If a, b, and c are integer and ab + c is odd, which of the m

Question

If a, b, and c are integer and ab + c is odd, which of the must be true?

I. a + c is odd
II. b + c is odd
III. abc is even

(A) I only
(B) II only
(C) III only
(D) I and III only
(E) II and III only

I understand the reasoning behind the correct answer, but the MGMAT book's solution also uses a graph which I cannot understand (please see attached file). Can someone explain why under both a and b in the row for two, it is listed as Odd, and then Even for the c column? The book doesn't explain how it sets up the graph.

Thanks

Bunuel · Accepted Answer

They've listed all possible scenarios for a, b, and c. As each of them can be either even or odd (2 option for each) then there are total of 2*2*2=8 scenarios possible. Then they evaluated each, to see which scenario makes ab+c odd and after that picked these scenarios to work with options I, II, and III.

Personally I'd approach this question in another way. 
 ab+c=odd , means:
1.  ab=even  (which means that  at least one  of them is even) and  c=odd ;
OR:
2.  ab=odd  (which means that both are odd) and  c=even .

We can see that in both cases at least one is even thus option III ( abc=even ) is always true.

Now, for I: if  c=odd  (case 1) and  a=odd  (so  b=even ) then  a+c=even
eq{odd} , so this option is not always true.

Exactly the same for option II: if  c=odd  (case 1) and  b=odd  (so  a=even ) then  b+c=even
eq{odd} , so this option is not always true.

Answer: C (III only).

Hope it's clear.

rdevorse · Answer

Ahhh, ok. Clearly, I missed the word "Scenario" on the top left corner lol. Now it makes sense. I do prefer your method. Thanks so much

BDSunDevil · Answer

why are we not considering 0 for c?

Bunuel · Answer

If  c=0=even  then  abc=0=even , so III holds true for this particular value of  c  as well.

abhinaya · Answer

Hi guys,
Can we just do this by substituting,
like I take say a=1,b=2 and c= 3 which gives ab+c = 5 , holds true for b+c is odd and abc is odd
Secondly a=2,b=5 and c=7 gives ab+c=17, holds true for a+c is odd and abc is odd.
Considering both we come to a conclusion that abc is odd alone.
Hope that helps!

bumpbot · Answer

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If a, b, and c are integer and ab + c is odd, which of the m

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If a, b, and c are integer and ab + c is odd, which of the m

Prep Toolkit

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