 must also be an integer since it is the product of 2 integers.
(II) While n^2 is an integer, since n^2 = n x n, then n^2 is an integer if n is an integer; it is unclear whether n is an integer here; NOT sufficient…”

Well…, if n^2 is an integer and it is the product of 2 integers (nxn) then n should be an integer too right?!?


From OG11 page 331 ex 132
If the integer n is greater than 1, is n equal to 2?
(I) n has exactly two positive factors
(II) The difference of any two distinct positive factors of n is odd.

Same as the other exercise, I do understand the explanation for statement (I), but I get lost when OG11 explains the statement (II). Here is what OG says about (II):

“…Note that if n>2 and n is odd, then 1 and n are factors of n, and their difference is even. Also, if n>2 and n is even, then 2 and n are factors of n, and their difference is even.
Thus, no integer greater than 2 satisfies this statement. However, n=2 does satisfy this statement since 1 and 2 are the only positive factors of 2 and their difference is odd; SUFFICIENT…”

Ps- if you decide to help me with above, would you pls tell me what would be (in your opinion) the main takeaway for such problems? I am going thru OG11 not just doing the exercises, but trying to get a main takeaway from each of them, as suggested by Ron in a recent post; https://www.beatthegmat.com/og-vs-others ... ight=bible . Btw, the strategy is working pretty well so far.

Cheers!

Remember whenevet you have square in options, it must not be almost trusted. There could be exceptions.

Option A gives the fact that square of n is an integer

Even when n is not an integer e.g. sq root 2, Option A=Square of n =integer

And when n=integer e.g. 2, Option A=square if n=integer

hence, we cannot predict whether n is an integer or not ( Exceptions we saw was n =sq root, we still get Option A an integer


B- In the contrast with A, if square root of the n is an integer, n has to be an integer

s qrt 4=2
sq rt 16=4
sq rt 9=3

In all these case, 4, 16 and 9 only when there are integers, their sq rt would be an integer

Hence, IMO B

tks iamcste. now is clear.

just one question; what do you mean by "...Remember whenevet you have square in options, it must not be almost trusted. There could be exceptions...".
what sort of exceptions? could you list one or two? is it common in the gmat?
tks once again.

GMATCHPOINT wrote:tks iamcste. now is clear.

just one question; what do you mean by "...Remember whenevet you have square in options, it must not be almost trusted. There could be exceptions...".
what sort of exceptions? could you list one or two? is it common in the gmat?
tks once again.

exceptions

X>0 Find X

1. Square of X is 4


here from stmt 1 , X can be +2 or -2

but we know X>0, hence X=+2

hence, here if you go with general assumption that square of X is not worth trusting, you will assume that answer is not possible hence this is problem based