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Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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16 Oct 2019, 21:31
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That x^2 + y^2 is even, given x and y are integers, implies either x is even and y is odd or x is odd and y is even. We can't be certain which of the two integers is odd and which is even. But what we can be certain of is that when we multiply x and y, it will be even.
So only option E must be an even number considering xy results in an even number irrespective of which of the two integers is even.
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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16 Oct 2019, 21:42
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x^2 + y^2 is odd only when one is definitely even and the other one definitely odd
(A) x --> Can be even or Odd --> NO
(B) y --> Can be even or Odd --> NO
(C) x+y --> Even + Odd or Odd + Even = Odd always --> NO
(D) xy+y --> x(y + 1) --> Case 1: If x = odd, y = even ; x(y + 1) = odd*odd = Odd --> Case 2: If x = even, y = odd ; x(y + 1) = even*even = Even --> Two outcomes are possible --> NO
(E) xy = odd*even or even*odd = Even always --> YES
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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16 Oct 2019, 21:55
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Just the sum of two odd and even numbers will be odd.so, one of thr x² or y² are odd. We know just the odd number to the power of 2 will be odd. So, one of the x or y must be odd and their sum will be odd too. But their product will be surelly even. Option E
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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16 Oct 2019, 22:27
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If x and y are integers and x2+y2 is odd, which of the following must be even?
If x2 + y2 is odd, this can be inferred that one of x2 and y2 is odd, and another is even. So, we'll get either x is odd, y is even OR x is even, y is odd.
Now, let's see each answer choice on which choice yield EVEN
(A) x - can be both even/odd (B) y - can be both even/odd (C) x+y - definitely odd: since if x is even, y is odd and x+y = odd OR if y is even, x is odd, x+y = odd (D) xy+y can be both even/odd, if x is even, y is odd; xy+y = odd OR if y is even, x is odd; xy+y = even (E) xy - one of x and y needs to be even, which even * any number = even - CORRECT answer choice
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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17 Oct 2019, 02:22
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Given: x and y are integers => (x,y)= 0, +I, -I x^2 + y^2 = odd => x and y have opposite even-odd nature. (e+ o => o)
Q Type: Must be true
1. x - can be even or odd 2. y - can be even or odd 3. x+ y => odd (given) 4. xy+ y ----- can be even or odd if x=2, y =3 ,then xy+ y = 6+3 = 9 (odd) if x=3, y=2, then xy+ y = 6+ 2 = 8 (even)
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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17 Oct 2019, 04:56
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Imo. E
If x and y are integers and x^2+y^2 is odd, which of the following must be even?
x^2+y^2 = odd means one is even and another one is odd, but can't say which one is odd or even. Hence, A & B out.
(A) x - may be even or odd (B) y - may be even or odd (C) x+y - must be odd (D) xy+y - xy = even & y = even or odd. So, xy +y = even or odd (E) xy - must be even.
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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17 Oct 2019, 06:59
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Raising an integer by any power will not change its odd/even property. Also note, Odd + Odd = Even Even + Even = Even Even + Odd = Odd So in order for x^2 + y^2 to be odd, one of the variables has to even and one has to be odd. Using numbers we can start by x = 2 and y = 3 or x = 3 and y = 2.
A.) x = 2, yes if x = 2 - no if x = 3 (incorrect as it could or could not be even) B.) same as above C.) x + y, 2 + 3 = 5 which is odd (incorrect) D.) xy + y - if x = 2/y = 3, 2(3) + 3 = 6 + 3 = 9 (ODD), if x = 3/y = 2, 3(2) + 2 = 6 + 2 = 8, (EVEN) (could be either so incorrect) E.) xy - 2(3) = 6 (EVEN)
Note, Odd * Odd = Odd Even * Odd = Even Even * Even = Even
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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17 Oct 2019, 07:45
Quote:
If x and y are integers and x^2+y^2 is odd, which of the following must be even?
(A) x (B) y (C) x+y (D) xy+y (E) xy
x^2+y^2= Odd, is possible in two case given below: 1. x is odd and y is even 2. x is even and y is odd.
A. Wrong. x can be even or odd. B. Wrong. y can be even or odd. C. Wrong. In both the cases, x+y is odd. D. Wrong. xy+y=Even*odd+Odd=Even+odd=Odd or Odd*even+even=Even. E. Correct.
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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17 Oct 2019, 21:06
If x and y are integers and x^2+y^2 is odd, which of the following must be even?
If x and y are integers and x^2+y^2 is odd, meaning either one of them must be even and the other must be odd. if x is odd, y is even if x is even, y is odd
(A) x; can be either even or odd depends on y (B) y; can be either even or odd depends on x (C) x+y; odd plus even is odd therefore not correct (D) xy+y; if x is odd the equation is even if x is even the equation is odd therefore not correct (E) xy; odd multiply even is always even yay correct
therefore E
gmatclubot
Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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17 Oct 2019, 21:06
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78% (00:55) correct 
