Common Data Sufficiency Mistakes-Part II

Welcome to part two of a three-part series on common mistakes that students make when answering GMAT Data Sufficiency questions.

In this article, we’ll examine mistakes related to assumptions about number classifications.

Mistake #1 - Assuming that values are integers

Consider this partial/rudimentary question:

What is the value of x?

(1) 5 < x < 7

If we assume that x is an integer, then we’ll incorrectly conclude that x must equal 6, and that statement 1 is sufficient. However, since there’s no reason to assume that x is an integer, it’s also possible that x = 5.5 or x = 6.2345, which means statement 1 is insufficient.

On a similar note, if you’re told that 3k is an odd integer, you cannot then assume k is an odd integer. For example, k could equal 1/3, in which case is it definitely not an odd integer.

So, unless you’re specifically told that a certain value is an integer, don’t assume that it is one.

Mistake #2 - Assuming that values are non-integers

To set this up, try this question:

What is the population of Townville?

(1) The population is greater than 5 but less than 180

(2) 17% of Townville’s population works at the local mill

Clearly, statements 1 and 2 are insufficient on their own, but are the combined statements sufficient?

Yes.

Here’s why. Let T = the population of Townville. Since 17% of the population works at the mill, then we can write: (17/100)T = the number of mill workers.

At this point, it would seem that there are several possible values for T. However, since we’re talking about humans, the number of mill workers must be a positive integer. So, for example, Townville’s population cannot equal 10, since 17% of 10 is 1.7, which would mean that 1.7 people work at the mill.

So, the population, T, must be such that 17% of T equals a positive integer. Since statement 1 states that the population is greater than 5 and less than 180, we can be certain that the population must be 100, since this is the only population that will yield an integer value for the number of mill workers. So, the two statement combined are sufficient, and the answer is C.

Notice that how that last question differs from this question:

What is the volume of liquid in Gary’s glass?

(1) The volume is greater than 5 ml and less than 180 ml

(2) 17% of the liquid is alcohol

In this case, the volume of liquid need not be an integer. So, the two statement combined are insufficient, and the answer is E.

So, watch out for situations in which integer values are implied, and situations in which integer values are not implied.

Mistake #3 - Assuming that values can be negative

To set this up, try this partial question:

If N people visited Maltania in 2009, what is the value of N?

(1) N^2 – N – 72 = 0

Many students will recognize that this equation will yield two different values for N. However, before we conclude that statement 1 is insufficient, we should actually solve it for N.

Start with N^2 – N – 72 = 0

Factor to get (N – 9) (N + 8) = 0

So, N = 9 or N = -8

Since N must be a positive integer, we can eliminate the possibility that N = -8, which means N must equal 9. So, statement 1 is sufficient.

So, the important takeaway in all of this is that we must be careful about the assumptions we make about unknown values when answering Data Sufficiency questions. 

Now it’s time to test your skills. Try answering the following questions:

http://www.beatthegmat.com/qr-49-how-many-integers-n-are-there-such-that-r-n-s-t132406.html  

http://www.beatthegmat.com/k-a-positive-t118782.html

http://www.beatthegmat.com/confused-on-the-solutions-given-in-og-13-t179210.html