Conditional Reasoning Practice: Test Your Skills

Well before I explain the answer, consider this. In Wason’s original 1977 study, which has come to be one of the most common tests of logical reasoning in the world of experimental psychology, not even 10% of respondents answered correctly. Similarly discouraging results were obtained in a 1993 follow-up.^{[1] [2]}

Still think you’ve got it?

The Answer

The answer is that you need to turn over exactly two cards: THE NUMBER 8, and THE COLOR ORANGE.

Those are the only two cards that can tell you anything about the rule, “if even, then red”. I’ll show you why. Let’s take each card individually and consider what might happen when we flip it.

The 3

On the other side of this odd-numbered card is either the color red, or some other color. So what if we see red? What have we learned about our rule, “even –> red”? Nothing! Odd numbers, like 3, can be paired with red and our rule could be broken. But odds can also be paired with red and our rule could be true. It simply tells you nothing. Believing that it does is to fall victim to a Mistaken Negation interpretation of the original rule, where you assumed not having an even (so having an odd) meant you couldn’t have a red. We only know about reds going with evens. Reds going with odds is entirely irrelevant.

The proper analysis is that when you don’t have your sufficient condition, an even, you can’t know anything about the necessary, red. So an odd number like 3 never starts our conditional linkage, and leads us nowhere.

Similarly, what do we learn if we see not-red, like orange or blue? Nothing, once more. Odd-numbered cards can be any color without consequence to our rule. Odds simply don’t matter.

The 8

Again, flipping over the 8 could reveal either red or not-red. If we see red, the rule holds true at that point—although be careful; it hasn’t been proven, it’s only been met!—but what if we see some other color? Then we’ve broken the rule and shown that it’s untrue. Remember, the rule says an even needs red!

So turning over the 8, or any other even-numbered card, would be required. Those cards have the potential to disprove the rule by revealing a non-red color. If we start our conditional with an even and don’t arrive at our required red, the rule falls apart.

The Red

When we turn over a colored card we’ll find a number, either even or odd. As noted above, “positive, whole” rules out zero and fractions. If we see an even, great! The rule’s been met, although, as before, NOT confirmed.

And if we see an odd? Well just like with the 3, red isn’t restricted by the rule to evens, any more than odds are restricted by the rule to non-reds! So a red with an odd tells you absolutely zilch. Believing that it does is to fall victim to a Mistaken Reversal interpretation of the original rule, where you assumed red told you (required) an even. That’s against your arrow, and must always be avoided when making conditional inferences.

The Orange

Our final card, and you need to flip it. Why? Because, like the 8 (even) it has the potential to invalidate our rule. If you turn a not-red card and see an even number, then a rule stating all evens are red is clearly not true.

This is the principle of Contrapositives, where losing the necessary condition (having a non-red color, here) means you cannot have the sufficient, an even. So having the sufficient—seeing an “orange/4,” say—would show the rule’s relationship can be broken, and the rule itself is therefore false.

Well, how’d you do? If you struggled or fell victim to one (or both) of the mistakes I described, don’t be too hard on yourself. Again, over 90% of people have traditionally answered incorrectly. But hopefully with the explanations above you can see the logic that underlies this process, and how a solid understanding of conditional reasoning can take you incredibly far when deconstructing the LSAT.

Just how far?

Conditional reasoning is an extremely common concept on the exam. It appears on average in around 15% of Logical Reasoning questions, and approximately 30% of Logic Games. So needless to say it’s critical that you master it before test day. As promised, here are some resources to help you do just that:

Conditional Reasoning Resources

• An amazing, and amazingly extensive, discussion of conditional reasoning diagramming by Dave Killoran.
• Another analysis of conditional diagramming by Dave.
• A thoughtful exploration of just how frequently conditional reasoning appears on the LSAT.
• One more from Dave Killoran, this time breaking down the relationship between contrapositives and circular reasoning.
• An article in our Free Help Area to assist you when dealing with multiple sufficient and necessary conditions.
• A site dedicated to psychology/logic experiments where you can practice Wason Selection Task scenarios further.

Conditional reasoning tends to be a universally challenging concept at first, but with time and practice and the right resources, it can absolutely be conquered. Get to it!