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

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Math Expert
Joined: 02 Sep 2009
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If x and y are integers, and x/y is not an integer then which of the [#permalink]

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23 Oct 2016, 09:45
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55% (hard)

Question Stats:

46% (00:48) correct 54% (00:53) wrong based on 196 sessions

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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

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Posts: 207
Concentration: Operations, Entrepreneurship
If x and y are integers, and x/y is not an integer then which of the [#permalink]

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23 Oct 2016, 10:05
1
Bunuel wrote:
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

x and y could be co-primes

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Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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23 Oct 2016, 10:54
X/Y not integer,either x<y or x, y are co prime ... No musts ... E

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Manager
Joined: 27 Aug 2015
Posts: 94
Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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24 Oct 2016, 00:01
I think E bcz with examples we can prove all no must be true.
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Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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04 Feb 2017, 04:26
rakaisraka wrote:
I think E bcz with examples we can prove all no must be true.

Hi. I don't understand how can you divide an Odd Number by an even no. and get an integer value.
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Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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04 Feb 2017, 04:56
1
Shruti0805 wrote:
rakaisraka wrote:
I think E bcz with examples we can prove all no must be true.

Hi. I don't understand how can you divide an Odd Number by an even no. and get an integer value.

Hi,
as per question stem x and y are integers but x/y is not integer. This is must be true each statement has to be true to be answer.

A. x is odd and y is even. - x = 3 , y = 2 -- this satisfies the question stem but x =4 and y=3 also satisfies the question stem but y is odd.
B. x is odd and y is odd. -- x = 3 , y=5 => you can take odd even examples in this too.
C. x is even and y is odd. => similar to A
D. x<y => x=2 , y=3 or x=4, y=3
E. None of the above> implies none must be true.
hope it helps
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Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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12 Feb 2017, 21:25
Bunuel wrote:
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

Bunuel, The question wants us to try the options by picking numbers.
But, I think the question should mention x and y are POSITIVE integers. If we say that x and y are (just) integers, y can be 0. In that case x/y is Not a Number.

Please correct me if I am wrong.
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Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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13 Feb 2017, 13:00
1
Hi All,

This question can be solved by TESTing VALUES (and coming up with examples that DISPROVE each of the wrong answer choices). Since X and Y are INTEGERS and X/Y is NOT an integer, you could quickly come up with a variety of examples of what X and Y COULD be, including....

1/2, 2/3, 3/2, 4/3, 6/4, 7/3, etc.

As such, you can quickly eliminate each of the first 4 answer choices.

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Joined: 22 Nov 2016
Posts: 13
Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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31 Mar 2017, 11:10
Hi rakaisraka,
According to option A, X is odd and Y is even
We dont have any such examples through which we can get integer value, then how can we say that it is not always true, please explain
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Joined: 22 May 2017
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Re: If x and y are integers, and x/y is not an integer then which of the [#permalink]

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24 Mar 2018, 14:06
rakaisraka wrote:
Shruti0805 wrote:
rakaisraka wrote:
I think E bcz with examples we can prove all no must be true.

Hi. I don't understand how can you divide an Odd Number by an even no. and get an integer value.

Hi,
as per question stem x and y are integers but x/y is not integer. This is must be true each statement has to be true to be answer.

A. x is odd and y is even. - x = 3 , y = 2 -- this satisfies the question stem but x =4 and y=3 also satisfies the question stem but y is odd.
B. x is odd and y is odd. -- x = 3 , y=5 => you can take odd even examples in this too.
C. x is even and y is odd. => similar to A
D. x<y => x=2 , y=3 or x=4, y=3
E. None of the above> implies none must be true.
hope it helps

Still not clear!!!
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If x and y are integers, and x/y is not an integer then which of the [#permalink]

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24 Mar 2018, 14:22
Bunuel wrote:
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

Since we have a "must be true" question and the following details: x,y are integers and $$\frac{x}{y}$$ is not an integer.

If we can provide an alternative case for each of the answer options,we will end up with Option E as the answer!

Consider the following cases

1. x=6(even), y=4(even) and $$\frac{x}{y} = \frac{6}{4}$$ is not an integer
This eliminates Option A,B, and C.

2. x=4 and y=6. $$\frac{x}{y} = \frac{4}{6}$$ and is not an integer
This eliminates Option D.

Therefore, we are left with Option E(None of the above) and it is our answer!
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If x and y are integers, and x/y is not an integer then which of the   [#permalink] 24 Mar 2018, 14:22
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