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If x and y are integers, is the sum of x and y even?
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11 Apr 2016, 04:07
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If x and y are integers, is the sum of x and y even? (1) \(x^2\) = \(y^2\) (2) \(x^3\) = \(y^3\)
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Re: If x and y are integers, is the sum of x and y even?
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11 Apr 2016, 11:25
find out x+y= even or not. 1. x^2=y^2 , by rearranging, we can write this as (x+y)(xy)=0; x+y=0 and 0 is even number so sufficient. 2. x^3y^3 =0 by rearranging we do not about x+y so not sufficient.
Hence answer is A.



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Re: If x and y are integers, is the sum of x and y even?
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Updated on: 14 Apr 2016, 21:14
Bunuel wrote: If x and y are integers, is the sum of x and y even?
(1) x^2 = y^2 (2) x^3 = y^3 x + y = even? Statement 1: x^2 = y^2 Case 1: Either x = y (x = 2 and y = 2) or x = y (x = 2 and y = 2) Hence x + y = 2x or 0 Yes, the sum is even Sufficient Statement 2: x^3 = y^3 x = y (x = 2 and y = 2 OR x = 2 and y = 2) Therefore x + y = 2x Yes, the sum is even. Sufficient Option D



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Re: If x and y are integers, is the sum of x and y even?
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14 Apr 2016, 02:12
lipsi18 wrote: find out x+y= even or not. 1. x^2=y^2 , by rearranging, we can write this as (x+y)(xy)=0; x+y=0 and 0 is even number so sufficient. 2. x^3y^3 =0 by rearranging we do not about x+y so not sufficient.
Hence answer is A. Hi lipsi18, In the statement 1, either of (x+y) or (xy) can be zero. Hence we cannot say that x + y = 0



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Re: If x and y are integers, is the sum of x and y even?
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14 Apr 2016, 09:06
Is it B ? If so, will provide my line of reasoning.



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Re: If x and y are integers, is the sum of x and y even?
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14 Apr 2016, 21:13
subhamoycomputer wrote: Is it B ? If so, will provide my line of reasoning. Hi subhamoycomputer, The correct option here should be D. However do post your reasoning as to why you thing option A is insufficient.



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Re: If x and y are integers, is the sum of x and y even?
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14 Apr 2016, 21:25
If x and y are integers, is the sum of x and y even?
(1) x^2 = y^2 (2) x^3 = y^3
x + y even?
Statement 1:
x^2 = y^2. This implies x = y or x =y.
Either way x+y will be even (0 or 2x).
Statement 2:
X^3 = y^3.
Implies x = y.
So x + y is 2x, which is even.
So each statement is individually sufficient.
Answer D.



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Re: If x and y are integers, is the sum of x and y even?
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15 Apr 2016, 05:03
Here in both the cases we can say that both x and y must have the same odd/even nature hence x+y=even hence D
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Re: If x and y are integers, is the sum of x and y even?
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16 Apr 2016, 02:43
If x and y are integers, is the sum of x and y even? (1) x^2 = y^2 (2) x^3 = y^3 There are 2 variables (x and y) in the original condition. In order to match the number of variables to the number of equations, we need 2 more equations. Since the condition 1) and the condition 2) each has 1 equation, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get 1)=2), from which we can obtain x=y=odd or x=y=even. The answer is always yes and the conditions are sufficient. Therefore, the correct answer is D. For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.
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Re: If x and y are integers, is the sum of x and y even?
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18 Apr 2016, 03:31
Bunuel wrote: If x and y are integers, is the sum of x and y even?
(1) x^2 = y^2 (2) x^3 = y^3 The Answer is D..Check for pairs (0,0) ...(1,1)....(1,1)
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Re: If x and y are integers, is the sum of x and y even?
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18 Apr 2016, 03:44
Balajikarthick1990 wrote: Bunuel wrote: If x and y are integers, is the sum of x and y even?
(1) x^2 = y^2 (2) x^3 = y^3 The Answer is D..Check for pairs (0,0) ...(1,1)....(1,1) You are correct... But for (1), check for x=y.. May be important in some other Q x=1, y=1 ; x=1, y=1; x=1,y=1; x=1, y=1
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Re: If x and y are integers, is the sum of x and y even?
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18 Apr 2016, 18:29
Let me understand, is 0 considered even?
Because if we use x = y Then the answer would be 0 for option A



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Re: If x and y are integers, is the sum of x and y even?
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18 Apr 2016, 20:07
douglasvg wrote: Let me understand, is 0 considered even?
Because if we use x = y Then the answer would be 0 for option A hi, 0 is EVEN but it is neither NEGATIVE nor POSITIVE...
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Re: If x and y are integers, is the sum of x and y even?
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20 Dec 2018, 07:59
Bunuel gmatbusters VeritasKarishma chetan2uCould you share your approach? Q is asking: Are both x and y even or odd? For St 1, I took x = y which is same as: x = y and x = y or xy = 0 or x + y = 0 Hence implying, both x and y have to be even/odd. What is St 2 saying? How do I interpret odd powers of integer?
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Re: If x and y are integers, is the sum of x and y even?
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20 Dec 2018, 08:20
1) x²=y² So, x²y²=0 So, (x+y)(xy)=0 Either x+y=0 where 0 is even. Or xy=0 where 0 is even. If the difference of two integers is even, their sum is also even.
So statement (1) is sufficient.
(2) Cube of a number preserves the sign. So x³=y³ means x=y, say x=y=a So the sum will always be even =2a.
So statement (2) is sufficient.
Both are statements alone are sufficient so option D is the correct answer
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If x and y are integers, is the sum of x and y even?
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20 Dec 2018, 08:24
if \(x^ a = y ^a\), where a is an even integer we get x = +/ y
But, if \(x^ b = y ^b\), where b is an odd integer we get x = y Good news, odd power are even easier to handle Hence for Statement 2, sum of x and y = 2x or 2y = even adkikani wrote: Bunuel gmatbusters VeritasKarishma chetan2uCould you share your approach? Q is asking: Are both x and y even or odd? For St 1, I took x = y which is same as: x = y and x = y or xy = 0 or x + y = 0 Hence implying, both x and y have to be even/odd. What is St 2 saying? How do I interpret odd powers of integer?
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If x and y are integers, is the sum of x and y even?
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