It is currently 27 Jun 2017, 02:21

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

Intern
Status: Beginner
Joined: 09 Jan 2012
Posts: 26
Location: United States (TX)
If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

### Show Tags

17 Jan 2012, 07:05
1
KUDOS
1
This post was
BOOKMARKED
00:00

Difficulty:

15% (low)

Question Stats:

80% (01:53) correct 20% (01:08) wrong based on 84 sessions

### HideShow timer Statistics

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

Attachments

screen-capture-117.jpg [ 57.2 KiB | Viewed 3192 times ]

_________________

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

Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

### Show Tags

17 Jan 2012, 07:33
3
KUDOS
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.
_________________
Intern
Status: Beginner
Joined: 09 Jan 2012
Posts: 26
Location: United States (TX)
Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

### Show Tags

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
_________________

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

Senior Manager
Joined: 13 May 2011
Posts: 307
WE 1: IT 1 Yr
WE 2: Supply Chain 5 Yrs
Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

### Show Tags

17 Jan 2012, 10:23
why are we not considering 0 for c?
Math Expert
Joined: 02 Sep 2009
Posts: 39709
Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

### Show Tags

17 Jan 2012, 16:16
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.
_________________
Intern
Joined: 27 Feb 2013
Posts: 4
Re: If a, b, and c are integer and ab + c is odd, which of the m [#permalink]

### Show Tags

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
Similar topics Replies Last post
Similar
Topics:
2 A, B, and C are consecutive odd integers such that A < B < C. 2 01 Jun 2017, 15:15
3 If A,B,C are three integers and AB+C is even ; which of the following 3 03 Aug 2016, 08:10
19 If a, b, c and d are positive integers and a/b < c/d, which 9 13 Sep 2016, 20:51
39 For integers a, b, and c, if ab = bc, then which of the foll 12 20 Jun 2017, 06:35
8 If a, b, c, and d are integers and ab2c3d4 > 0, which of the 5 30 Nov 2016, 01:44
Display posts from previous: Sort by