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If x and y are positive odd integers, then which of the following must [#permalink]
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26 Feb 2015, 05:53
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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, 06:17
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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)^(x1) + 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. Sorry for the clumsy explanation



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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, 07:09
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I. x^(y+1)>> (odd)^even=odd II. x(y+1)>>(odd)*even=even III. (y+1)^(x1) + 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.
answer 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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26 Feb 2015, 19:16
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Answer = A. I only \(odd^{(odd+1)} = odd^{even} = odd\) \(odd * (odd+1) = odd * even = even\) \((odd+1)^{(odd1)} + 1 = even^{even} +1 = even + 1 = odd\) However, this contradicts for x = 3, y = 1
\((3+1)^{11} + 1 = 1 + 1 = 2\)Question asked is "must be odd", so answer = 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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27 Feb 2015, 09:31
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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)^(x1) + 1 = (1+1)^(11) +1 = 2^0 + 1 = 1+1 = 2. So, no.
ANS 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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28 Feb 2015, 01:46
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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)^(x1) + 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)^(x1) + 1 = (3+1)^(11) + 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)^(x1) + 1 = (3+1)^(31) + 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.  Optimus Prep's GMAT On Demand course for only $299 covers all verbal and quant. concepts in detail. Visit the following link to get your 7 days free trial account: http://www.optimusprep.com/gmatondemandcourse



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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 Mar 2015, 04:54



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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, 14:35
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.
thus, 1 alone is correct.



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Re: If x and y are positive odd integers, then which of the following must [#permalink]
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12 Oct 2016, 17:51
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)^(x1) + 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!



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Re: If x and y are positive odd integers, then which of the following must [#permalink]
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13 Apr 2017, 01:46
Option Ax,y are positive Odd integers. Odd: O, Even: E & Fraction: F I. x^(y+1) = O^(O + 1) = O^E = O II. x(y+1) = O(O + 1) = O(E) = E III. (y+1)^(x1) + 1 = (O + 1)^(O  1) + 1 = (E)^(E) + 1 = E + 1 = O  Spl. Case, if x = 1 then (y+1)^(x1) + 1 = (y+1)^(0) + 1 = 1 + 1 = 2 =E
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Re: If x and y are positive odd integers, then which of the following must [#permalink]
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06 Sep 2017, 00:28
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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)^(x1) + 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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If x and y are positive odd integers, then which of the following must [#permalink]
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06 Sep 2017, 01:37
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)^(x1) + 1
A. I only B. II only C. III only D. I and III E. None of the above
Kudos for a correct solution. x is odd, so (x1) is even. y is odd, so (y+1) is even. I.\(x^(y+1) = {odd} ^ {even} = odd\) II. \(x(y+1) = odd * even = even\) III. \((y+1)^(x1) + 1 = {even}^{even} + 1\) OR \({even}^0 +1\) = odd OR even So, Only I is correct. Answer A
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If x and y are positive odd integers, then which of the following must [#permalink]
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24 Sep 2017, 23:53
No calculations required.
I. \(x^{(y+1)}\)=\(odd^{(odd+1)}\)any odd no raised to any odd or even power will always be odd.
II. x(y+1)=odd(odd+1)=odd(even)any number multiplyed with even no will always be even
III. \((y+1)^{x1}\) + 1=
Let x=3(odd)
\((odd+1)^{(odd1)}\)+1=\((even)^{(31)}\)+1=odd or
Let x=1(odd)
\(even^{(11)}\)+1=\(even^{(0)}\)+1=1+1=2(any integer raised to zero is 1) even
Hence 3rd option can be odd or even.
Answer1




If x and y are positive odd integers, then which of the following must
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