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Numbers - Odd and Even

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Numbers - Odd and Even

by surajgarg » Fri Jul 23, 2010 7:24 am
If a and b are both positive integers, is (b^(a+1))-(b*a^b) odd?

1. a+(a+4)+(a-8)+(a+6)+(a-10) is odd
2. (b^3)+3(b^2)+5b+7 is odd

OA - D

I did figure out that statement 2 is sufficient. How to work out with statement 1?[/spoiler]
Last edited by surajgarg on Fri Jul 23, 2010 8:36 am, edited 1 time in total.
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by akdayal » Fri Jul 23, 2010 8:16 am
Incomplete question. conditions do not make sense.
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by surajgarg » Fri Jul 23, 2010 8:37 am
akdayal wrote:Incomplete question. conditions do not make sense.
Really sorry for that. Correction done.
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by akdayal » Fri Jul 23, 2010 9:46 am
If a and b are both positive integers, is (b^(a+1))-(b*a^b) odd?

1. a+(a+4)+(a-8)+(a+6)+(a-10) is odd
2. (b^3)+3(b^2)+5b+7 is odd
take st1: a + (a +4) + (a -8) + (a + 6) + ( a-10) is odd
==> 5a -8 == odd
==> odd - even = odd ==> a is odd

Now main question
b(b^a - a^b) ------------ (1)
lets say if b is even +ve then clearly (1) will be even.
lets say b is odd then (1) becomes like
odd (odd^odd - odd^odd) ==> odd*(odd -odd) ==> odd *even ==> even
hence even

So statement 1 alone is suff

Now st2 is also suff as you have already mentioned that it is clear.
basically if you expand st2 you will get b is even

Hope this will help you
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