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by vinay1983 » Thu Sep 12, 2013 1:36 am
vipulgoyal wrote:if a and b are both positive integers, is b^(a+1) - ba^b
1. a is odd
2. b is even

In source ans is B but i think it is D
Hi can you correct the question?I feel it is incorrect what the question is asking for?
You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!
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by vipulgoyal » Thu Sep 12, 2013 3:10 am
I have edited the qustion

Is b^(a+1) - ba^b odd
1. a is odd
2. b is even
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by vinay1983 » Thu Sep 12, 2013 3:30 am
vipulgoyal wrote:if a and b are both positive integers, is b^(a+1) - ba^b
1. a is odd
2. b is even

In source ans is B but i think it is D
I cannot understand this?Please help.What does this mean?

is b^(a+1) - ba^b
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by vipulgoyal » Thu Sep 12, 2013 3:35 am
Is b^(a+1) - ba^b odd

b whole power a+1 - b*a power b
we can simplify

b^a * b - b * a^b
b(b^a - a^b)
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by ganeshrkamath » Thu Sep 12, 2013 3:48 am
vipulgoyal wrote:if a and b are both positive integers, is b^(a+1) - ba^b odd
1. a is odd
2. b is even

In source ans is B but i think it is D
Statement 1. a is odd.
Case 1: b is even. The result will be even - even = even
Case 2: b is odd. The result will be odd - odd = even
Sufficient.

Statement 2. b is even.
The result will be even - even = even
Sufficient.

Choose D

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by [email protected] » Thu Sep 12, 2013 11:50 am
Hi vipulgoyal,

You are correct. The correct answer IS D, not B

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by ceilidh.erickson » Thu Sep 12, 2013 1:20 pm
Several posters have correctly simplified the expression:
b(b^a - a^b)

But let's think further about what it would take for this expression to be ODD. For a product to be odd, both of the terms in that product need to be odd. So b has to be odd; if it's even the whole product would be even.

What would make b^a - a^b odd? Well given that b has to be odd we know that an odd number taken to any positive integer power will also be odd, so b^a is odd. That means that a would have to be even, because ODD - EVEN = ODD.

So the conditions that we need to get an odd product are:
b is odd
a is even

If either of these is violated, we'll get an even product.

1) This violates our second condition. We'd have either:
even(even - odd) = even
odd(odd - odd) = even
Sufficient

2) This violates our first condition. Since we're multiplying b by the terms in the parentheses, that product has to be even.
Sufficient
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