Winning The Data Sufficiency Game

by on September 17th, 2009

In many ways, Data Sufficiency is like a high-stakes poker game.  The key to winning is to guess what your opponents want you to do – and do the exact opposite.  In this case, your opponents are the GMAT test writers, and by understanding a few of the bluffs and scams they try to run on you, you can guess the right answer on a Data Sufficiency question – even if you actually have no idea how to solve the problem. Here are a few of their favorite set-ups:

1. The Old One-Two

One of the test writers’ favorite tricks is to hit you with one easy statement and one hard one.  Here’s an example:

What is the probability that a randomly chosen resident of Town X is female?

1) Town X has 10,000 male residents and 15,000 female residents.

2) If the number of male residents of Town X were to increase by 20%, the number of male residents of Town X would be 80% of the number of female residents of Town X.

Statement 1 is obviously sufficient to answer the question, but Statement 2 is confusing and intimidating.  The test writers are trying to get you to choose answer choice A – Statement 1 is sufficient, Statement 2 is not – and that’s exactly what most people will pick.  But a smart test-taker sees the trap and guesses that there probably is a way to answer the question using Statement 2 alone, and chooses D – each statement alone is sufficient – the correct answer.

The lesson here is simple:

  • When you are faced with one easy statement that obviously answers the question, and one complicated statement, the complicated statement probably works, and the answer is probably D.

Wondering how to answer the question using Statement 2 alone? An explanation appears at the end of this article.  But even if you didn’t see how to solve the problem with Statement 2 alone, smart guessing can still lead you to the right answer.

2. Too Much Information

Often, the test writers will try to trick you into thinking you need more information than you really do.  Here’s an example:

If b does not equal 0, what is the value of {4a}/{3b}?

1) a = b + 2

2) a = 2b

You may have learned that when you have two variables, you need two equations to solve.  For that reason, most people will choose C – neither statement alone is sufficient, but both statements together are sufficient – thinking that by using both equations, they can solve for both variables, and then use those numbers to answer the question.  But C is only an option if neither statement works alone.  In this case, statement 2 alone will actually answer the question.  Try dividing both sides of statement 2 by b.

You’ll get a/b = 2

Then multiply both sides by 4/3 and you get {4a}/{3b} = 8/3

Since the question asked for the value of {4a}/{3b}, you now have enough information to answer the question – even though you don’t actually know the value of a or b.  So the correct answer is B.

The lesson here is:

  • When the question involves 2 variables, and asks for some combination of the two variables, you can usually answer the question without solving for the individual variables.

Try just manipulating the statements to transform them into whatever the question is asking for.  Chances are that one of the two statements ALONE will be sufficient, and the answer will be A or B.

3. The Useless Statement

Sometimes, one of the two statements just doesn’t matter.  Here’s an example:

If x^2 does not equal 1, does x^2+1 = a/{x^2 - 1} ?

1) x^4 = a+1

2) x<0

On a complicated question like this one, most people will fall into one of two traps: they’ll either choose C (neither statement alone is sufficient, but both together are sufficient) because they figure they need as much information as possible, or E (both statements together are insufficient) because they simply can’t see any way to solve the problem.  But some good guessing strategy can actually lead you to the right answer.

Take a look at statement 2 for a moment.  It tells us that x is a negative number.  But since all the equations we’re given involve x^2 or x^4, is it going to make any difference whether x is positive or negative? No, because whether x is positive or negative, x^2 or x^4 will still be positive.  So Statement 2 adds no useful information at all.  This means that either statement 1 is going to work by itself (answer choice A,) or there’s no way to solve the problem (choice E.) Since we know most people will get scared and pick E, the smart guessers will go with A, reasoning that even though they can’t see how to solve the problem with that ugly equation, there just might be a way.  And they would be correct.  For an explanation, see below.

The lesson here is:

  • If one statement provides no useful information, the answer must be either that the other statement works alone (A or B,) or that the question cannot be answered (E.) And the more complicated the question looks, the less likely the answer is to be E.

Solutions for the first and third examples appear below, but if you read these solutions and think “I never would come up with that on my own,” that’s OK!  The key is to learn to guess smart when you’re not sure how to solve the problem.


Example One, Statement 1:

Remember that we’re being asked for the probability that resident of Town X is female.  To solve for a probability, you don’t need the actual numbers – a percentage, ratio, or fraction will work just fine. We can write an equation with statement 1, if m represents the males and f represents the females:

m + .2m = .8f

1.2m = .8f

Divide both sides by f and by 1.2, and you get:

m/f = .8/1.2 = 8/12 = 2/3

So the ratio of males to females is 2 to 3.  From there we can calculate the probability of choosing a male or a female.

Example Three, Statement 1:

Let’s try playing with the equation in the question:

x^2 + 1 = a/(x^2-1)

Multiplying both sides by (x^2-1) gives us (x^2 + 1) (x^2 - 1) = a

If we FOIL the left side, we get x^4 - 1 = a, and if we add 1 to both sides, we get x^4 = a + 1.  That’s identical to Statement 1.  Anytime the question can be manipulated to match the statement, or the statement can be manipulated to match the question, the statement is sufficient.


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