Now that you've had an introduction to data sufficiency, we can start talking about how to approach these problems. And one of the central strategies revolves around eliminating answers. The data sufficiency answer format lends itself very well to eliminating answers. Now, first of all, it's very important to memorize the answer choices. This was something discussed in the previous video, but I want to emphasize it here. Read full transcript
It really is one of the keys to data sufficiency success, memorizing the five answer choices. So again, here are the five standard answer choices, and let me point out there's an interesting division here. I'll use color. Statements number, statements A, B, and D are what you might call the Alone statement.
The word, alone, appears in them. Statements C and E, you might call the Together statements. The word, together, appears in those. And so what do I mean by this? Well, the very first task on data sufficiency is to consider each statement alone by itself.
So, you consider statement number one alone, and then you leave it aside, and you consider statement number two alone. And by deciding on this statements, whether they are sufficient or not, often that leads you to choice A, B, or D. Only when you are in the situation that neither statement is sufficient by itself, then you have to put them together and figure out what happens when they're together.
So it's only after you figure out that that you can answer C or E. So C and E are some, in some sense, logically, they follow the processes that you're using to figure out choices A, B, and D. So let's see how this plays out. I realize that's all very abstract. We have, is x greater than 5.
That's our prompt question. Statement number one tells us that x equals 4. Well, if x equals 4, it's definitely not greater than 5. So that allows us to give a definitive answer to the prompt question. That's very not to confuse the prompt question with the sufficiency question. The prompt question is, is x greater than 5?
The answer is clearly no. The sufficiency question is, do we have enough information to give a definitive answer? Yes. We gave a definitive answer of no, so this is definitely a sufficient piece of information.
If statement number one is sufficient, well, that means that either A could be the answer or D could be the answer, depending on whether statement number two is sufficient. But it means immediately, we can eliminate B, C, and E. So let's think about this. First of all, this makes our job much easier.
When we go down to statement number two, all we have to determine, is statement number two by itself sufficient? That's the only thing we have, we would have to determine, and then we'd be done with the problem. Notice also, suppose statement number two were something that you found absolutely mathematically incomprehensible.
Suppose you had no clue what to do with statement number two. But you were at least able to figure out that statement number one was sufficient. Well, at this point, you'd be in a position to apply something called solution behavior. Solution behavior is when you guess after strategically eliminating some of the answer choices.
This is not the same as random guessing. When you randomly guess from five answer choices, on average you will not gain any ground. But if you can strategically eliminate answers and then guess from the remaining answers, that, that is something that on average will move you forward. So that's very important.
It's somewhat anti-intuitive, but it's very important to consider. That solution behavior, guessing once you eliminate answers, is actually something that is to your advantage. And data sufficiency is ideal for this, because making a decision about even one statement allows you to eliminate answers. Let's look at another scenario.
Suppose we have the same prompt question, is x greater than 5, statement number 1 says, x is greater than 2. Well, hm, something could be greater than 2, like, say 3, and still be less than 5. Or it could be greater than 2, like 7, and could be greater than 5. So in other words, consistent with this statement, we could answer the prompt statement either way.
And so that means that this statement by itself is not sufficient to give us an answer to the prompt question. So we know statement number one is not sufficient, immediately A can't be right and D can't be right, but the answer could be B, C, or E. So right away, just making this one decision allows us to eliminate two answer choices.
Let's look at this scenario. Here, statement number one will be something that either is too difficult, or we haven't looked at yet, or something like that. And I'll point out incidentally, if the two statements are wildly different in their lengths, they always make it the case that statement number one is the really long one, and statement number two is the short, easy one.
And for that reason, sometimes it's more advantageous to start with statement number two. So here we have the prompt question, does y equal 8? A very simple prompt question. Statement number two says y is less than 2. Well, if something is less than 2, it definitely does not equal 8.
So again, we have a definitive answer to the prompt question. A definitive answer of no. And that means the statement is sufficient, because we are able to produce a definitive answer. So this is a sufficient statement. If statement number two is sufficient, the answer could be B, the answer could be D, but choices A, C, and E are now out.
It is not possible for either one of, for any of those to be the correct answer. Let's look at another scenario. Here, same prompt question, does y equal 8? And now we have in statement number two, y is greater than 2. Well, again, a prompt, same problem as we encounter earlier. y could be greater than 2, y could be 3 or 4, or it could be 8, so it could equal 8 or it may not equal 8.
So this statement by itself is not sufficient. If statement number 2 is not sufficient, what does that mean? Well, B can't be the answer, and D can't be the answer. So the answer could be A, C, or E. Any of those could be the answer. So it's very important to appreciate, each piece of information you can determine about the sufficiency of either statement allows you to eliminate some of the answer choices.
And so, this is helpful as a strategic approach in answering them. You can eliminate as you go and narrow things down to one answer. And if you get stuck, even then, it's helpful, because you can use solution behavior. In other words, you have strategically eliminated some answers, and therefore, it is advantageous to guess from the remaining answers.