# Data Sufficiency

## The SBC GMAT Files

Fear Not Data Sufficiency; Think As A Test Writer

One of the most feared question types on the GMAT, Data Sufficiency provides a wide array of traps and pitfalls to trick the test-taker into choosing the wrong answer. Part of the difficulty stems from a common misconception, the seeds of which are planted right at the beginning – the instructions.

The data sufficiency instructions in the Official guide (12th ed, p. 272) include the following note:

In data sufficiency questions that ask for the value of a commodity, the data given in the statements are sufficient only when it is possible to determine exactly one numerical value for quantity.

Pretty straightforward, right? This piece tends to stick in test taker’s mind, but the long and wordy sentence above is usually paraphrased as a much shorter and effective “need to find a single value for x.” Which, as it happens, is not always exactly the same thing. The crafty people who write DS questions are well aware of this very human tendency to sacrifice accuracy for grey cell storage space, so they come up with something like this official guide question:

What is the value of |x|?
(1) x = -|x|
(2) x2 = 4

The first statement is a timed underwater aquatic mine designed to take out your brain’s early-warning sonar systems. Trying to solve for x is meaningless here, and will only serve to confuse – there are numerous values of x that will satisfy this equation. The one thing you CAN learn from (1) is that x must be negative: the absolute value of x is positive or zero, so -|x| must be negative or zero. We then get that x = something negative or zero. That’s great, but it’s not sufficient to answer the question.

After the shock waves of stat. (1) have died down, we quickly move to stat. (2):   x2 = 4 means that x can equal either 2 or -2, which is insufficient since x has more than one value. Ah, but wait! stat. (1) then limits us to the negative value of x = -2, so the combination is sufficient and the answer is C, right?

Or so the question writer would have us believe.

This question uses the classic trope of trying to make the solver forget what the question asked in the first place. The above analysis would be perfectly correct if the question had asked for the value of x: only the combination of the statements limits x to a single value, as the instructions require. However, the question actually asked for the value of |x|, not x itself; an absolute value is always non-negative, regardless of whether x itself is positive or negative. Thus, both x = 2 and x = -2 actually give a single value of 2 for the quantity required by the question:  |2| = |-2| = 2, so stat. (2) is actually sufficient to answer the question with a single value on its own.