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Stat 1: odd + even = even ...not this..we have to get odd... or even+even = even ...this can be both y and y^5 integer type is same. or odd+even = even...not this or even + odd = odd...this can be both y and y^5 integer type is same...x can be even...Sufficient..
Stat 2: x = 2y...whatever the value of y be...x will always even..since y is multiplied by 2.
Re: If x and y are integers, is x even?
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26 Sep 2016, 06:27
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Top Contributor
Bunuel wrote:
If x and y are integers, is x even?
(1) x + y = y⁵
(2) x + y = 3y
Some important rules: 1. ODD +/- ODD = EVEN 2. ODD +/- EVEN = ODD 3. EVEN +/- EVEN = EVEN
4. (ODD)(ODD) = ODD 5. (ODD)(EVEN) = EVEN 6. (EVEN)(EVEN) = EVEN
Target question:Is x even?
Given: x and y are integers
Statement 1: x + y = y⁵ Subtract y from both sides to get: x = y⁵ - y Let's examine the two possible cases: y is EVEN and y is ODD case a: y is ODD. So, x = y⁵ - y = ODD⁵ - ODD = ODD - ODD = EVEN case b: y is EVEN. So, x = y⁵ - y = EVEN⁵ - EVEN = EVEN - EVEN = EVEN In both possible cases, x is even. So, x MUST be even. Since we can answer the target question with certainty, statement 1 is SUFFICIENT
Statement 2: x + y = 3y Subtract y from both sides to get: x = 2y If x equals the product of 2 and some integer, then we can be certain that x is even Since we can answer the target question with certainty, statement 2 is SUFFICIENT
Re: If x and y are integers, is x even?
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26 Sep 2016, 09:49
Bunuel wrote:
If x and y are integers, is x even?
(1) x+y=y^5
(2) x+y=3y
Statement 1: Sufficient
x = y^5-y => x= y(y^4-1)
Assuming y as even : y^4 - 1 = EVEN - ODD = ODD y(y^4-1) = EVEN*ODD =EVEN therefore x is even Assuming y as odd : y^4 - 1 = ODD - ODD = EVEN y(y^4-1) = ODD*EVEN =EVEN therefore x is even
Statement 2: Sufficient
x+y=3y can be re-written as x = 2y => x is divisible by 2 therefore x is even
Answer is D __________________________________ +1 Kudos if you like the solution
Re: If x and y are integers, is x even?
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19 Nov 2016, 08:08
Here we need to get whether x is even or not Statement 1 x+y=y^5 hence x=y^5-y here if y=odd x=odd-odd=even if y=even x=even-even=even Hence x is always even hence sufficient Statement 2 x+y=3y x=2y as y is an integer => 2y is always even Hence Sufficient Hence D
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