Bunuel wrote:
If a and b are integers such that a + b = 5, which of the following is true?
I. The product of a and b is odd.
II. If a is odd, b is even.
III. If a is negative, b is positive.
A. I only
B. II only
C. I and II
D. II and III
E. I, II and III
Since our numbers our very small, we'll try picking different numbers instead of solving explicitly.
This is an Alternative approach.
We'll try easy value for a,b: first 0,5 then 1,4 and if we need another than 2,3 or -1, 6.
I. 0*5=0 so this is false.
II. if a = 5 then b = 0, so it is even. if a = 1 then b = 4, so it is even. If a = 3 then b = 2 so it is even.
Even if we're not sure why the statement is true, after 3 examples we should feel OK guessing that it is true.
(Additionally, trying these examples will hopefully have reminded us that odd - odd = even. This is the proof that II is true)
III. a = -1 --> b = 6. a = -2, b = 7.
At this point it should be clear that we've hit on a trend: making a smaller will only make b larger so it is definitely positive.
All in all, I is False, II is true, III is true
(D) is our answer.
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