Is x a negative number?

(1) x^2 (squared) is a positive number.

(2) x · |y| is not a positive number.

Hi Guys,
statement 1 tells us that x cannot be 0. But it can be +ve or -ve hence Inusfficient.
statement 2 tells us that x cannot be +ve. But it can be -ve or it can be 0. Hence Insufficient.

But if we combine 1 and 2, surely, we can rule out both 0 and +ve values but a negative x is common to both 1 and 2; x should be negative. Should the answer hence be C?

nothing wrong seems to me.
UPA

What happens if x = 2 and y = 0??

make sure you track the status of each variable separately.

you ruled out 0 for x, but not for y. therefore, as captain said in the post above this one, x can still be positive, if y is 0.

tricky tricky

Got it guys (Captain and Ron), thanks. It is so easy to miss a condition. May be writing down will avoid this.

Write EVERYTHING down. Your pen should be moving constantly - I will literally write down 2+2. It doesn't take me any more time to write while I think and I can avoid careless mistakes and/or overlooking important little details if I make it a habit to write down absolutely everything.

Many thanks Stacey. This is a gem of an advice and I have already started following it. I can see the difference it makes. Your suggestion has just re-confirmed that I must carry on doing that. You are the best.
I dont take notes while doing CR and SC though. Do you suggest it is worthwhile? I am comfortable with SC now but for CR I have still some way to go.

yeah

i swear, the last time i forgot to write 'breathe in, breathe out' on the top of the paper, i almost choked to death. wait what?

you don't have time to take notes on s.c., except for making a PROCESS OF ELIMINATION CHART (nothing fancy - just a chart with ABCDE's that you cross off when you have eliminated the answer choices). that's more essential than you might think - it's much easier than you think to get lost, and forget which answer choices you've eliminated, on a s.c. problem with really really really long answer choices.

for c.r., i would suggest making a diagram for LONGER passages, and for ANY passage that you can't read right through and understand on your first pass through it. in other words, if you hesitate AT ALL while you read a passage, then you should immediately start making a diagram.
for shorter and/or easily understood passages, diagrams are largely unnecessary.

Many thanks Ron for the suggestions. I shall try to follow them. Did not realise that you had replied to this post hence took longer to reply.