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# If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2

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Re: If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2 [#permalink]
Bunuel wrote:
If x and y are integers, is $$3x^4 + 4y$$ even?

(1) $$x^3$$ is even

(2) $$y^{2x} + 3$$ is even

Are You Up For the Challenge: 700 Level Questions

target $$3x^4 + 4y$$ even?
possible when x is even
#1
$$x^3$$ is even
would be possible only when x is even so sufficient
#2
$$y^{2x} + 3$$ is even
value of y has to be odd ; but x can be even or odd so $$3x^4 + 4y$$ may or may not be even
insufficient
OPTION A
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Re: If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2 [#permalink]
Bunuel wrote:
If x and y are integers, is $$3x^4 + 4y$$ even?

(1) $$x^3$$ is even

(2) $$y^{2x} + 3$$ is even

Are You Up For the Challenge: 700 Level Questions

The question easy is enough we have to find out $$3x^4 + 4y$$ is even or not.

If both $$3x^4$$ and $$4y$$ will be odd or if both will even then their sum will be even as well.
Now, since $$4y$$ is 4 multiple, it will always be even. Therefore, we can ignore y and focus only on $$3x^4$$ or x

Now, let's take a look at (1)

$$x^3$$ is even. If an integer's cube is even then that integer has to contain 2. Therefore, $$x^4$$will be even as well.
Hence, $$3x^4$$ will be even. (Even*Odd=Even)

We know,
$$3x^4$$ is even and $$4y$$ is always even.
Therefore, $$3x^4 + 4y$$ is even. (Even + Even = Even)
Sufficient

Next, let's take a look at (2)
$$y^{2x} + 3$$ is even

As previously discussed , it doesn't matter what y is.
Therefore, insufficient
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Re: If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2 [#permalink]
Bunuel wrote:
If x and y are integers, is $$3x^4 + 4y$$ even?

(1) $$x^3$$ is even

(2) $$y^{2x} + 3$$ is even

Are You Up For the Challenge: 700 Level Questions

Dear Moderator,

Can we have the OE for this one if the OA is C, every one seems to be getting A as the answer. Thank you.
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Re: If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2 [#permalink]
stne wrote:
Bunuel wrote:
If x and y are integers, is $$3x^4 + 4y$$ even?

(1) $$x^3$$ is even

(2) $$y^{2x} + 3$$ is even

Are You Up For the Challenge: 700 Level Questions

Dear Moderator,

Can we have the OE for this one if the OA is C, every one seems to be getting A as the answer. Thank you.

___________________________
The OA is A. Edited. Thank you.
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Re: If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2 [#permalink]
3x^4+4y even?

4y will always be even as even* odd/even = even
This will be even only when 3x^4 is even (Even + Even = Even). 3x^4 will be even only when x is even as odd(3) * Even= Even.

This question generally asks: is x Even?

A) x^3 is even: This will only happen if x is Even. If x be odd then odd^odd = odd hence not possible. Sufficient

B)y^2x + 3 is even: This only means y^2x is odd (odd + odd = Even). This implies y is odd (Odd raise to even poser is odd). From here the nature of x cannot be known.
Insufficient.

Hence A.
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Re: If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2 [#permalink]
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Re: If x and y are integers, is 3x^4 + 4y even? (1) x^3 is even (2) y^2 [#permalink]
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