Carcass wrote:
If the sum of two integers is 6, then it must be true that
(A) both integers are even
(B) both integers are odd
(C) both integers are positive
(D) if one integer is negative, the other is positive
(E) if one integer is positive, the other is negative
Kudos for the right answer and explanation
Another approach.
We're asked to find a statement that MUST be true. So, if we can find a case where a statement is false, we can ELIMINATE that answer choice.
(A) both integers are even
: it could be the case that the numbers are 1 and 5. ELIMINATE A(B) both integers are odd
: it could be the case that the numbers are 2 and 4. ELIMINATE B(C) both integers are positive
: it could be the case that the numbers are -1 and 7. ELIMINATE C(D) if one integer is negative, the other is positive : Can't think of a counterexample so KEEP D for now
(E) if one integer is positive, the other is negative
: it could be the case that the numbers are 1 and 5. ELIMINATE EBy the process of elimination, the correct answer is D
Cheers,
Brent