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

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

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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


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


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[Reveal] Spoiler: OA

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

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New post 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.

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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New post 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.

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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New post 26 Feb 2015, 20:16
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Answer = A. I only

\(odd^{(odd+1)} = odd^{even} = odd\)

\(odd * (odd+1) = odd * even = even\)

\((odd+1)^{(odd-1)} + 1 = even^{even} +1 = even + 1 = odd\)

However, this contradicts for x = 3, y = 1

\((3+1)^{1-1} + 1 = 1 + 1 = 2\)


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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New post 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.

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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New post 28 Feb 2015, 02:46
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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)^(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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New post 02 Mar 2015, 05:54
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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.


MAGOOSH OFFICIAL SOLUTION:
Attachment:
must_be_odd.png
must_be_odd.png [ 24.51 KiB | Viewed 3553 times ]

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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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

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New post 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.

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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New post 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!

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

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New post 13 Apr 2017, 02:46
Option A

x,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)^(x-1) + 1 = (O + 1)^(O - 1) + 1 = (E)^(E) + 1 = E + 1 = O || Spl. Case, if x = 1 then (y+1)^(x-1) + 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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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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If x and y are positive odd integers, then which of the following must [#permalink]

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New post 06 Sep 2017, 02:37
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)^(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.


x is odd, so (x-1) 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. \((y+1)^(x-1) + 1 = {even}^{even} + 1\) 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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New post 25 Sep 2017, 00:53
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. \((y+1)^{x-1}\) + 1=

Let x=3(odd)

\((odd+1)^{(odd-1)}\)+1=\((even)^{(3-1)}\)+1=odd

or

Let x=1(odd)

\(even^{(1-1)}\)+1=\(even^{(0)}\)+1=1+1=2(any integer raised to zero is 1) even

Hence 3rd option can be odd or even.

Answer-1

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If x and y are positive odd integers, then which of the following must   [#permalink] 25 Sep 2017, 00:53
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