## Filling in Your Chart: A Data Sufficiency Primer

In last week’s post, I gave the following Data Sufficiency problem to be solved using a chart:

*A certain zoo has 288 mammals, 25 percent of which are female. What percent of the mammals in the zoo were born at the zoo?*

*(1) The number of male mammals that were born at the zoo is three times the number of female mammals who were not born at the zoo.*

*(2) The number of male mammals that were not born at the zoo is three times the number of male mammals that were born at the zoo.*

In that post, I mapped out exactly what the chart should look like:

Notice that I included not only each category, but also its total, which will end up being just as important. So once you have your chart, start filling it in appropriately.

The prompt tells us that there are 288 total animals, 25 percent of which are female. We are then asked what percent of the mammals are born at the zoo. Fill in all the information, and your chart should look like this:

Notice three very important things:

1. I used a question mark to very clearly denote the quantity I’m looking for — the TOTAL of the “Born” column.

2. I filled in EVERYTHING I could deduce from the given information. If I know that 25% of 288 is the female row, then 75% of 288 must be the male row. Don’t stop just because you’ve filled in everything mentioned! See if you can take things a step further.

3. This is Data Sufficiency; I don’t care what 25% of 288 is. I’m not going to waste time calculating it if I don’t need to. I’m more concerned that it is a DEFINITE QUANTITY, and thus I have a number for that box.

This brings up an interesting strategic point. If you really wanted to, you could just put a check mark (✓) in the box instead of “25% of 288″. That’s because you don’t care as much about the quantity itself; the most important thing is that SOME DEFINITE QUANTITY is in the box, and thus that box is accounted for.

If you follow that pattern, your chart would look like this:

Now let’s look at Statement 1. It says that the number of male mammals that were born at the zoo is three times the number of female mammals who were not born at the zoo. Okay, so we are given a ratio instead of some hard numbers. So how can we label the appropriate boxes? If you said variables, then you are right! If you represent the number of females not born at the zoo as *x*, then the male/born quantity will be *3x*. The end result should look like this:

Now, is this sufficient? Well no, because there’s no possible way to establish what quantity will replace the question mark. The chart makes this easy to see. Eliminate answer choices A and D.

So what about Statement 2? It says that the number of male mammals that were not born at the zoo is three times the number of male mammals that were born at the zoo. We can use the same process of assigning variables, but choose a different variable besides *x*, so we don’t get confused. You should get something like the following:

Is there anything we can deduce? Well yeah, because we have only one variable representing the male row. If we add y and 3y together, we get a definite number (as indicated by the check mark), so that means we can find y and thus the values in each of those boxes:

Is this sufficient? Well no, because there’s still no way to get a definite quantity for the question mark box.

Now we’ve narrowed down the answer choices to C and E. So which is it? Well… you tell me :).

I’ll leave the final step of combining the information to you guys, and you can leave an explanation in the comments. Good luck!