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Is A + B + C even?
(1) A - C - B is even
(2) (A - C)/B is odd
(1) A - C - B is even
(2) (A - C)/B is odd
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08 Apr 2012, 09:30
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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
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
General Discussion
17 Sep 2011, 15:22
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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
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
