akhilsuhag wrote:If a and b are both positive integers, is b^a+1 - ba^b odd?
(1) a + (a + 4) + (a - 8) + (a + 6) + (a - 10) is odd (2) b^3 + 3b^2 + 5b + 7 is odd

Statement 1:

Can be rewritten as (5a - 8) is odd. Now this gives us that a is odd.

Looking at the prompt:

b^a +1 - b. a^b

Now a is odd, so a^b is odd. We have two sub cases(either b is even or b is odd)

Case1: B is even
Makes b^a +1 odd and b.a^b Even;
We know Odd - Even = Odd
[spoiler]it means even^(even+1)- odd= what?

now my question is how can you say that Even^anything can be odd [/spoiler]

Case2: B is Odd
Makes b^a +1 even and b.a^b (odd * odd) is odd.

now Even - Odd = Odd again.

So we get odd in both cases and thus STATEMENT 1 IS SUFFICIENT.

Statement2:
b^3 + 3b^2 + 5b + 7 is odd. The only way this is possible is if B is EVEN. You can plug in odd and even numbers to check.

Again look at the prompt.

b^a +1 will always be odd (even +1) and b. a^b will always be even ( Even* anything = Even)

So, Odd - Even = Odd.

STATEMENT IS SUFFICIENT.

Therefore both statements are SUFFICIENT.

I was hoping for feedback and if experts can tell me if the approach is correct.

Thanks.

Tani Wolff - Kaplan wrote:I think the problem is reading the question. My understanding is that the original equation is:
(b^a)+1 - b(a^b) and I think you are reading it as b^(a+1) - b(a^b). Typing algebra can be prolbematic.