We had a rough weekend. What should have been a relaxing weekend away was hampered by my wife becoming extremely ill on Saturday night. After a long, slow, traffic-filled car ride home on Sunday, my 11-month old son had a very difficult night of illness. I was recounting the story to my mom and she declared “It’s contagious then.”
My mom’s reasoning follows a version of Occam’s Razor, which states that with competing hypotheses in play, you should choose the one that requires the fewest assumptions. In this situation (one person gets sick then another person gets sick) a contagious bug is the most likely solution. But it’s likely, not certain.
My son’s sickness could have been the result of a long car ride, or a hot day, or some completely unrelated bug. Those aren’t likely solutions, but they are possible. When you’re working on data sufficiency, it’s very important to remember that distinction.
Imagine a problem where you’re asked to determine whether some value is even. Maybe the first three values you check yield 2, 4 and 8 respectively. At that point you can conclude that it’s likely the value will always be even (and given limited time you may just need to select that answer). However, you don’t KNOW the value will always be even. Here are some things to keep in mind:
1. Test fractional values- Positive fractional values get smaller when squared. That’s a unique property that can yield different results and help you find that a statement is insufficient.
2. Test negative values- Don’t forget about the negatives! They often produce different results.
3. Test 0- Zeroes are not only useful to check, they’re usually very easy to calculate!
4. Test 1- Just like 0, ones are easy to plug in and have several properties that can help give you different results.
Remember, just because something is probably true, doesn’t mean it must be true and testing different kids of numbers can help you strengthen your hypothesis.