Q1.
2. If a number is divisible by 8, then 8 also divides any two numbers (separately) that add up to the number.
Answer
Sometimes true. The word that breaks it is any.
72 = 48 + 24 = 8 × 6 + 8 × 3 → both parts divisible by 8 ✓
72 = 50 + 22 → neither part divisible by 8 ✗
72 = 64 + 8 → both divisible by 8 ✓
72 = 70 + 2 → neither divisible by 8 ✗
72 = 50 + 22 → neither part divisible by 8 ✗
72 = 64 + 8 → both divisible by 8 ✓
72 = 70 + 2 → neither divisible by 8 ✗
Why it happens: a multiple of 8 can certainly be split as 8a + 8b, but it can also be split as p + q where p and q are anything at all — you just cut the pile wherever you like. Since some splits work and others do not, the statement is sometimes true.
Tip: a correct version does exist. If 8 divides the total and 8 divides one part, then 8 must divide the other part too — because the other part is (total – part), a difference of two multiples of 8.