Logical thinking on the GMAT and the Wason selection test

Logical thinking on the GMAT brings great returns. How good is your logical thinking?

Situation: In a deck of cards, any card has a letter on one side and a number on the other. The rule is that if a card has X one side then it has a 2 on the other side.

Question: What is the minimum number of cards you must turn to verify that rule?

The answer choices are:

A. Card X only

B. Cards X and 2

C. Cards X and 5

D. Cards X, 2, and 5

E. All cards

The answer is:

C. Cards X and 5.

This may seem counterintuitive but in fact is logically the correct answer.

A common response is B: Cards X and 2.

Remember however that the rule is that ‘if X then 2’, and not ‘if 2 then X’. An equivalent but more familiar argument is the following: if I am in Barcelona then I am in Europe. However, that does not mean that if I am in Europe I am in Barcelona. From this, we can conclude that turning card X is indeed necessary to prove the rule, but not turning card 2.

The trickier part is why we have to turn the card with the number 5 on it. Note that the question asks us for the movements we need to make to prove the statement ‘if X then 2’ given that every card has a letter on one side and a number on the other. What if we turn card 5 and find the letter X on it? Then the rule ‘if X then 2’ is false.

Hence, we must turn the card with number 5 on it to prove the rule.

This question is based on the Wason Selection test that is designed to test your logical thinking. The relevance to logical thinking on the GMAT is obvious. On a very abstract level, the Quant section tests logical thinking. The critical reasoning section is also a test of logical thinking, especially analysis of arguments and assumption questions. The good news is that logic is learnable skill. Remember to turn it on and improve it.

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