Question

Read the following conjecture.

Any number that is divisible by 4 is also divisible by 8.

Find a counterexample to show that the conjecture is false.

A) 24
B) 26
C) 12
D) 40

Answer 1

Any number is divisible by 4, if the last 2 digits are divisible by 4,

Any number is divisible by 8, if the last 3 digits are divisible by 8, unless the last 2 digits are a multiple of 8

Answer 2

Option C 12

Explanation:

Given is one conjecture that

Any number divisible by 4 is also divisible by 8

Let x be the number

Since x is divisible by 4, x is of the form 4m for some integer m.

x=4m

If m is odd, then we find that x cannot be divisible by 8, since m is not divisible by 2.

If m is even, then x can be divisible by 8

Hence the conjecture is any number which is an odd multiple of 4.

Example 12

12 = 4x3

Since 3 is odd 12 though multiple of 4 cannot be multiple of 8.