For integers x and y, when x is divided by y, the remainder

Question

For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true?

A. x is odd
B. xy is odd
C. x and y share no common factors other than 1
D. The sum x + y is odd
E. At least one of x and y is odd

Bunuel · Accepted Answer

For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true?

A. x is odd. Not necessarily true. Consider x=4 and y=3.

B. xy is odd. Not necessarily true. Consider x=4 and y=3.

C. x and y share no common factors other than 1. Not necessarily true. Consider x=3 and y=6.

D. The sum x + y is odd. Not necessarily true. Consider x=1 and y=3.

E. At least one of x and y is odd. If both x and y were even, then the remainder when x is divided by y would be even, not odd. Hence at least one of x and y is odd.

Answer: E.

Hope it's clear.

greatps24 · Answer

For integers x and y, when x is divided by y, the remainder is odd. Which of the following  must be true ?

A. x is odd.  May be. not must.  
B. xy is odd.  x= 6, y =5 R= 1. xy is not odd 
C. x and y share no common factors other than 1.  x=12 , y=9. r= 3. common factor = 3, 1 
D. The sum x + y is odd.  x= 3, y=5. r= 3. x+y = 8 even 
E.  At least  one of x and y is odd.  correct

stonecold · Answer

Here we the easiest way out is use the examples
Now by using 3/11 ; 3/9 and 3/12 => all options can be eliminated except the last one => E

devarshi9283 · Answer

I have got one more;

let X=nY+R (n= some quotient, R=remainder)
 
or X=nY+2k+1 (2k+1=odd remainder)

Now if Y is even;

X=nY+2k+1=even+even+1=odd

and if Y is odd;

X=(odd or even)+(even)+1
 =(odd or even)

So,
at least 1 of X and Y will always be Odd.

Kudos plz if you find this solution useful...

BrentGMATPrepNow · Answer

Since, the question asks "Which of the following  must  be true?", we can eliminate any answer choice that is not necessarily true. 
So let's test some values that satisfy the given conditions

For integers x and y, when x is divided by y, the remainder is odd . 
One possible case is that x = 9 and y = 6 (since 9 divided by 6 leaves remainder 3)
Check the answer choices . . . 
ELIMINATE B, since xy = 54, which is EVEN
ELIMINATE C, since 9 and 6 have a common factor of 3

Another possible case is that x = 6 and y = 5 (since 6 divided by 5 leaves remainder 1)
Check the answer choices . . . 
ELIMINATE A since x is EVEN

Another possible case is that x = 11 and y = 5 (since 11 divided by 5 leaves remainder 1)
Check the answer choices . . . 
ELIMINATE D since x is x + y = 16, which is EVEN

By the process of elimination, the correct answer is E

RELATED VIDEO
 https://www.youtube.com/watch?v=XCxgIR042tE

Adarsh_24 · Answer

While picking examples, if we keep the numerator the remainder we want and denominator greater than the numerator. We can get any remainder we need. I hope there is no flaw in my logic.

Kinshook · Answer

For integers x and y, when x is divided by y, the remainder is odd. Which of the following must be true?

If both x & y are even the remainder must be even.

A. x is odd
B. xy is odd
C. x and y share no common factors other than 1
D. The sum x + y is odd
E. At least one of x and y is odd

IMO E

Posted from my mobile device

bumpbot · Answer

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For integers x and y, when x is divided by y, the remainder

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For integers x and y, when x is divided by y, the remainder

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