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If (x + y)/(x − y) = 3 and x and y are integers, then which one of the

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If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 17 Jun 2017, 05:55
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A
B
C
D
E

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If \(\frac{x + y}{x − y} = 3\) and x and y are integers, then which one of the following must be true?

(A) x is divisible by 4
(B) y is an odd number
(C) y is an even integer
(D) x is an even number
(E) x is an irreducible fraction

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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 17 Jun 2017, 06:02
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Bunuel wrote:
If \(\frac{x + y}{x − y} = 3\) and x and y are integers, then which one of the following must be true?

(A) x is divisible by 4
(B) y is an odd number
(C) y is an even integer
(D) x is an even number
(E) x is an irreducible fraction


\(\frac{x + y}{x − y} = 3\)
x + y = 3x - 3y
2x = 4y
x = 2y

(A) x is divisible by 4 - Not necessarily true
(B) y is an odd number - Not necessarily true. Y could be either odd or even
(C) y is an even integer - Not necessarily true. Y could be either odd or even
(D) x is an even number - True since Y is multiplied by an even no
(E) x is an irreducible fraction - Not correct

Hence Answer D
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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 17 Jun 2017, 06:05
Since \(\frac{x + y}{x − y} = 3\)
x + y = 3x - 3y
2x = 4y -> x = 2y

The only condition which must be true is that x is an even number because even * odd/even = even
Hence, Option D is the answer
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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 17 Jun 2017, 08:08
Bunuel wrote:
If \(\frac{x + y}{x − y} = 3\) and x and y are integers, then which one of the following must be true?

(A) x is divisible by 4
(B) y is an odd number
(C) y is an even integer
(D) x is an even number
(E) x is an irreducible fraction


\(\frac{x + y}{x − y} = 3\)

Or, \(3x + 3y = x - y\)

Or, \(2x = -4y\)

Or, \(x = -2y\)

Thus, we have x must be an even number, hence correct answer must be (D)
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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 23 Jun 2017, 07:26
Since x+yx−y=3x+yx−y=3
x + y = 3x - 3y
2x = 4y -> (x = 2y)

The only condition which must be true is that x is an even number because even * odd/even = even
Hence, Option D is the answer
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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 26 Jun 2017, 17:59
Bunuel wrote:
If \(\frac{x + y}{x − y} = 3\) and x and y are integers, then which one of the following must be true?

(A) x is divisible by 4
(B) y is an odd number
(C) y is an even integer
(D) x is an even number
(E) x is an irreducible fraction


Let’s simplify the given equation:

x + y = 3(x - y)

x + y = 3x - 3y

4y = 2x

2y = x

So, we see that x is an integer multiple of 2, and thus it’s an even number.

Answer: D
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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 26 Jun 2017, 18:09
Top Contributor
Bunuel wrote:
If \(\frac{x + y}{x − y} = 3\) and x and y are integers, then which one of the following must be true?

(A) x is divisible by 4
(B) y is an odd number
(C) y is an even integer
(D) x is an even number
(E) x is an irreducible fraction


Others have provided great/eloquent solutions.
Here's the brute force method (which could take a while).

We're looking for a statement that MUST be true, so if we can find a situation in which the statement is not true, we can eliminate it.

(A) x is divisible by 4
If x = 6 and y = 3, then it is true that (x+y)/(x-y) = 3.
Here, x is NOT divisible by 4.
So, ELIMINATE A

(B) y is an odd number
If x = 12 and y = 6, then it is true that (x+y)/(x-y) = 3.
Here, y is NOT an odd number
So, ELIMINATE B

(C) y is an even integer
If x = 6 and y = 3, then it is true that (x+y)/(x-y) = 3.
Here, y is NOT an even integer
So, ELIMINATE C

(D) x is an even number
Can't disprove....keep moving

(E) x is an irreducible fraction
If x = 6 and y = 3, then it is true that (x+y)/(x-y) = 3.
Here, x is NOT an irreducible fraction
So, ELIMINATE E

Answer:

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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the  [#permalink]

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New post 26 Aug 2018, 13:40
I picked numbers for x and y: 10+5/10-5 =3. Only D was true.
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Re: If (x + y)/(x − y) = 3 and x and y are integers, then which one of the &nbs [#permalink] 26 Aug 2018, 13:40
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