Asad wrote:
Is (x – 2)(x – 3) > 0?
(1) x – 2 < 0
(2) x – 3 < 0
I think this is a simpler problem than some of the previous explanations make it seem!
When a DS question asks you "is the product of these two things positive," that's "GMAT code." What it really means is:
Do x-2 and x-3 have the same sign? (That is, are they both positive or both negative?)
You can go further with decoding this, too. Think: when are x-2 and x-3 both positive? If x is a big number, like 100, they'll definitely both be positive. If x is a medium-sized number, like 10, they'll still both be positive. This will be the case all the way down to x = 3, where the product will now be 0 instead of being positive.
So, they're both positive in the scenario where x > 3.
When are they both negative? If x is a very small number, like -100, they'll both be negative. And if x is a moderately small number, like -10, they'll still both be negative. In fact, they'll both be negative all the way up to x = 2, where the product will now be 0 instead of being negative.
So, they're both negative in the scenario where x < 2.
In other words, the answer to this DS question is "yes" if x is outside of the range from 2 to 3. And if x is in the range of 2 to 3, inclusive, then the answer would be "no."
What we're actually interested in is:
is x between 2 and 3, inclusive?Statement 1: This translates to "x < 2". If x is less than 2, we know it's definitely not between 2 and 3. So, this statement is sufficient.
Statement 2: This translates to "x < 3". If x is less than 3, it could be between 2 and 3 (for instance, it could be 2.5). Or, it could be less than 2, and therefore it would be outside of the range. So, this statement is insufficient.
Since statement 1 is sufficient and statement 2 is insufficient, the answer is A.