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If x and y are integers and x=50y + 69

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Intern
Joined: 03 Feb 2014
Posts: 10
If x and y are integers and x=50y + 69 [#permalink]

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08 Feb 2014, 06:05
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If x and y are integers and x=50y + 69, which of the following must be odd?

A. xy
B. x + y
C. x + 2y
D. 3x-1
E. 3x+1

How would you solve this question quickly?
[Reveal] Spoiler: OA
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Joined: 02 Sep 2009
Posts: 43866
Re: If x and y are integers and x=50y + 69 [#permalink]

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08 Feb 2014, 06:06
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Expert's post
Fabino26 wrote:
If x and y are integers and x=50y + 69, which of the following must be odd?

A. xy
B. x + y
C. x + 2y
D. 3x-1
E. 3x+1

How would you solve this question quickly?

$$x=50y + 69 = even*y+odd=even+odd=odd$$.

C. $$x + 2y=odd+even=odd$$.

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Intern
Joined: 30 Nov 2013
Posts: 33
Re: If x and y are integers and x=50y + 69 [#permalink]

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10 Feb 2014, 08:53
Another approach is to just change the subject so " X-50Y=69" . Now the only way to achieve the formula above is if X is odd and Y is multiplied by an even number because "odd-even" or "odd+even" is always odd. Hope it is clear
Senior Manager
Joined: 06 Aug 2011
Posts: 383
Re: If x and y are integers and x=50y + 69 [#permalink]

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10 Feb 2014, 11:41
watever value of y will be x will be even..

Because..even+odd=odd.. 50 is even here..and whenever even number multiply with any number it becomes even.. so 50*(any number) will be even+odd=odd

so after POE.. only option C ..shows that..2y is even+odd=odd..
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Re: If x and y are integers and x=50y + 69 [#permalink]

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05 Mar 2014, 01:33
I tried doing substitution & ended up wrong.

Seems plugins don't work for such type of problems
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Joined: 25 Apr 2012
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Re: If x and y are integers and x=50y + 69 [#permalink]

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05 Mar 2014, 23:19
PareshGmat wrote:
I tried doing substitution & ended up wrong.

Seems plugins don't work for such type of problems

Hi,

Plugin can work..

On careful observation you can notice that x= odd
y can be written as y=(x-69)/50
Now if (x-69)=150 or x=219 then y=3 or odd
but if (x-69)=100 or x=169 then y=even

Therefore x is odd and y can take any value. Clearly expression in C will be odd because x is odd and irrespective of y being even or odd 2y will always be even.
Hope it helps
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Re: If x and y are integers and x=50y + 69 [#permalink]

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04 Jul 2014, 03:15
Fabino26 wrote:
If x and y are integers and x=50y + 69, which of the following must be odd?

A. xy
B. x + y
C. x + 2y
D. 3x-1
E. 3x+1

How would you solve this question quickly?

x = 50y + 69, since y is integer, 50y will always be even hence 50y + 69 will be odd hence x = odd
you don't know whether Y is even or odd, so you need to try.

A: odd * even = even ; odd*odd= odd ->not true
B: odd + odd = even ; odd+even = odd -> not true
C: odd + 2*odd = odd ; odd + 2*even = odd -> TRUE, stop here.

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Joined: 07 Dec 2014
Posts: 906
Re: If x and y are integers and x=50y + 69 [#permalink]

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28 Jan 2018, 13:47
Fabino26 wrote:
If x and y are integers and x=50y + 69, which of the following must be odd?

A. xy
B. x + y
C. x + 2y
D. 3x-1
E. 3x+1

How would you solve this question quickly?

here are three things we know:
x is odd
2y is even
x+2y is odd
C
Re: If x and y are integers and x=50y + 69   [#permalink] 28 Jan 2018, 13:47
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