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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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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, 08:45
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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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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, 09:05
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, 09:54
X/Y not integer,either x<y or x, y are co prime ... No musts ... E

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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, 23:01
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, 03:26
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, 03:56
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, 20:25
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, 12:00
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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Special Offer: Save $75 + GMAT Club Tests Free Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/ *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Intern 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] ### Show Tags 31 Mar 2017, 10:10 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 Intern Joined: 22 May 2017 Posts: 5 Re: If x and y are integers, and x/y is not an integer then which of the [#permalink] ### Show Tags 24 Mar 2018, 13:06 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. Could you please explain ? 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!!! Experts please help with a detailed solution... Senior PS Moderator Joined: 26 Feb 2016 Posts: 3339 Location: India GPA: 3.12 If x and y are integers, and x/y is not an integer then which of the [#permalink] ### Show Tags 24 Mar 2018, 13:22 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! _________________ You've got what it takes, but it will take everything you've got Intern Joined: 05 Sep 2016 Posts: 29 Location: India Concentration: General Management, Operations WE: Engineering (Energy and Utilities) Re: If x and y are integers, and x/y is not an integer then which of the [#permalink] ### Show Tags 11 Aug 2018, 20:04 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 A. Case A: X=5,Y=2 X/Y-not integer, BUT, if x=5,y=0( remember 0 is also an even number), then,x/y=undefined . B. X=5,Y=5, X/Y=Int. doesn't satisfy condition, X=5,Y=7 X/Y= not an integer, satisfy condition. C.X=12,Y=3 X/Y=Int. , X=12, Y=5 X/Y=not an integer. D. For not only X<Y but also For X>Y condition X/Y=not Int. can be satisfied. E. ANSWER. Intern Joined: 05 Sep 2018 Posts: 4 Re: If x and y are integers, and x/y is not an integer then which of the [#permalink] ### Show Tags 08 Oct 2018, 12:56 Shouldn't the answer be a? x and y are integers but x/y is not an integer (its not given that x/y is a fraction, just not an integer) a. x=1(odd), y=0(even) --> not defined (not an integer), condition holds. b. both odd --> can be an integer, eliminated. c. x=0 (even), y=1 (odd) ---> 0 (integer), eliminated. d. x<y--> x=0, y=1 ---> 0 (integer), eliminated. e. clearly a must be true so eliminated. EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 13536 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If x and y are integers, and x/y is not an integer then which of the [#permalink] ### Show Tags 08 Oct 2018, 13:48 Hi prateek25, When a Quant question asks "which of the following must be true" what it's really asking is "which of the following is ALWAYS true no matter how many different examples you can come up with?" Since X and Y are integers and X/Y is NOT an integer, we can come up with lots of examples that fit these details: 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 (including Answer A). GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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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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08 Oct 2018, 14:13
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

$$x,y\,\,{\text{ints}}$$

$$\frac{x}{y} \ne \operatorname{int}$$

$$?\,\,\,:\,\,\,{\text{true}}\,$$

To prove that a certain statement is false, give a counterexample to it!

(x,y) = (2,3) refutes statements (A), (B)

I explain: 2, 3 (for x and y respectively) are integers and 2/3 is not an integer. Therefore these choices are viable.
From the fact that x is NOT odd, (A) and (B) are refuted (even without looking at y)!

(x,y) = (3,2) refutes statements (C) and (D)

I explain: 3, 2 (for x and y respectively) are integers and 3/2 is not an integer. Therefore these choices are viable.
From the fact that x is NOT even, (C) is refuted (even without looking at y).
From the fact that x is NOT less than y, (D) is refuted.

The correct answer is therefore (E).

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
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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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09 Oct 2018, 05:14
Top Contributor
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

The key word here is must
So, if we can find a case in which an answer choice is NOT true, then we can eliminate that answer choice.

A. x is odd and y is even.
x = 3 and y = 11 satisfies the condition that x/y is not an integer
Since y is NOT even, we can ELIMINATE A

B. x is odd and y is odd.
x = 4 and y = 6 satisfies the condition that x/y is not an integer
Since x is NOT odd, we can ELIMINATE B

C. x is even and y is odd.
x = 5 and y = 6 satisfies the condition that x/y is not an integer
Since x is NOT even, we can ELIMINATE C

D. x < y
x = 5 and y = 2 satisfies the condition that x/y is not an integer
Since x > y, we can ELIMINATE D

Cheers,
Brent
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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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09 Oct 2018, 06:58
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

Plug in numbers to check -

(A) x = 3 and y = 2 ; x/y = 3/2 (Possible)
(B) x = 5 and y = 7 ; x/y = 5/7 (Possible)
(C) x = 2 and y = 3 ; x/y = 2/3 (Possible)
(D) x = 2 and y = 3 ; x/y = 2/3 (Possible)

(E) Answer must be (E) as none fits in perfectly....

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Re: If x and y are integers, and x/y is not an integer then which of the   [#permalink] 09 Oct 2018, 06:58
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