Is A + B + C even?

Question

Is A + B + C even?

(1) A - C - B is even

(2) (A - C)/B is odd

Aj85 · Answer

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

siddharthmuzumdar · Answer

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)

BN1989 · Answer

I think the OA is incorrect.

1)A-B-C 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) (A-C)/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.

Bunuel · Answer

Is  a+b+c  an even integer? 
 
It's important to note that we're not provided with information that  a ,  b , and  c  are integers.
 
(1)  a-c-b  is even. 
 
If all the variables are integers, then  a+b+c  will indeed be even. However, if they're not, for instance if  a=3.5 ,  b=1 , and  c=0.5  (such that  a-c-b=2 , which is even), then  a+b+c=5 , which is odd. Not sufficient.
 
(2)  \frac{a-c}{b}  is odd. 
 
The scenario is similar to the first one: if the variables are integers, then  a+b+c  will be even, but if they're not, for example if  a=3.5 ,  b=1 , and  c=0.5  (in this case  \frac{a-c}{b}=3 , which is odd), then  a+b+c=5 , an odd number. Not sufficient.
 
(1)+(2) The sum  a+b+c  could be even or odd (again, if the variables are integers, the answer would be YES, but if  a=3.5 ,  b=1 , and  c=0.5 , the answer is NO). Thus, the combination of conditions is still not sufficient.

Answer: E

GMATinsight · Answer

Please find the solution as attached.

ANswer: Option E

vyascd · Answer

Is this method correct?

There are 3 variables A, B and C. We require 3 equations to solve this.
But we are only given 2 equations. 
So E. 
 Cherry on top is the fact that it is not given as A, B and C are integers.

MathRevolution   Bunuel

GMATinsight · Answer

I call the use of such a method, a suicide attempt by a serious GMAT aspirant... 1st statement alone would have been sufficient to answer this question if only the "cherry-on-the-top" were given.

Solve DS as GMAT expects it to be solved... not as a few wizards explain it...

bumpbot · Answer

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Is A + B + C even?

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