If a and b are odd inetegers, which of the following is necessarily true ?
a) ab is even.
b) ab(a-1)(b-1) is divisible by 8.
c) ab(a+1)(b+1) is divisible by 8.
d) a^2 - B^2 is divisible by 8.
e) a^2b is divisible by 3.
Integer
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This about number properties - specifically even/odd which is often best tested by pluggin in numbers when you don't knwo the rule. But this question is badly written because if you plug in 1 for each of the answers you see that none of them have to be true. Even if you assume the question says if a and b are distinct odd integers then you have to make them different and you see that if you plug in 1 and -1 they are all false - can you give me the source of the question?
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problems says which option is necessarily true.
so if we look at answer choices then except D other may or may not be true.
So i think option D is correct one.
options:
A) is false as ab will always be odd
B) in ab(a-1)(b-1), there are two even numbers and to be divisible by 8 there has to be at
least 3 even nmbers( three 2's), so this may or may not be correct
C) similar reasoning as B , this may or may not be correct.
D) is correct, always divisible by 8
E) similar reasoning as B & C.
so if we look at answer choices then except D other may or may not be true.
So i think option D is correct one.
options:
A) is false as ab will always be odd
B) in ab(a-1)(b-1), there are two even numbers and to be divisible by 8 there has to be at
least 3 even nmbers( three 2's), so this may or may not be correct
C) similar reasoning as B , this may or may not be correct.
D) is correct, always divisible by 8
E) similar reasoning as B & C.