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Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. If x and y are integers and x = 50y + 69, which of the follo  Question banks Downloads My Bookmarks Reviews Important topics
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Founder  Joined: 18 Apr 2015
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If x and y are integers and x = 50y + 69, which of the follo [#permalink]
Expert's post 00:00

Question Stats: 70% (01:20) correct 30% (01:25) wrong based on 40 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

_________________ GRE Prep Club Legend  Joined: 07 Jun 2014
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GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
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Re: If x and y are integers and x = 50y + 69, which of the follo [#permalink]
3
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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

 y x= 50y + 69 A) xy B) x + y C) x + 2y D) 3x — 1 E) 3x + 1 even odd even odd odd even even odd odd odd even odd even even

Hence option C is the only correct choice. As other option may or maynot be odd
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Sandy
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Re: If x and y are integers and x = 50y + 69, which of the follo [#permalink]
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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

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
_________________

Brent Hanneson – Creator of greenlighttestprep.com  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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