SAT Math Multiple Choice Practice Question 349: Answer and Explanation

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Question: 349

19. If at least one wuzzle is grumpy, then some fuzzles are lumpy.

If the statement above is true, then which of the following must also be true?

A. If all wuzzles are grumpy, then all fuzzles are lumpy.
B. If no wuzzle is grumpy, then all fuzzles are lumpy.
C. If all fuzzles are lumpy, then all wuzzles are grumpy.
D. If no wuzzle is grumpy, then no fuzzle is lumpy.
E. If no fuzzle is lumpy, then no wuzzle is grumpy.

Correct Answer: E


E Any statement of the form "If A is true, then B is true" is logically equivalent to "If B is not true, then A is not true." Try this with some common-sense examples of such statements. For instance, saying "If I am under 16 years old, then I am not allowed to drive" is the same as saying "If I am allowed to drive, then I must not be under 16 years old." The statement in (E) is logically equivalent to the original.

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