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GMAT Data Sufficiency: Small Details In The Question Stem

When doing a GMAT Data Sufficiency problem, it is easy to miss important information provided by the the question stem. Many students immediately go to work on the two statements, without making note of critical facts in the question itself. This rush can lead you down the wrong path, since the stem often gives crucial information about variables.

On data sufficiency, you are often ‘testing values’ or ‘picking numbers’ to see whether a statement is sufficient. There are a few crucial details to keep in mind when testing values:

1) Can the variable be positive, negative, or zero?

2) Is the variable restricted to integers, or can it be a decimal or a fraction?

3) Are you given the relationship between two variables (such as ‘consecutive’ or ‘consecutive even’)?

Some of the harder questions on the GMAT test your ability to note these small details. Consider the following problem (from Official Guide to the GMAT, Quantitative, 2nd Edition):

How many integers n are there such that r < n < s ?

(1) s – r = 5
(2) r and s are not integers

(take a moment and solve this problem – answer and discussion below)

I’d evaluate the statements using a table to test different values. Evaluating statement 1, you might write down

[table id=2 /]

The table shows a pattern – there’s always 4 numbers such that r < n < s. Thus statement 1 is Sufficient.

Evaluating statement 2, we have no idea of the value of r and s, so there could be any number of integers between them. So statement 2 is insufficient, and the answer is A.

…or is it?

If you think about it carefully, you may see that we neglected to test non-integer values for Statement 1. If we do include non-integer values for this statement, we see the number of integers between r and s could be either 4 or 5. Thus, statement 1 is Insufficient. See below:

[table id=3 /]

Now taking the statements together, we know that the difference between r and s is 5, and we know that r and s are not integers. Thus, there can only be 5 integers between the two variables, and the correct answer is C.

In the rush to solve a Data Sufficiency problem, the importance of small details in the Question Stem is often overlooked. This example shows the necessity of paying careful attention to these details. In particular, note key words like ‘integers’ and information about the variable’s range (whether it can be positive, negative, or zero).

– Matt,