GMAT Tip of the Week: Data Sufficiency the Smart(phone) Way

GMAT Tip of the WeekLet’s say you were in the market for some new technology, and let’s say your friend introduced you to a guy who sold used, refurbished gadgets at a huge discount. And let’s say he gave you this choice – you could buy:

A) An iPhone 5 for $50

or

B) A digital camera for $40

or

C) Both an iPhone 5 and a digital camera for $75

Now, you have a few tech goals in mind. You want to be able to send text messages, update Twitter, use Google maps on the go, and upload pictures to Facebook and Instagram. Which deal do you take?

You take the iPhone only deal for $50, right? Why don’t you take the camera too? That’s right – because option A already contains a digital camera! You don’t need to pay for another one. And because you know that the first option already gives you everything you need, you don’t pay for both products together. Agreed?

Well, that’s the game on many Data Sufficiency questions. Often times in a Data Sufficiency question one of the statements will already (but subtly) include the information from the other one. Which means, like in the case above, before you pick option C (both together) you’d better make sure you can’t do it with option A or option B alone. Here’s what we mean in a couple examples:

EXAMPLE 1:

Is 0 < x < 1 ?

(1) x^2 < x

(2) x > 0

In this case, many people pick option C, both together. But wait – you don’t want to buy a digital camera (the fact that x is positive) if your iPhone already has one. So let’s spend a little time playing with the features of that iPhone, or statement 1. Would a negative number even be possible given statement 1, or do we know already that x is positive? Try it: if x were to be -2, x^2 is 4…in that case x is not greater than x^2, so -2 wouldn’t work. And if x were -1/2, then x^2 is POSITIVE 1/4. Again, x is less than (not greater than) x^2. So neither a negative integer nor a negative fraction will work. Statement 1 already tells us that x is positive, so we don’t need to “buy” statement 2. It pays to take the time to – to continue the analogy – play with the features of the iPhone (statement 1) to see whether it already gives us the camera features we might want in statement 2.

Now let’s see a more advanced example.

EXAMPLE 2:

Julie is selling lemonades in two sizes, small and large. Small lemonades cost $0.52 and large lemonades cost $0.58. How many small lemonades did Julie sell?

(1) Julie sold a total of 9 lemonades.

(2) Julie’s total revenue from the sale of lemonades was $4.92

Now, by the time you take your GMAT you should be able to come up with formulas for these statements pretty quickly:

(1) S + L = 9

(2) .52S + .58L = 4.92

And you should really quickly recognize that with two variables and two equations, you’ll be able to solve for S with both statements together. But that’s a little too easy for a test like the GMAT – especially when there’s a hidden piece of information that you can add to those two statements. Julie can’t sell 2.75 small lemonades – the values of S and L must be integers. So that should give you pause – if you take both statements together you’re leaving important information on the table. So at this point it pays to see whether the iPhone (statement 2) already has a digital camera (statement 1) embedded in it. Remember – the GMAT is a business test…it will reward you for being efficient with resources and for maximizing your ROI. It’s foolish in business to pay $75 for two products when one would accomplish the task for $50; similarly, it’s foolish to blindly pick C in 30 seconds when there’s a decent chance that the answer could be B. And how can you tell? If it were, indeed, an iPhone, you could spend some time playing with it to see if it would do exactly what the camera would. And that’s the goal here.

You know that if you have the statement “S + L = 9″ you can pair that with statement 2 to solve for S. So try to see whether statement 2 includes that information by “borrowing” it. Could S + L be anything but 9? See if it can be 10:

If she sells 10 (the hypothetical) but still only makes $4.92 (what we know from statement 2) she’d have to sell cheaper lemonades to keep the revenue down, so let’s try all 10 at the cheapest price. That’s 10(.52) = 5.20, which is already too much. There’s no way she can sell 10 or more!!!

If she sells 8 (another hypothetical) but still brings home $4.92 (what we know from statement 2) she’d have to sell more expensive lemonades to make up for the fact that she’s selling fewer items. So let’s try 8 of the most expensive. That’s 8(.58) = 4.64, which isn’t enough. She can’t sell 8 or less, so we’ve just used statement 2 to prove that it already tells us the information from statement 1. Statement 2 is sufficient alone.

Now, this step is a little tricky for many, but look at what we just did – we had a hunch that we didn’t need to “buy” both statements because one might already have all the features of the other, like the iPhone with the built-in camera. So with those features in mind (S + L = 9) we set out to prove that the second statement included them, by “borrowing” them from statement 1. On tricky Data Sufficiency problems in which a trap answer like C in this case seems far too easy, this is an effective strategy to make sure you only pay for what you need. So keep this iPhone analogy in mind to maximize your statement efficiency on the GMAT; after all, at least for now, the GMAT won’t let you ask Siri.

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