An important aspect to pay attention to with GMAT data sufficiency, is the constraints. When talking about constraints, I mean more than just x>0, but also the ones that are not as obvious. For example, if you are asked for a number of people, you know that it has to be an integer, because you can’t have ½ of a person. These constraints can sometimes make or break a problem. Take a look at these this example:
Bob had a planning committee meeting. The planning committee has 8 people on it and only planning committee members attended the meeting. How many people were at the meeting?
(I) Not all members of the planning committee attended this meeting.
(II) No more than one member of the committee was absent.
This problem is essentially asking you for the value of integer x and tells us that x is less than or equal to 8. (I) then tells us that x < 8 or we can be more specific and say that x is less than or equal to 7, because we know it has to be an integer less than 8. However, it is still insufficient, because it doesn’t tell us the exact number
(II) then tells us that x is greater than or equal to 7, because no more than 1 person was absent. Again this isn’t sufficient but it tells us that it has to be 7 or 8. Together, these two pieces of information tell us all we need to know. Essentially:
(I) 7 ≤ x
(II) x ≥ 7
The only option for x is then 7, so both together are sufficient. Had we not taken the time to think about the hidden constraint, we probably would have thought that the two pieces of information meant that,
8 > x > 7
Which is insufficient and would have led us to an incorrect answer.
As always, the GMAT will try to trick you by putting in subtle restraints, so it is always important to make note of them. Some ways they imply additional constraints are:
- Saying the number is an integer
- Making the numbers countable, which means they must be positive integers
- Any weight or height must be positive
- Any length is the side of a triangle square or the circumference of a circle must be positive
It is important to take note of both stated and implied restraints and utilize all of them, so that you are using as much of the information that you can.