S1) As you said, both positive or both negative. Insufficient.

S2) To get a positive sum, we could add two positives, or we could add a positive and a negative (10 + -3 = 7, for instance). Insufficient.

Taken together, the only way both statements can be true is if both variables are positive. Thus, x must be positive. Sufficient.

[quote="Bill@VeritasPrep"]S1) As you said, both positive or both negative. Insufficient.

S2) To get a positive sum, we could add two positives, or we could add a positive and a negative (10 + -3 = 7, for instance). Insufficient.

Taken together, the only way both statements can be true is if both variables are positive. Thus, x must be positive. Sufficient.[/quote]

Could you please elaborate on your last point? Or maybe show an algebraic way? Thanks so much.

With two terms, we have three possible situations:

1. both positive
2. both negative
3. one positive, one negative

If we have two positive values, (say 4 and 2), they always have a positive product (8) and a positive sum (6).

Two negative values (-4 and -2) always have a positive product (8) and a negative sum (-6).

One positive and one negative (4 and -2) will always have a negative product (-8), but could have a positive or negative sum (4 + -2 = 2; -4 + 2 = -2).

Number properties are tested fairly often, so it's definitely worth spending some time memorizing them.

I was in a way more difficult arena of algebra. Common sense + number properties is sometimes enough. Thanks so much. Its so easy, its almost embarrassing.


[quote="Bill@VeritasPrep"]With two terms, we have three possible situations:

1. both positive
2. both negative
3. one positive, one negative

If we have two positive values, (say 4 and 2), they always have a positive product (8) and a positive sum (6).

Two negative values (-4 and -2) always have a positive product (8) and a negative sum (-6).

One positive and one negative (4 and -2) will always have a negative product (-8), but could have a positive or negative sum (4 + -2 = 2; -4 + 2 = -2).

Number properties are tested fairly often, so it's definitely worth spending some time memorizing them.[/quote]

myfish wrote:I was in a way more difficult arena of algebra. Common sense + number properties is sometimes enough. Thanks so much. Its so easy, its almost embarrassing.

One big giveaway that number properties and logic are the way to go are when we have inequalities involving 0 on side. Essentially, the question is telling us that whatever's on the other side is positive or negative, so we should able to attack it without actually spending the time required to solve.