kiran120680 wrote:
If a,b, and c are three positive integers such that at least one of them is odd, which of the following statements must be true?
A. a + b + c is odd
B. a + b + c and abc have the same even-odd nature
C. 100a + 10b + c is odd
D. If b/2 and c/2 are integers, 2a+b/2+c/2 is even
E. None of the above
The question asks "What
MUST be true?"
So, if we can show that an answer choice need not be true, we can ELIMINATE it.
A. a + b + c is oddIf a = 1, b = 2 and c = 3, then a + b + c = 1 + 2 + 3 = 6, which is NOT odd
ELIMINATE A
B. a + b + c and abc have the same even-odd natureIf a = 2, b = 2 and c = 3, then a + b + c = 2 + 2 + 3 = 7 (ODD)
If a = 2, b = 2 and c = 3, then abc = (2)(2)(3) = 12 (EVEN)
ELIMINATE B
C. 100a + 10b + c is oddIf a = 1, b = 1 and c = 2, then 100a + 10b + c = 100(1) + 10(1) + 2 = 112, which is NOT odd
ELIMINATE C
D. If b/2 and c/2 are integers, 2a + b/2 + c/2 is evenIf a = 1, b = 6 and c = 4, then b/2 and c/2 are integers
However, 2a + b/2 + c/2 = 2(1) + 6/2 + 4/2 = 2 + 3 + 2 = 7, which is NOT even
ELIMINATE D
By the process of elimination, the correct answer is E
Cheers,
Brent
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