If (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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Number theory
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prat_agl
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The equation will become --
x+y = 3x-3y
or 2y = x
Now check the answers.
A) not necessary. If Y = 1 x is not divisible by 4.
B) Not necessary. Y can be odd or even.
C) Not necessary. Y can be odd as well.
D) Not necessary. if Y is -ve, then X is also -ve number.
E) Since Y is an integer, X is 2Y which will be an integer. correct answer.
x+y = 3x-3y
or 2y = x
Now check the answers.
A) not necessary. If Y = 1 x is not divisible by 4.
B) Not necessary. Y can be odd or even.
C) Not necessary. Y can be odd as well.
D) Not necessary. if Y is -ve, then X is also -ve number.
E) Since Y is an integer, X is 2Y which will be an integer. correct answer.
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vk_vinayak
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Solving the equation we get x=2y. Since it is given that both x and y are integers, x MUST be even.
Ans is D.
Ans is D.
- VK
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vk_vinayak
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Negative integers CAN be even (as long as they are multiple of 2). Since it is given that x is an integer, we can discard E, which says x is some sort of fraction.prat_agl wrote:The equation will become --
x+y = 3x-3y
or 2y = x
Now check the answers.
A) not necessary. If Y = 1 x is not divisible by 4.
B) Not necessary. Y can be odd or even.
C) Not necessary. Y can be odd as well.
D) Not necessary. if Y is -ve, then X is also -ve number.
E) Since Y is an integer, X is 2Y which will be an integer. correct answer.
- VK
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Ian Stewart
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You can write integers as fractions if you like. The integer 2 can be written as the "irreducible fraction" 2/1, for example, or as the reducible fraction 6/3.vk_vinayak wrote:
Since it is given that x is an integer, we can discard E, which says x is some sort of fraction.
And that's why answer choice E here doesn't make any mathematical sense, since no matter what x is, it can be written as a fraction, and it can be written as a non-fraction (as a decimal, say). So while it certainly must be true in this question that x is even, and D must be true, it really isn't possible to say one way or the other about E, because it's not at all clear what answer choice E is even supposed to mean. I'm not sure where this question is from, but it's certainly not a real GMAT question.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com
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subhash.sonu39
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I think you are right, D will be a right answer because of this equation 2y = x.vk_vinayak wrote:Solving the equation we get x=2y. Since it is given that both x and y are integers, x MUST be even.
Ans is D.
properties of real numbers
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vk_vinayak
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Yes. Negative integers can be either EVEN or ODD.prat_agl wrote:if y is -1 then x is -2.
Can we consider a -ve number as even or odd?
Eg: -1, -3, -17, 1, 3, 17 => ODD.
-2, -8, 10, 44, 98 => EVEN
- VK
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