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!
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!
