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Is A + B + C even? [#permalink]
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23 May 2010, 21:31
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Is A + B + C even? (1) A  C  B is even (2) (A  C)/B is odd
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Is A + B + C even? [#permalink]
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24 May 2010, 02:09
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Is A + B + C even?Note that we are not told that a, b and c are integers. (1) \(acb=even\), if the variables are integers then \(a+b+c\) will be even but if they are not: \(a=3.5\), \(b=1\), \(c=0.5\) > \(acb=2=even\), but \(a+b+c=5=odd\). Not sufficient. (2) \(\frac{ac}{b}=odd\). The same here: if the variables are integers then \(a+b+c\) will be even but if they are not: \(a=3.5\), \(b=1\), \(c=0.5\) > \(\frac{ac}{b}=3=odd\), 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: Even/Odd [#permalink]
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17 Sep 2011, 15:22
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 ) (AC)/b = odd
again, let A = 10.5, B =2 and c =4.5
(10.54.5)/2 = 3 =ODD, AND A+B+C = 17 = ODD
BUT Let A= 8, B= 2 And C =2
> (AC)/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: Is A+B+C even? 1) ACB is even 2) (AC)/B is odd [#permalink]
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16 Dec 2011, 22:49
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) ACB is even 2) (AC)/B is odd [#permalink]
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17 Dec 2011, 12:13
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 ABC is even only in below cases ACB EEE EOO (E=Even, O=Odd) OOE OEO in all cases A+ B +c will be even . stmt 2: AB/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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Is A + B + C even? [#permalink]
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Updated on: 29 Jul 2012, 07:01
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Is A + B + C even?
(1) A  C  B is even
(2) (A  C)/B is odd
Originally posted by catty2004 on 08 Apr 2012, 08:17.
Last edited by Bunuel on 29 Jul 2012, 07:01, edited 2 times in total.
Edited the question



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Re: Odd/Even (Ultra hard) from Math Flashcard [#permalink]
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08 Apr 2012, 08:41
I think the OA is incorrect.
1)ABC can only be even, if either all are even or two are odd and one is even, in both cases a+b+c is even.
2) (AC)/B can be odd if all are even or if all are odd, so A+B+C is even or odd, which makes the statement insufficient.
IMO A is correct.



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Re: Is A + B + C even? (1) A  C  B is even (2) (A  C)/B is [#permalink]
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08 Apr 2012, 09:30
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catty2004 wrote: Is A + B + C even?
(1) A  C  B is even
(2) (A  C)/B is odd Notice that we are not told that a, b and c are integers. Q: is \(a+b+c=even\)? (1) \(acb=even\), if the variables are integers then \(a+b+c\) will be even but if they are not, for example if \(a=3.5\), \(b=1\), \(c=0.5\) then \(acb=2=even\), but \(a+b+c=5=odd\). Not sufficient. (2) \(\frac{ac}{b}=odd\). The same here: if the variables are integers then \(a+b+c\) will be even but if they are not for example if \(a=3.5\), \(b=1\), \(c=0.5\) then \(\frac{ac}{b}=3=odd\), 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? (1) A  C  B is even (2) (A  C)/B is [#permalink]
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11 Oct 2012, 10:54
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sanjoo wrote: Bunuel wrote: catty2004 wrote: Is A + B + C even?
(1) A  C  B is even
(2) (A  C)/B is odd Notice that we are not told that a, b and c are integers. Q: is \(a+b+c=even\)? (1) \(acb=even\), if the variables are integers then \(a+b+c\) will be even but if they are not, for example if \(a=3.5\), \(b=1\), \(c=0.5\) then \(acb=2=even\), but \(a+b+c=5=odd\). Not sufficient. (2) \(\frac{ac}{b}=odd\). The same here: if the variables are integers then \( a+b+c\) will be even but if they are not for example if \(a=3.5\), \(b=1\), \(c=0.5\) then \(\frac{ac}{b}=3=odd\), 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. I was asking abt statement 2.. U said..if it were mentioned that a b and c are intergers than A+b+c=even ..and then this statement wud b sufficient.. But i got this now..i have solved this ..bt i tuk some time while proving this statemt 2 ... It goes like this: Q: Is A+B+C= EVEN S1: ABC= Even i.e. We can write ABC= 2N =>A=2N + B+C Substituting in the main equation we get 2N+2(B+C)=2[N+B+C] Now, N is an Integer, but we dont know whether, B+C= Integer or not. Hence N+B+C mayor may not be an Integer. Therefore, S1 is insufficient. Same case with Statement 2, which on simplification gives, A=(2N+1)B + C => A+B+C= 2(B+C+NB) Again same same scenario, We are not aware whether, the value in the parenthesis is an Integer or not. Hence, S2 is also Insufficient. S1 & S2 together also does not resolve the issue of whether B+C is integer or not. Hence answer is E. I hope this is clear. Thanks



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Re: Is A + B + C even? [#permalink]
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30 Nov 2014, 15:35
Note that we are not told that a, b and c are integers. Q: is a+b+c=even? (1) acb=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 —> acb=2=even, but a+b+c=5=odd. Not sufficient. (2) \fracacb=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 —> \fracacb=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. Course GMAT onsite in Chile Claudio Hurtado GMAT CHILE
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Is A + B + C even? [#permalink]
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15 Apr 2015, 03:43
K is integer for sure.
1. A  (B+C) = 2K => A = 2K + B + C A +B + C = 2K +2B + 2C = 2(K + B + C)
If B: Integer; C = 0.5 => A + B + C = 2(K+B) + 1
2. (A  C)/B = 2k +1 => A  C = 2kB + B => A = 2kB + B + C => A + B + C = 2(kB + B + C) If B: Integer; C = 0.5
=> A + B + C = 2(kB + B) + 1
Quite tricky.



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Re: Is A + B + C even? [#permalink]
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16 Apr 2015, 06:12
What a great question! I started this one writing out all the cases but then realized we don't know if a,b and c are integers. Got answer E and thought it took me at most 2.5 mins... nope just over 3:50. Although I finally got it, this question has made me realize I really need to improve my speed.
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Re: Is A + B + C even? [#permalink]
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10 Dec 2017, 00:15
catty2004 wrote: Is A + B + C even?
(1) A  C  B is even
(2) (A  C)/B is odd Please find the solution as attached. ANswer: Option E
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Re: Is A + B + C even?
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