5
QuizMultiple Choice

Logic and Reasoning — Quiz

Question 5 • MASTER COURSE Geometry

Galen wrote the statement "If the sum of the digits in a number is divisible by 3, the original number is divisible by 3." Which statements are true regarding his work? Choose three correct answers.

Answer
A
The conclusion of the statement is written before the hypothesis.
B
An equivalent statement is "If the sum of the digits in a number is divisible by 3, then the original number is divisible by 3."
C
The hypothesis of the statement is "the sum of the digits in a number is divisible by 3."
D
The statement is not a conditional statement because it does not include both an "if" and a "then" clause.
E
The statement can be proven true or false.

Explanation

The statement has the conditional form “If P, then Q”: P is “the sum of the digits in a number is divisible by 3,” and Q is “the original number is divisible by 3.” Adding “then” makes the wording in choice B equivalent, and choice C correctly identifies the hypothesis P. The claim can be checked mathematically, so it can be proven true or false, as choice E says. The conclusion does not come first, and a conditional can be understood even when “then” is omitted.

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