ostrowskiamy wrote:"Is x<y?"

(1) 2x<3y
(2) xy>0

Target question: Is x<y?

Statement 1: 2x<3y
There are several pairs of numbers that meet this condition. Here are two:
Case a: x=5 and y=4, in which case x is greater than y
Case b: x= -2 and y= -1, in which case x is less than y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: xy>0
There are several pairs of numbers that meet this condition. Here are two:
Case a: x=5 and y=4, in which case x is greater than y
Case b: x= -2 and y= -1, in which case x is less than y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
There are still several pairs of numbers that meet both conditions. Here are two:
Case a: x=5 and y=4, in which case x is greater than y
Case b: x= -2 and y= -1, in which case x is less than y
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent

When you see inequality problems in DS, you want to think about all of the kinds of numbers that behave differently: positives/negatives, fractions/integers, and 0, 1, and -1.

It's good that you were able to eliminate each statement on its own; this means that you were thinking about positives and negatives. But this statement gives me pause:

I feel more comfortable testing numbers instead of recalling all the rules in these instances

It's fine to test numbers with inequalities, but you have to be systematic about it! You can't just test numbers at random. You need to ask yourself - have I tested different categories of numbers that behave differently? Your number-testing checklist should have looked like this:

- positives and negatives
- fractions and integers
- 0
- 1 and -1

Which each of these, your goal should be to PROVE INSUFFICIENCY. Can we test different cases to get a YES answer and a NO answer? As Brent proved, you can.

When we combine the statements, we know that 2x < 3y, and that xy > 0 (in other words, they have the SAME SIGN). That only rules out one positive, one negative, but there are still plenty of other cases to test. Be systematic in your number testing!