Question

You are a math teacher who gives your students this problem to solve. If x is divisible by 8, then it is divisible by 6. This statement is False if x equals _________________.

a) 12
b) 24
c) 48
d) 36

Answer 1

The statement is logically flawed, as all provided options are divisible by both 8 and 6, making the question inaccurate. A correct counterexample not listed would be 32.

Step-by-step explanation:

The statement 'If x is divisible by 8, then it is divisible by 6' is false if we find a number that is divisible by 8 but not by 6. Among the options given, 12 (a), 24 (b), 48 (c), and 36 (d), the correct answer would be 48. While 48 is divisible by 8 (48 ÷ 8 = 6), it is not divisible by 6 without a remainder (48 ÷ 6 = 8 with no remainder, therefore it is divisible by 6). Thus, the given options were checked incorrectly; each of them is divisible by both 8 and 6. The statement in question itself is logically flawed. For a counterexample, we could use a number like 32, which is divisible by 8 but not divisible by 6.