Hi All,
We're told X/Y > 2 which means that X and Y are either BOTH positive or BOTH negative. The question asks if (3X + 2Y) < 18. This is a YES/NO question. This DS question has some useful Number Properties in it and can be solved by TESTing VALUES.
To start, there are some patterns worth noting:
If both X and Y are NEGATIVE, then the answer to the question is YES (and there'd be no reason to even do the math).
If both X and Y are POSITIVE, then the math IS required because the answer to the question COULD be YES or NO (depending on how big X and Y are).
1) (X - Y) is less than 2
This tells us that X and Y must be relatively "close" to one another, BUT we also know that X/Y > 2, which means that X is MORE THAN TWICE Y. These 2 Facts severely LIMIT the possibilities...
X = 2, Y = 1/2....3(2) + 2(1/2) IS < 18 The answer is YES
X = 3, Y = 1.1....3(3) + 2(1.1) IS < 18 The answer is YES
X CAN'T = 4 (or larger) because there's no value for Y that "fits" both Facts
If X and Y are negative, then we get another YES
Fact1 is SUFFICIENT
2) (Y - X) is less than 2
Here, we can use any of our TESTs from Fact 1
X = 2, Y = 1/2 ....The answer is YES
But we also need to consider any other possibilities...
X = 100, Y = 1....3(100 + 2(1) is NOT < 18 and the answer is NO
Fact 2 is INSUFFICIENT
Final Answer:
GMAT assassins aren't born, they're made,
Rich