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Math Expert V
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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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Question Stats: 45% (01:18) correct 55% (01:14) wrong based on 238 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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If x and y are integers, and x/y is not an integer then which of the  [#permalink]

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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

IMO Answer could be 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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X/Y not integer,either x<y or x, y are co prime ... No musts ... E

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Manager  B
Joined: 27 Aug 2015
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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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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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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 ? Manager  B
Joined: 27 Aug 2015
Posts: 86
Re: If x and y are integers, and x/y is not an integer then which of the  [#permalink]

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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
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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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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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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]

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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.

GMAT assassins aren't born, they're made,
Rich
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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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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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Re: If x and y are integers, and x/y is not an integer then which of the  [#permalink]

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

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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.
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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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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.
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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]

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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
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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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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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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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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]

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