It’s all anyone can talk about today – LeBron James has decided to reverse “The Decision” and return home to play for Cleveland. In doing so he forced many people to change their minds.
Let’s take a look at some of those people:
-LeBron himself, who once decided to leave and now comes home as the prodigal son
-Cavaliers owner Dan Gilbert, who once wrote a scathing letter about James the week he left the Cavs for South Beach
-Cavaliers fans, who once burned LeBron’s jersey and rallied against him
-Dwayne Wade, who just last week opted out of a $40 million contract to restructure his deal to create space to attract more players to his and LeBron’s Heat team
-And hopefully you, in the way that you approach Data Sufficiency
What does that mean? Consider this question:
A Miami-based sporting goods store is selling LeBron James #6 jerseys at a deep “everything must go” discount. If each jersey sells for (not one, not two, not three, but…) four dollars, how much revenue did the store earn from the sale of discounted LeBron James jerseys on Friday?
(1) On Friday, the store sells 100 of the white jerseys LeBron wore for home games, and 80 of the black jerseys that LeBron wore for away games.
(2) On Friday, the store sold 50 of the red jerseys that LeBron wore for nationally-televised Sunday games.
After statement 1, you were probably thinking “sufficient” and taking your talents to A or D, right? “Home” and “Away” seem mutually exclusive, so shouldn’t that tell you that there were 180 jerseys sold total at $4/each? If you made The Decision to pick either A or D, you’re not alone…and you have a lot of reason to feel confident. But like LeBron has shown us, it’s never too late to change your mind. Statement 2 supplies information that *should* give you reason to change your mind about statement 1 – there’s a third type of jersey that the store sold, and so statement 1 didn’t tell the complete story. Statement 2 helps to prove that statement 1 actually wasn’t sufficient, allowing you to change your mind and reconsider your answer*.
(*This problem probably doesn’t have a valid solution since there’s no great way to tell mathematically if there might be a 4th type of jersey; this wouldn’t appear as a question on the actual test, but the logic of “statement 2 should prove to you that you didn’t know everything you thought you did on statement 1” is absolutely fair game)
The lesson, really, is this – although “the book” says that you should treat the statements as completely separate, wisdom will show you that often one statement will give you a clue about the other and allow you to change your mind. Typically this happens when:
-One statement is OBVIOUSLY not sufficient
-One statement is OBVIOUSLY sufficient
In either of these cases, that obvious piece of information will likely shed some light on what may be important for the other statement. For example:
Is a/b > c?
(1) a > bc
(2) b < 0
Here statement 1 may well look sufficient…but look how obviously unhelpful statement 2 is. Why is it there? To alert you to the fact that b could be negative – in which case you would have to flip the sign when dividing by b in statement 1:
Statement 1 when b is positive: a > bc becomes a/b > c (YES!)
Statement 2 when b is negative: a > bc becomes a/b < c (NO!)
So while you may have quickly made The Decision – in a youthful spirit of hubris – that statement 1 is sufficient, patience and maturity should lead you to reconsider after statement 2 offers useless-by-itself information that can only serve as a clue: maybe you should change your mind!
Such is the game of Data Sufficiency – much like in NBA Free Agency, hasty, youthful decisions can be reversed, and often on challenging questions the correct answer requires you to let “the other statement” convince you that you’ve made a mistake. So learn from LeBron – it’s okay to change your mind; maybe, in fact, that’s The Decision that’s correct.
By Brian Galvin