[spoiler]Solution: A
Explanation: While this question can be answered with conceptual thinking and/or number picking, it is tedious and error prone. The best approach is with algebra:
In the question stem you learn that ac + b is odd, and in statement 1 you learn that ac + ab is even. If you add the two expressions together you know that the result will be odd (odd + even = odd) and the combined expressions will be: ac + b + ac + ab = 2ac + ab + b or 2ac + b(a+1) As a result you know that 2ac + b(a+1) is odd and because 2ac is always even then b(a+1) must be odd. When a product is odd, both components must be odd so b is odd and statement 1 is sufficient. If you do the same with the second statement (combine it with the expression from the question stem) know that ac + b + b + c must be even (odd + odd = even). Simplifying this means that 2b + c(a+1) is even. This leaves the possibility that b is either odd or even as either 2b must be even but b could be odd or even. Answer is A. The biggest takeaway from this problem is to not forget algebraic manipulation, as people tend to gravitate toward number picking on these types of problems.[/spoiler]
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is b odd ?
Source: Beat The GMAT — Data Sufficiency |
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Brent@GMATPrepNow
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Target question: Is b odd?himu wrote:If a, b, and c are integers and ac + b is odd, is b odd?
(1) ac + ab is even
(2) b + c is odd
Given: ac + b is odd
Statement 1: ac + ab is even
It's given that ac + b is odd, and statement 1 says that ac + ab is even.
Since we know that odd - even = odd, we know that . . .
(ac + b) - (ac + ab) = odd
Simplify to get: b - ab = odd
Factor: b(1 - a) = odd
IMPORTANT: If the product of two integers is odd, then both integers are odd.
So, we know that (1 - a) must be odd AND b must be odd.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: b + c is odd
One approach here is to look for contradictory cases that satisfy the given information. Here are two such cases:
Case a: a = 0, b = 1, c = 0, in which case b is odd
Case b: a = 1, b = 2, c = 1, in which case b is even
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Answer = A
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
