Beware of the “Unique occurences” on DS

How you should approach Data Sufficiency questions? Let us see the problem: What is the value of x? (1) x^2 = 25 (2) 8 < 2x < 12 You may quickly say “oh it’s 5” to both of them. 5 is the square root of 25, and the second equation simplifies to 4 < x < 6, and what number is between 4 and 6? It’s 5. Be prepared for a negative value of x (-5 satisfies Statement 1) and for nonintegers (x could be 4.00001 or 5.9999 given Statement 2). Knowing those contingencies, wisely recognize that you need both statements to guarantee one exact answer (5) for x. Keep these unique occurrences written down at the top of your paper on test day: Negative, Zero, Noninteger, Infinity, Biggest/Smallest Value. That way, you’ll always check for those unique situations before you submit your answer, and you’ll have a much better shot at a challenge-level problem like this: The product of consecutive integers a, b, c, and d is 5,040. What is the value of d? (1) d is prime (2) d < c < b < a   Searching for consecutive integers, you’ll likely factor 5,040 to 7, 8, 9, and 10 (the 10 is obvious because 5,040 ends in a 0, and then when you see that the rest is 504 and know that’s divisible by 9, and you’re just about done). And so with Statement 1, you’ll see that the only prime number in the bunch is 7, meaning that d = 7 and Statement 1 is sufficient. And Statement 2 seems to support that exact same conclusion – as the smallest of the 4 integers, d is, again, 7. Right? Enter notes: did you consider zero? (irrelevant) Did you consider nonintegers? (they specified integers, so irrelevant) Did you consider negative numbers? That’s the key. The four consecutive integers could be -10, -9, -8, and -7 meaning that d could also be -10. That wasn’t an option for Statement 1 (only positives are prime) and so since you did the “hard work” of factoring 5,040 and then finally got to where Statement 2 was helpful, there’s a high likelihood that you were ready to be finished and saw 7 as the only option for Statement 2. This is why  reminders are so helpful: on harder problems, the “special circumstances”, having taken a backseat to the larger challenges of math. Keep list handy at the top of your noteboard and you, will be prepared for all situations.