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If x and y are integers and x^2 + y^2 is odd, which of the following
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16 Oct 2019, 21:20
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78% (00:55) correct 22% (01:04) wrong based on 73 sessions
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Competition Mode Question 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) \(xy\)
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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
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.
The right answer is therefore E.



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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, 21:35
\(x^2+y^2\) is odd; Either x is odd and y is even, or x is even and y is odd.
A. x can be odd or even, as explained above.
B. y can be odd or even, as explained above.
C. x+y must be odd(O+E or E+O)
D. xy+y can be even or odd (E+O or E+E)
E. xy must be even (E*O or O*E)
E



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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, 21:42
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
IMO Option E



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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, 21:55
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 Posted from my mobile device
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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, 22:27
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



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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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17 Oct 2019, 02:22
Given: x and y are integers => (x,y)= 0, +I, I x^2 + y^2 = odd => x and y have opposite evenodd 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)
5. xy  always even Correct answer E



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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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17 Oct 2019, 03:13
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 \(x^2+y^2=odd…e+o=odd\) (A) x: x=(o,e) (B) y: y=(o,e) (C) x+y: o+e=o (D) xy+y: y(x+1)=o(e+1)=o(o)=o (E) xy: oe=e Answer (E)



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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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17 Oct 2019, 04:56
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.
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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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17 Oct 2019, 06:12
for the given condition to to be valid of x2+y2 is odd either of them has to be even and odd so IMO E ; xy will be even
If x and y are integers and x2+y2 is odd, which of the following must be even?
(A) x (B) y (C) x+y (D) xy+y (E) xy



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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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17 Oct 2019, 06:36
For the x^2 + y^2 to be odd, x,y must be odd and even in either combination
So only xy values will be even
OA:E
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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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17 Oct 2019, 06:59
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



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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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17 Oct 2019, 07:03
x and y are integers \(x^{2}+ y^{2}\)— odd number
—> In order \(x^{2}+ y^{2}\) to be odd number, one of x and y must be odd integer.
Which of the following must be even?
A) x could be odd
B) y could be odd
C) x+y — as above mentioned, odd+even=odd number
D) xy+y= y*(x+1) could be even or odd number —> if x=0(even) and y=1 1*(0+1)=1 (odd number)
E) xy =even*odd= even ( always true)
The answer is E
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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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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.



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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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17 Oct 2019, 10:04
If x and y are integers and \(x^2+y^2\) is odd, which of the following must be even? Expression \(x^2+y^2\) is odd .e. o.o + e.e OR e.e or o.o. Hence if x is odd then y is even and viceaversa. Let's check (A) x It can be ether odd or even. (B) y Same as above (C) x+y o + e OR e + o. Always Odd. (D) xy+y o.e + e = e OR e.o + o = o. Either even or Odd case. (E) xy o.e OR e.o. Both cases are even. Answer E.
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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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17 Oct 2019, 10:22
X^2 + y^2 = odd This implies => odd + even = odd.
Means one if them must be ODD and one of them must be EVEN. Since (odd)^2 = odd and (even)^2 = even.
Implies xy = even!
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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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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




Re: If x and y are integers and x^2 + y^2 is odd, which of the following
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