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

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Intern
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Joined: 09 Jan 2012
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Location: United States (TX)
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If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

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17 Jan 2012, 07:05
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77% (01:57) correct 23% (01:08) wrong based on 74 sessions

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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
[Reveal] Spoiler: OA

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screen-capture-117.jpg [ 57.2 KiB | Viewed 2594 times ]

_________________

"Continuos effort - not strength or intelligence - is the key to unlocking our potential." - Winston Churchill

Math Expert
Joined: 02 Sep 2009
Posts: 32616
Followers: 5653

Kudos [?]: 68616 [3] , given: 9816

Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

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17 Jan 2012, 07:33
3
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Expert's post
rdevorse wrote:
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

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 $$a+c=even\neq{odd}$$, 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 $$b+c=even\neq{odd}$$, so this option is not always true.

Hope it's clear.
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Intern
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Joined: 09 Jan 2012
Posts: 26
Location: United States (TX)
Followers: 1

Kudos [?]: 11 [0], given: 3

Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

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17 Jan 2012, 07:37
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
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"Continuos effort - not strength or intelligence - is the key to unlocking our potential." - Winston Churchill

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Kudos [?]: 216 [0], given: 11

Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

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17 Jan 2012, 10:23
why are we not considering 0 for c?
Math Expert
Joined: 02 Sep 2009
Posts: 32616
Followers: 5653

Kudos [?]: 68616 [0], given: 9816

Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

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17 Jan 2012, 16:16
Expert's post
BDSunDevil wrote:
why are we not considering 0 for c?

If $$c=0=even$$ then $$abc=0=even$$, so III holds true for this particular value of $$c$$ as well.
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Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

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29 Apr 2013, 16:15
rdevorse wrote:
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

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!
Re: If a, b, and c are integer and ab + c is odd, which of the m   [#permalink] 29 Apr 2013, 16:15
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