In a previous post I discussed the tendency that people have to “go on a hunch” on Data Sufficiency questions. This is a big no-no because DS questions are designed to punish people for making unwarranted assumptions. Generally speaking it is best to try to prove what you think to be true on Data Sufficiency. Nevertheless, there are some cases in which it would not be wise to go that far, cases in which it might be better to make a good educated guess rather than spend a lot of time proving out your hunches.
The Problem That Most People Have: Not Pushing the Statements Far Enough
The problem that most people have on Data Sufficiency is that they don’t realize how far they need to go to prove the statements to be sufficient or not sufficient. Test takers are often satisfied with thinking that a statement is sufficient or not sufficient even though they are not really that sure. But as I often tell the people that I tutor, when you are 80% sure on Data Sufficiency that really means that you have about a 50% chance of getting the question right. That is because the statements are designed to appear one way when in fact they are the opposite (i.e, they appear to be sufficient when in fact they are not). So generally speaking you should push the statements further until you reach near 100% certainty on your judgment (see my post about “going on a hunch” for more about how to “prove” the statements are what you think they are).
The Crucial Decision Point
Yet there are cases in which it might be better to not spend the time to reach that higher level of certainty. Essentially there are 2 factors that you need to consider when you are evaluating a statement and deciding how far to go. You need to weigh your level of certainty against the amount of time that it would take to reach a higher level of certainty. For example, if you are close to 100% certain that a statement is sufficient and if it would take another 2 minutes to prove that it is sufficient, it would probably be best to take the educated guess that you have and not spend the extra 2 minutes. If, on the other hand, you are 75% sure and it would only take an additional 30 seconds to be more certain, that is an easy decision: spend the extra 30 seconds.
An Example
Let me give some examples of both sides of that decision process. I am going to use a question that I used before in another post because it so perfectly illustrates how this decision making process should unfold. Consider the first example:
In the above question, the statements don’t appear to be sufficient individually at first glance. Statement 2 definitely cannot be sufficient because without knowing what k is there would be no way to know what the remainder is since essentially we would be free to add whatever we want to 3^22 and could therefore change the remainder. Therefore we can say with certainty that statement 2 cannot be sufficient. Most people look at statement 1 and think the same thing: if we don’t know anything about n, we cannot answer the question. There are 2 things, however, that should give you pause. First, n is related to the exponent and is not just a number that we are adding on to the 3^(4n+2) so it could be that there is some pattern in what results when you take 3 to different exponents. The other thing is that if you conclude that statement 1 is also not sufficient, you would end up at answer choice C, which seems suspiciously obvious in this case. Of course if we know the value of n and k we will be able to answer the question. That is almost certainly too straightforward for a Data Sufficiency question.
So at this point you would find yourself at an important decision point, one that presents itself on many DS questions. The answer could possibly be C, though that is unlikely. The only plausible alternative, given that we know that statement 2 is definitely not sufficient, is that the answer could be A. Now, here is where you need to think about the amount of time it would take to prove that statement 1 is sufficient or not and weigh that against how certain you are about what the answer is on this question. If you were really unsure and if you thought you could work out very quickly whether there is a pattern with statement 1 such that it would be sufficient, then it might be worth doing that. However, if you feel really confident that the answer cannot be C and that choice A is the only plausible alternative and if you further realize that it will take you a very long time to prove that statement 1 is sufficient, it would probably be better to just guess A and move on. The answer in the end is A.
Another Example
Lets take a look at another example, one that will illustrate the other way that this decision process can unfold. Again this is a question I have used in other posts:
Tom, Jane, and Sue each purchased a new house. The average (arithmetic mean) price of the three houses was $120,000. What was the median price of the three houses?
(1) The price of Tom’s house was $110,000
(2) The price of Jane’s house was $120,000
On this question most people blow through statements 1 and 2, believing them each to be not sufficient and then come to choice C. But again, just like the last question, choice C seems deceptively easy. Of course knowing 2 of the home prices and the average would be enough to calculate the third and therefore the median. Again we face this all important decision point. How certain are we and how long would it take to achieve a higher level of certainty? Well in this case it really doesn’t take too long to test out numbers and see if we can indeed get more than 1 median. On statement 1 we can, and so most people then assume that statement 2 is also not sufficient since it seems to provide the exact same type of evidence as statement 1.
But again, how certain are we and how long would it take to become more certain? Most people are pretty sure in this case that statement 2 is not sufficient, but again it would not take very long to test numbers to see if we can get 2 different medians. If it takes an extra 30 to 45 seconds to be completely certain, that is probably worth it. Consider that if you don’t spend that extra 30-45 seconds and get the question wrong then you have wasted much more than 30-45 seconds. So again, if you are not close to 100% certain and if it wouldn’t take that long to be more certain, it is worth spending the time. In this case you would be rewarded for pushing statement 2 because it actually is sufficient, much to most people’s surprise.
Conclusions
To summarize, it is important on the one hand to push the statements and try to arrive at an answer with a very high degree of certainty. “Thinking” that a statement is sufficient or not sufficient is just not enough on Data Sufficiency since things so often turn out to be contrary to expectation. That said, there is an important decision point that comes on every DS question when you must ask yourself, “how certain am I and how much time would it take to become significantly more certain?” If you are almost 100% certain and achieving a higher level of certainty would take a long time, it is probably best to go with your gut and move on. But if you are not nearly as certain and if it would not take that much time to achieve a higher level of certainty then you should probably spend the time to really prove what you think to be true.