Algebra 6th ed. chapter 10 (p. 143)

[WojciechG915]

I'm struggling to understand the logic of explanation given to 2nd statement of the question at the beginning of chapter 10 in Algebra book. The question is as follows:

Is m < n ?

(1) m < n^2

(2) |m| < n

The right answer is (B). According to my reasoning it should be (E). I agree that (1) is definitely not sufficient. However, (2) is not either. It is written that "no matter how many cases you try for for statement (2), you are always going to get a YES answer". I disagree, since if I take e.g. m = - 5, n = 4 then I get NO answer as |-5|> 4. I'm really confused with this question. For me both statements don't work as I can plug in any number for m and n, which will prove it insufficient. Or maybe I'm just too tired and need a fresh look at this, but anyway I could use some help. Thanks.

[RonPurewal]

the problem is that you haven't really learned how DS works yet. this is a common issue—DS is, after all, a 'weird' problem type that was invented expressly for this test—but it needs to be addressed forthwith.

in particular, you should fix your understanding ON EASY PROBLEMS before you start working harder ones!

the problem here is that you're addressing the GIVENS as though they were QUESTIONS.
that's not how this works.

e.g.,
Is x < 10?
(1) x < 15
(2) x < 5

the answer to this problem is (B).
if you use the same logic you're applying to the question here, you'll think it's (A).

make sure you can run through this problem and understand that it's (B). THEN scroll to the next post (where i'll address the issue with the problem in the thread).

[RonPurewal]

...so, as stated above, you're (mistakenly) treating the STATEMENTS as though they were QUESTIONS.

like here:

if I take e.g. m = - 5, n = 4 then I get NO answer as |-5|> 4.

...no.
that's not a 'NO answer'.
rather, you have a pair of numbers that doesn't obey the statement... so that pair DOES NOT COUNT AT ALL. it's not a 'yes' answer; it's not a 'no' answer. it's just not a thing at all.

[RonPurewal]

one concrete way to address this issue is to 'decorate' the statements as follows, EVERY TIME, until the process has become instinctive:

for statement 1:
IF I KNOW [whatever statement 1 says], THEN [QUESTION] ?

for statement 2:
IF I KNOW [whatever statement 2 says], THEN [QUESTION] ?

so, for statement 2 here, you have
IF I KNOW that |m| < n, THEN ... is m < n ?

if you do this it's probably easier to see why your case (m = –5 and n = 4) is irrelevant. (the 'IF I KNOW' part is not kidding. you can't violate it.)