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Re: If x and y are positive odd integers, then which of the following must [#permalink]

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26 Feb 2015, 07:17

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Bunuel wrote:

If x and y are positive odd integers, then which of the following must also be an odd integer?

I. x^(y+1) II. x(y+1) III. (y+1)^(x-1) + 1

A. I only B. II only C. III only D. I and III E. None of the above

Kudos for a correct solution.

I think the answer to this question is A only because anything to the power of odd will always be odd as odd*odd = odd. In case of II y+1 will be even as odd+odd = even and from even*odd = even In case of III anything to the power of even will churn out even only.

Re: If x and y are positive odd integers, then which of the following must [#permalink]

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26 Feb 2015, 08:09

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I. x^(y+1)>> (odd)^even=odd II. x(y+1)>>(odd)*even=even III. (y+1)^(x-1) + 1>>(even)^even+1>>even+1>> odd if x is not equal to 1 and if x=1 then its (even)^0+1=1+!=2 even.

Re: If x and y are positive odd integers, then which of the following must [#permalink]

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27 Feb 2015, 10:31

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I also say A.

I used 1 as an odd, positive number to test: I. x^(y+1) = 1^(1+1) = 1^2=1, and a second effort: 3(1+1) = 3^2 = 9. So, yes. II. x(y+1) = 1(1+1) = 1*2 = 2. So, no. III. (y+1)^(x-1) + 1 = (1+1)^(1-1) +1 = 2^0 + 1 = 1+1 = 2. So, no.

If x and y are positive odd integers, then which of the following must also be an odd integer?

I. x^(y+1) II. x(y+1) III. (y+1)^(x-1) + 1

A. I only B. II only C. III only D. I and III E. None of the above

Kudos for a correct solution.

The best way to do this is to assume values and put it in the equation. Let x = 1 and y = 3 Option I: x^(y+1) = 1^(4+1) = 1^5 = 1 (ODD) Option II: x(y+1) = 1(3 + 1) = 1(4) = 4 (EVEN) Option III: (y+1)^(x-1) + 1 = (3+1)^(1-1) + 1 = 4^0 + 1 = 1 + 1 (EVEN)

But since we've got a power of 0, let us reconfirm with another value of x. Let x = 3.

So, option III: (y+1)^(x-1) + 1 = (3+1)^(3-1) + 1 = 4^2 + 1 = 17 (ODD). So option III doesn't give a unique answer.

So option I MUST always be odd. Hence option A.

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Re: If x and y are positive odd integers, then which of the following must [#permalink]

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02 Jan 2016, 15:35

tricky one... we can eliminate B, C, and E right away.

1 is true, since an odd number raised to a positive number power will always be odd. the third one, if x>1, then it will be odd, but if x=1, then everything is equal to 2, and not odd.

Re: If x and y are positive odd integers, then which of the following must [#permalink]

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12 Oct 2016, 18:51

Bunuel wrote:

If x and y are positive odd integers, then which of the following must also be an odd integer?

I. x^(y+1) II. x(y+1) III. (y+1)^(x-1) + 1

A. I only B. II only C. III only D. I and III E. None of the above

Kudos for a correct solution.

I tested the three statements choosing positive, odd values for x and y. I used x=1 and y=3 first, then x=3 y=5 next. I realized about halfway through that number properties could've done it even quicker!

Re: If x and y are positive odd integers, then which of the following must [#permalink]

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06 Sep 2017, 01:28

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If x and y are positive odd integers, then which of the following must also be an odd integer?

I. x^(y+1) II. x(y+1) III. (y+1)^(x-1) + 1

i) always odd as odd raise to anything which is even or odd= odd ii) x(y+1) , since y is odd so y+1 will be even and => even x odd = even iii) (y+1)^(x11) + 1 let y =1 , x= 1 both odd => 2^0 +1 = 2 even

Hence i) is always odd.

ANSWER IS A _________________

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