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Is A + B + C even?

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Is A + B + C even? [#permalink] New post 23 May 2010, 20:31
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

14% (01:45) correct 85% (01:55) wrong based on 14 sessions
Is A + B + C even?

(1) A - C - B is even

(2) (A - C)/B is odd
[Reveal] Spoiler: OA

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Re: Is A + B + C even? [#permalink] New post 24 May 2010, 01:09
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dimitri92 wrote:
Is A + B + C even?

1. A - C - B is even

2. (A - C)/B is odd


Note that we are not told that a, b and c are integers.

Q: is a+b+c=even?

(1) a-c-b=even, if the variables are integers then a+b+c will be even but if they are not: a=3.5, b=1, c=0.5 --> a-c-b=2=even, but a+b+c=5=odd. Not sufficient.

(2) \frac{a-c}{b}=odd. The same here: if the variables are integers then a+b+c will be even but if they are not: a=3.5, b=1, c=0.5 --> \frac{a-c}{b}=3=odd, but a+b+c=5=odd. Not sufficient


(1)+(2) a+b+c may or may not be even (again if variables are integers: YES but if a=3.5, b=1, c=0.5 answer is NO). Not sufficient.

Answer: E.
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Re: Is A + B + C even? [#permalink] New post 24 May 2010, 01:56
thanks...i made a mistake by assuming that they are integers...

ans E.
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Re: Even/Odd [#permalink] New post 17 Sep 2011, 14:22
statement 1 ) A - c -b is even

let A = 10.5, B =2 and c =4.5

10.5 - 4.5 -2 = 4 =even, but A+B+C = 17 (NOT EVEN.)

Pick A,B,C AS 2 THEN A- B- C = -2 = even , A+B+C =6 (EVEN )

STATEMENT 1 INSUFFICIENT.

Statement 2 ) (A-C)/b = odd

again, let A = 10.5, B =2 and c =4.5

(10.5-4.5)/2 = 3 =ODD, AND A+B+C = 17 = ODD

BUT Let A= 8, B= 2 And C =2

> (A-C)/B = 3 = ODD, BUT A + B +C = 12 = EVEN

STATEMENT 2 INSUFFICIENT.


the same values as i have listed above will also prove combining both statements dont provide any definitive answer either.

Answer E
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Re: Even/Odd [#permalink] New post 17 Sep 2011, 23:16
Aaah missed that a,b,c are not integers, in case of integers answer has to be A
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Re: Even/Odd [#permalink] New post 17 Oct 2011, 21:04
Darn it! Fell for a trap here.

I assumed that all my values were integers and that got me falling for D.
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Re: Even/Odd [#permalink] New post 22 Oct 2011, 11:18
Damn, did not check for non-integer values:(
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Re: Even/Odd [#permalink] New post 03 Nov 2011, 18:02
OMG, a b c does not necessarily be integers. A trap here that causes me to choose D instead
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Re: Is A+B+C even? 1) A-C-B is even 2) (A-C)/B is odd [#permalink] New post 16 Dec 2011, 21:49
E it is.

I tried to solve algebraically. However, I have a question.

If it were mentioned that all three numbers were integers, how would the answer change? How to figure this out algebraically? (Without having to pick numbers)
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Re: Is A+B+C even? 1) A-C-B is even 2) (A-C)/B is odd [#permalink] New post 17 Dec 2011, 11:13
i dont an algebric way to do it but here is a simple permutation on A,B,C "if given is that A, B , C are integers" .

then option 1 A-B-C is even only in below cases
A-C-B
E-E-E
E-O-O (E=Even, O=Odd)
O-O-E
O-E-O
in all cases A+ B +c will be even .

stmt 2: A-B/C is odd

A/C - B/C should be odd.
E O
O E


A/C can be even in both cases E/E or E/O eg: 4/2 or 6/3.
B/C can be even in both cases E/E or E/O eg: 4/2 or 6/3.

in the same way we can do for Odd case .

i.e. this stmt is insuff.
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Re: Is A+B+C even? 1) A-C-B is even 2) (A-C)/B is odd [#permalink] New post 18 Dec 2011, 22:27
jitbec wrote:
E.

What is the point of mentioning just the answer that you figured out? The OA is already known. If you could provide an effective method to solve the problem, it would be highly appreciated.
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Re: Is A+B+C even? 1) A-C-B is even 2) (A-C)/B is odd [#permalink] New post 18 Dec 2011, 22:43
Lucky2783 wrote:
i dont an algebric way to do it but here is a simple permutation on A,B,C "if given is that A, B , C are integers" .

then option 1 A-B-C is even only in below cases
A-C-B
E-E-E
E-O-O (E=Even, O=Odd)
O-O-E
O-E-O
in all cases A+ B +c will be even .

stmt 2: A-B/C is odd

A/C - B/C should be odd.
E O
O E


A/C can be even in both cases E/E or E/O eg: 4/2 or 6/3.
B/C can be even in both cases E/E or E/O eg: 4/2 or 6/3.

in the same way we can do for Odd case .

i.e. this stmt is insuff.


Hi I am not quite clear about your explanation for statement 2. I think you have interchanged two of the variables too. Could you please elaborate? Would be grateful.
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Re: Is A + B + C even? 1. A - C - B is even 2. (A - C)/B is odd [#permalink] New post 18 Jun 2012, 09:10
Hey Bunuel can you explain why the integer solutions are true, ie can you give a complete solution for how you would think this through in 2 mins
Re: Is A + B + C even? 1. A - C - B is even 2. (A - C)/B is odd   [#permalink] 18 Jun 2012, 09:10
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