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Number theory

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by harpritsn » Fri Aug 24, 2012 6:14 am
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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by prat_agl » Fri Aug 24, 2012 7:22 am
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.
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by vk_vinayak » Fri Aug 24, 2012 7:58 am
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.
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by vk_vinayak » Fri Aug 24, 2012 8:02 am
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.
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.
- VK

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by Ian Stewart » Fri Aug 24, 2012 3:18 pm
vk_vinayak wrote:
Since it is given that x is an integer, we can discard E, which says x is some sort of fraction.
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.

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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by subhash.sonu39 » Fri Aug 24, 2012 11:20 pm
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.
I think you are right, D will be a right answer because of this equation 2y = x.
properties of real numbers
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by prat_agl » Fri Aug 24, 2012 11:33 pm
if y is -1 then x is -2.
Can we consider a -ve number as even or odd?
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by vk_vinayak » Sat Aug 25, 2012 2:38 am
prat_agl wrote:if y is -1 then x is -2.
Can we consider a -ve number as even or odd?
Yes. Negative integers can be either EVEN or ODD.
Eg: -1, -3, -17, 1, 3, 17 => ODD.
-2, -8, 10, 44, 98 => EVEN
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