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

(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.

Re: Is A+B+C even? 1) A-C-B is even 2) (A-C)/B is odd [#permalink]

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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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Notice 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, for example if \(a=3.5\), \(b=1\), \(c=0.5\) then \(a-c-b=2=even\), 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 for example if \(a=3.5\), \(b=1\), \(c=0.5\) then \(\frac{a-c}{b}=3=odd\), 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.

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, 09:54

1

This post received KUDOS

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) \(a-c-b=even\), 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 \(a-c-b=2=even\), 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 for example if \(a=3.5\), \(b=1\), \(c=0.5\) then \(\frac{a-c}{b}=3=odd\), 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.

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: A-B-C= Even i.e. We can write A-B-C= 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.

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) \fraca-cb=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 —> \fraca-cb=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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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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