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

Question

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

Bunuel · Accepted Answer

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

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

Answer: C.

Zatmah · Answer

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

sanjoo · Answer

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..

PareshGmat · Answer

I tried doing substitution & ended up wrong.

Seems plugins don't work for such type of problems

WoundedTiger · Answer

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

unceldolan · Answer

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.

Answer C

gracie · Answer

here are three things we know:
x is odd
2y is even
x+2y is odd
C

Chanchal2809 · Answer

How to cross verify Even Odd Situation

ijustwantagoodjob · Answer

What if x and y are both equal to 0? => x+2y = 0 and since 0 is considered an even number, doesn't that make the answer choice incorrect?

Bunuel · Answer

x = y = 0 does not satify x = 50y + 69, so this case is not possible.

findingmyself · Answer

Plugging in does work for this kind of problem:

Take Y=(1,0 and-2)

Always take a mix of positive and negative integers since the question is asking integers

When Y=1, X=119
When Y=0, X=69
When Y=-2, X=169

From all the above cases, only X+2Y satisfied the criteria of odd

A. XY--> Doesnt work when Y=0
B. X+Y--> Doesnt work when Y=1
D. 3X-1--> Doesn't work in all cases because of ODD-ODD
E. 3X+1-->Doesnt work in all cases because of ODD-ODD

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

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GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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My Rewards