If x and y are integers, and x/y is not an integer then which of the

Question

If x and y are integers, and x/y is not an integer then which of the following must be true?

A. x is odd and y is even.
B. x is odd and y is odd.
C. x is even and y is odd.
D. x<y
E. None of the above

sumitkrocks · Answer

A. x is odd and y is even.
will always be a fraction -true

This range of sets, however, exclude many other sets such as even/ even with denominator larger etc.. Eliminate

B. x is odd and y is odd.
can be an integer i.e 3/3 = 1
Eliminate

C. x is even and y is odd.
can be an integer i,e 6/3 = 2
Eliminate

D. x<y true
2/4, 3/9, 2/5, 5/7

6/5 x>y still not an integer
Eliminate

E. None of the above
This is the right choice IMO

TarunKumar1234 · Answer

If x and y are integers, and x/y is not an integer then which of the following must be true?

A. x is odd and y is even. -> It means, x and y are integers and x/y is not an integer. But, if x =2 and y=3 then, still x/y won't be an integer. We are missing some cases in this option.
B. x is odd and y is odd. -> It means, x and y are integers and x/y can be or cannot an integer. But, still we are missing few cases, such as x =2 and y =4 then x/y won't be integer. Incorrect.
C. x is even and y is odd. -> It means, x and y are integers and x/y can be or cannot an integer. But, still we are missing few cases, such as x =3 and y =5. Incorrect.
D. x<y -> x/y cannot be an integer for x >y. So, we still missed few cases. Incorrect.
E. None of the above -> It is correct.

So, I think E.

ayushk09 · Answer

any odd no divided by even will not be integer, hence A seems to be right option
for option D x<y , let x=-2 and y=2 then x/y will be -1, is an integer (no where it is mentioned that x,y are positive integers)
for B - x=3,y=3, x/y =1 not must be true
for C - x=6, y=3, x/y = 2 , not must be true

in view of above E is also rejected.

Hence A seems to be logical answer.

CEO2021 · Answer

Bunuel

please check for any typo in question

Seems ans A is correct one

Bunuel · Answer

The most efficient approach to solve this problem is to evaluate each option by testing some numbers.

A. x is odd and y is even.

While it is true that x/y is not an integer in this case, the question asks which of the following  must  be true, not which  could  be true. This option is not always true, as can be seen with the counterexample of x = 2 and y = 4.

B. x is odd and y is odd.

Not necessarily true. Consider x = 2, and y = 4.

C. x is even and y is odd.

Not necessarily true. Consider x = 2, and y = 4.

D. x<y

Not necessarily true. Consider x = 5, and y = 4.

E. None of the above

Therefore, the answer is E.

KarishmaB · Answer

If  \frac{x}{y}  is not an integer, is it necessary that x should be odd and y should be even? NO
x and y both could be odd or x could be even and y could be odd etc.
e.g.  \frac{3}{5}, \frac{4}{3}  etc.
Hence answer is not (A)

We need to find what does " \frac{x}{y}  is not an integer" imply about x and y.
All it implies is that y is not a factor of x. Either could be odd or even.

Answer is (E)

joe123x · Answer

I understand that none of the answers is true always.

-generally when we are asked "what must be true?" Do we assume the following " what is always has to be true regardless"? Thank you in advance.

Posted from my mobile device

KarishmaB · Answer

There are 3 different concepts - must be true, could be true, complete range This post discusses all 3: https://anaprep.com/algebra-must-be-tru ... questions/ Our original question asks for "must be true" which means that it has to be true under all circumstances in which x/y is not an integer while x and y are integers. Check out this blog post too: https://anaprep.com/algebra-game-must-b ... questions/ It discusses how exactly to handle "must be true" questions. You need to focus on "what is given" and "what is asked".

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If x and y are integers, and x/y is not an integer then which of the

Prep Toolkit

Top 5 GMAT Debrief Videos

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

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If x and y are integers, and x/y is not an integer then which of the

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

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards