GyanOne
Quote:
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
Using statement (1):
5a-8 is odd
=> a is odd
Now evaluating b^(a+1) - b(a^b), we get b^even -b*odd
If b is even, the expression is even^even - even = even
If b is odd, the expression is odd^even - odd = even
Therefore in either case, we can say that the expression is not odd. Sufficient.
Using statement 2:
b^3 + 3b^2 + 5b + 7 is odd
=> b^3 + 3b^2 + 5b is even
=> b is even (because if b is odd, the expression would be odd + odd + odd = odd)
Now evaluating b^(a+1) - ba^b
we get even^(a+1) - even*a^odd
= even - even*a^odd
= even
Therefore statement (2) is sufficient.
The answer should therefore be (D).
Hi guys,
I have a question about statement 1
Simplifying main stem: b^(a+1) - b(a^b) gives us b[(b^a) - (a^b)]
From statement 1 we get that a has to be odd
Then to see if statement 1 is S, we try odd/even values for b and see that all of them give even answers, except when a=3 b=3, which yield and answer of 0, which isnt considered neither even or odd.
Am I not understanding something here, which prevents the use of these values?
Thanks in advance!