As you will find out from this video from the new GMAT tutorial series produced by PrepAdviser and examPAL, Data Sufficiency questions always follow the same format. We are given an opening statement in the form of:
“Knowing that [something] is true, are the following statements enough to tell [something else]?” Then we are given two separate statements, numbered one and two.
Here is an example:
If x is an integer, is (x+1) divided by x an integer?
So, what do we have here?
X is an integer – that is the information we know is true.
Is (x+ 1)/x an integer? That is what we are asked if we can or cannot tell, given the following statements.
Then we are given two different statements. Statement 1 gives a piece of information – 2/x is an integer, and statement 2 gives a different piece – x is a positive even integer.
We are then given five answer choices:
Their phrasing is a bit long, but fortunately it is always the same, so we can easily memorize them:
A - The first statement ALONE is sufficient to answer the question.
B - The second statement ALONE is sufficient.
C - Combined: Both statements must be combined in order for us to have enough information to answer the question.
D - Divided: Each statement, on its own, gives us sufficient information to answer the question. Statement 1 is enough on its own and statement 2 is also enough on its own.
E - Impossible: The data given, even when combined, is insufficient to solve the question.
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Now, the most common mistake people make in Data Sufficiency questions is over-solving – actually solving the question. We never have to do this! Data Sufficiency never asks us to solve a question, but rather it always shows us a question and asks: can it be solved?
For this reason, we always want to start by taking a logical approach: looking at the question and trying to figure out what types of things we can tell given this kind of information.
If we cannot see any logic, we can always go for an alternative approach and try and use numbers instead of variables to solve the question. In this case, our aim is to look for two different cases that result in contradictory answers – which means that the data is insufficient.
And if the given data is not in its simplest form, we may use the precise approach of looking for a specific rule or an algebraic simplification that will make it easier to figure out the logic behind the question.
So, returning to the example, let’s see how we can solve it logically:
Let’s look at (1): 2/x is an integer. This means x could be 1, 2 or -2 – not enough information to choose between them! Let’s cross out (A) and (D).
Now let’s look at (2) on its own: x is a positive even integer. If x is even, then x+1 is definitely odd. So, x+1/x is odd/even – this cannot be an integer, which answers our question. So (2) is sufficient to answer on its own – the answer is B.
Let’s look at another example:
If ab=64, is a larger than 8?
Using the logical approach, we will start by looking at statement 1: b is smaller than 8, and larger than 0. First of all, knowing b is positive tells us that a must be positive as well in order for a times b to equal 64. Second, when we get ranges, it is often useful to use an extreme value in order to figure out the logic for the entire range: let’s pretend b=8. If that is the case, a will also be 8.
However, b is less than 8 – which means, logically, a has to be larger. This is our solution!
So statement 1 is sufficient, meaning we will cross out B, C, and E.
Now let’s look at statement 2: a^2 > 64. Now, we must remember to ignore the information in statement 1 and look at this on its own: if a^2 > 64, a definitely could be larger than 8 (9, 10, 100 all work) – but it could just as easily be -9.
Therefore, statement 2 is insufficient. We will eliminate D, and there we have it – A is our answer!
These were just two examples on some of the tactics we can use in Data Sufficiency. Hopefully, you got the taste of it.