Problem Solving

is x^2 + y even? x and y are positive

1) x, y are consecutive integers
2) x + 2y = 1

OA D

What you have to know is that x^2 will "follow" x in being odd or even. This is easy to understand if you look at it like this:
a. x^2 = x*x - if x is even, then x*x will also be even, since you have (even)*(even)
b. x^2 = x*x - if x is odd, then x*x will also be odd, since it's (odd)*(odd)

1. If x and y are consecutive, this means that one will be odd and one will be even. Since x^2 is either odd or even depending on whether x is odd or even. So you get that x^2 + y = odd + even (not necessarily in this order), which will be odd.
2. x + 2y = 1 tells us that x is odd, since 2y is even. The only odd integer to fit this will be 1, which gives us 2y = 0 and y = 0. This means that x^2 + y = 1, which is odd. However, I'm kindda intrigued by that "x and y are positive" thing. IMHO, it should be non-negative instead of postivie.
But maybe I'm missing smth....
Oh well, anyway, my answer would be D

DanaJ wrote:What you have to know is that x^2 will "follow" x in being odd or even. This is easy to understand if you look at it like this:
a. x^2 = x*x - if x is even, then x*x will also be even, since you have (even)*(even)
b. x^2 = x*x - if x is odd, then x*x will also be odd, since it's (odd)*(odd)

1. If x and y are consecutive, this means that one will be odd and one will be even. Since x^2 is either odd or even depending on whether x is odd or even. So you get that x^2 + y = odd + even (not necessarily in this order), which will be odd.
2. x + 2y = 1 tells us that x is odd, since 2y is even. The only odd integer to fit this will be 1, which gives us 2y = 0 and y = 0. This means that x^2 + y = 1, which is odd. However, I'm kindda intrigued by that "x and y are positive" thing. IMHO, it should be non-negative instead of postivie.
But maybe I'm missing smth....
Oh well, anyway, my answer would be D

guys,

Cannot we use +ve fractions here for the 2nd statement? As the question only specify +ve .

like x = 1/2 and y = 1/4

if we use x = 1/2 and y = 1/4, then we get x^2 + y equal to 1/2.
Can fractions be even or odd numbers?

hardik.jadeja wrote:if we use x = 1/2 and y = 1/4, then we get x^2 + y equal to 1/2.
Can fractions be even or odd numbers?

1/2 = .5 which is odd
1/4 = .25 which is odd

Thus we still get that both parts are sufficient to meet the condition.

I wonder what the source of this question is, as usually the gmat keeps both statement without having a contradiction between them. In this question, in the first statement we are given the information that X and Y are integers. The second statement is not possible with X and Y positive integers. What's your opinion:

shulapa wrote:I wonder what the source of this question is, as usually the gmat keeps both statement without having a contradiction between them. In this question, in the first statement we are given the information that X and Y are integers. The second statement is not possible with X and Y positive integers. What's your opinion:

My opinion: this is a horrible question.

As Shulapa notes, on the actual GMAT the two statements will NEVER contradict each other.

In this question, there are no values for x and y that fit both statements. If one tried to combine the statements, there would be no possible answer to the question. "No possible answer" doesn't mean "insufficient", it means "this question sucks and don't worry about it, you'll never see it on Test Day".

For all posters: please cite the source of your question so we know if we should take it seriously. I'd be vary wary of ANY question coming from the same source as this one.

As an aside, please make sure you post questions in the relevant sub-forum. This thread should be in the Data Sufficiency section.

shulapa wrote:I wonder what the source of this question is, as usually the gmat keeps both statement without having a contradiction between them. In this question, in the first statement we are given the information that X and Y are integers. The second statement is not possible with X and Y positive integers. What's your opinion:

you don't find these kind of questions in real exam..

Two statements can't contradict each other when Answer is D..

comming to the question: (if we forget the contradiction part)

2nd statment.

x+2y =1

0<y <1/2 1/2<x<1

clearly x^2+y <1.. not even integer.. so. it is not even number.

D is the answer.