Bunuel wrote:
Is a > bc?
(1) a/c > b
(2) c > 3
Kudos for a correct solution.
VERITAS PREP OFFICIAL SOLUTIONPlaying “middle school hearts”, many test-takers will run through this progression:
Step one: If you multiply both sides by c, you get a > bc so this looks sufficient*. The answer, then, would be A or D.
Step two: Forget everything you learned about statement 1 since you’ve already made your decision about it. Statement 2 is clearly insufficient on its own, so the answer must be A*.
(*we know the math here is slightly flawed; demonstration purposes only!)
But here’s how you’d play the game as an adult, or as a 700-level test-taker:
Step one: Same thing – if you multiply both sides by c you’ll get a > bc, so this one looks sufficient.
Step two: Wait a second – statement 2 is absolutely worthless. And statement one wasn’t *that* hard or interesting. Maybe the author of this question is “shooting the moon”…
Step three: Look at both statements together, reconsidering statement 1 by asking myself if statement 2 matters. If statement 2 is true and c is, say, 10, then a/10 > b would mean that a > 10b, so this still holds. But what if c is -10, and statement 2 is not true. a/(-10) > b would mean that when I multiply both sides by -10 I have to flip the sign, leaving a < -10b. This time it’s not true. Statement 2 *seems* worthless but in actuality it’s essential. Statement 1 is not sufficient alone; as it turns out I need statement 2.
What’s the difference between the two methodologies?
The 500-level, “middle school hearts” approach – NEVER consider the statements together unless they’re each insufficient alone – leaves you vulnerable to the author’s bait. On hard questions, authors love to shoot the moon…that’s their best chance of tricking savvy test-takers.
The 700-level, “playing hearts with grownups” approach seems counterintuitive, much like saving your king of hearts and knowingly accepting points in a hearts game would seem strange to a seventh-grader. But it’s important because it saves you from that bait. On a question like this, it’s easy to think that statement 1 is sufficient; abstract algebra is great at getting your mind away from numbers like negatives, zero, fractions… But statement 2′s worthlessness (ALONE) functions two ways: it’s a trap for the unsuspecting 500-level types, and it’s a reward for those who know how to play the game. That worthless statement 2 is akin to the author leading a high heart early in the game – the novice player sees it as a freebie; the expert considers “why did she do that?” and re-examines statement 1 by asking specifically “what if statement 2 weren’t true; would that change anything?”.
Remember, when you’re taking the GMAT you’re playing against other very-intelligent adults, and so the authors of these questions have a responsibility to “shoot the moon”. While the rules of the game dictate that you don’t want to consider the statements together until you’ve eliminated A, B, and D, there’s a caveat – if you have reason to believe that the author of the question is trying to trick you (which is very frequently the case on 600+ level questions), you have to consider what one statement might tell you about the other; you have to play the game.
I used your approach in the below question. if apply your approch in the below question, then i have to go for
for the question above.
But now you are coming with another approch. Which one is the right one? The one in the below question or the one in this question? Both question seem quite the same.