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If x and y are integers, is x an even integer?

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anilnandyala
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If x and y are integers, is x an even integer? [#permalink] If x and y are integers, is x an even integer?   09 Jan 2011, 08:45
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If x and y are integers, is x an even integer?

(1) x(y + 5) even integer
(2) 6y^2 + 41y + 25 is even integer­
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Bunuel
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Re: If x and y are integers, is x an even integer? [#permalink] If x and y are integers, is x an even integer?   09 Jan 2011, 09:07
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anilnandyala
if x and y are integers , is x an even integer

a) x(y+5) even integer
b) 6y^2+41y+25 is even integer

If x and y are integers , is x an even integer

(1) x(y+5) even integer --> in order the product of the integers to be even at least one of the multiples must be even --> either \(x=even\) and in this case \(y\) can be even or odd, or \(y=odd\) (in order \(y+5\) to be even) and in this case \(x\) can be even or odd. Not sufficient.

(2) 6y^2+41y+25 is even integer --> \(6y^2\) is even in any case, so \(41y+25=even\) --> \(41y+25=odd*y+odd=even\) --> \(y=odd\), still not sufficient, as no info about \(x\).

(1)+(2) As from (2) \(y=odd\) then from (1) it's not necessary \(x\) to be even. Not sufficient.

Answer: E.
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micahman
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Re: If x and y are integers, is x an even integer? [#permalink] If x and y are integers, is x an even integer?   28 Jun 2024, 20:28
if y = odd then x (odd ) = even ... x must be even... what am I missing?
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prabhanjan19
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Re: If x and y are integers, is x an even integer? [#permalink] If x and y are integers, is x an even integer?   03 Jul 2024, 21:57
Bunuel

Um, I thought 'a' is sufficient enough!

Consider the statement x(y+5)

i. If y is odd, then y+ 5 is even --> x(y+5) becomes x * even = even --> x here has to be even.

ii. If y is even, then y+5 is odd --> x(y+5) becomes x * odd = even --> For this to be true, x has to be even.

Why isn't the answer 'A'?­
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Re: If x and y are integers, is x an even integer? [#permalink] If x and y are integers, is x an even integer?   03 Jul 2024, 22:44
prabhanjan19
Bunuel

Um, I thought 'a' is sufficient enough!

Consider the statement x(y+5)

i. If y is odd, then y+ 5 is even --> x(y+5) becomes x * even = even --> x here has to be even.

ii. If y is even, then y+5 is odd --> x(y+5) becomes x * odd = even --> For this to be true, x has to be even.

Why isn't the answer 'A'?­

In your first scenario, if (y+5) is even, x does not have to be even for the product to be even.

X = odd
Odd * even = even

X can be even or odd, so you get a YES/NO for the stem; therefore statement 1 is insufficient alone.

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Re: If x and y are integers, is x an even integer? [#permalink]
03 Jul 2024, 22:44
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Bunuel
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