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If x and y are integers and x = 50y + 69, which of the follo

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If x and y are integers and x = 50y + 69, which of the follo [#permalink] New post 05 Mar 2017, 09:08
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Question Stats:

72% (01:17) correct 27% (01:08) wrong based on 22 sessions


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
[Reveal] Spoiler: OA

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Re: If x and y are integers and x = 50y + 69, which of the follo [#permalink] New post 11 Mar 2017, 17:44
Expert's post
Explanation

Construct the following table


Remember:

even + odd = odd
even+ even= even
odd + odd = even


even * even = even
even* odd = even
odd*odd = odd



yx= 50y + 69A) xyB) x + yC) x + 2y D) 3x — 1E) 3x + 1
evenoddevenoddodd eveneven
oddoddoddevenodd eveneven


Hence option C is the only correct choice. As other option may or maynot be odd
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Re: If x and y are integers and x = 50y + 69, which of the follo [#permalink] New post 15 Oct 2017, 15:21
Expert's post
Carcass 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


The key word here is MUST

So, if we can show that an answer choice CAN be false, we can eliminate it.

If x = 50y + 69, then one possible solution is y = 0 and x = 69
In other words x is ODD and y is EVEN

Now check the answer choices...
A) xy = (ODD)(EVEN) = EVEN
ELIMINATE A

B) x + y = ODD + EVEN = ODD
KEEP B for now

C) x + 2y = ODD + (2)(EVEN)
= ODD + EVEN
= ODD
KEEP C for now

D) 3x — 1 = (3)(ODD) - 1
= (ODD)(ODD) - ODD
= ODD - ODD
= EVEN
ELIMINATE D

E) 3x + 1 = (3)(ODD) + 1
= (ODD)(ODD) + ODD
= ODD + ODD
= EVEN
ELIMINATE E

We're now left with answer choices B and C
So let's test another pair of values...

If x = 50y + 69, then another possible solution is y = 1 and x = 119
In other words x is ODD and y is ODD

Now check the remaining answer choices...

B) x + y = ODD + ODD = EVEN
ELIMINATE B

By the process of elimination, the correct answer is C

Cheers,
Brent
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Re: If x and y are integers and x = 50y + 69, which of the follo   [#permalink] 15 Oct 2017, 15:21
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If x and y are integers and x = 50y + 69, which of the follo

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