Data Sufficiency

I have a feeling that you meant to specify that a, b and c are INTEGERS. So, I have worded the question accordingly.

Max@Math Revolution wrote:If a, b and c are INTEGERS, is the sum a+b+c even?

1) abc is even
2) ac is odd

Some important rules for intgers:
1. ODD +/- ODD = EVEN
2. ODD +/- EVEN = ODD
3. EVEN +/- EVEN = EVEN

4. (ODD)(ODD) = ODD
5. (ODD)(EVEN) = EVEN
6. (EVEN)(EVEN) = EVEN

ADDITIONAL RULE: In ANY product of integers, if there is 1 or more EVEN numbers, the entire product will be EVEN. So, the if a product of integers is ODD, we can conclude that all of the numbers are ODD.
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Target question: Is the sum a+b+c even?

Statement 1: abc is even
From this, we can conclude that 1 or more of the numbers is EVEN
This statement doesn't FEEL sufficient, so I'll TEST some values.
There are several values of a, b and c that satisfy statement 1. Here are two:
Case a: a = 1, b = 2 and c = 2, in which case a+b+c = 5. So, the sum a+b+c is ODD
Case b: a = 1, b = 1 and c = 2, in which case a+b+c = 4. So, the sum a+b+c is EVEN[/color]
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Aside: For more on this idea of plugging in values when a statement doesn't feel sufficient, you can read my article: https://www.gmatprepnow.com/articles/dat ... lug-values

Statement 2: ac is odd
This means that a and c are ODD. However, we have no info about b.
There are several values of a, b and c that satisfy statement 1. Here are two:
Case a: a = 1, b = 1 and c = 1, in which case a+b+c = 3. So, the sum a+b+c is ODD
Case b: a = 1, b = 2 and c = 1, in which case a+b+c = 4. So, the sum a+b+c is EVEN[/color]
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 2 tells us that a and c are ODD
Statement 1 tells us that at least one of the numbers is EVEN. Since a and c are ODD, it must be the case that b is EVEN.
This means that a+b+c = ODD+EVEN+ODD = EVEN
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Max@Math Revolution wrote:Is a+b+c=even?

1) abc=even
2) ac=odd

If a, b and c are not restricted to integer values then the correct answer is E.

Here's why

Target question: Is the sum a+b+c even?

Jump all the way to...
Statements 1 and 2 combined
Consider these two CONFLICTING cases:
Case a: a = 1, b = 1 and c = 2, in which case a+b+c = 4. So, the sum a+b+c is EVEN
Case b: a = 1/2, b = 2 and c = 6, in which case a+b+c = 8.5. So, the sum a+b+c is NOT EVEN
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer = E

Cheers,
Brent