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Re: If, x, y, and z are integers, is x even? [#permalink]

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23 Jun 2015, 05:22

If, x, y, and z are integers, is x even?

(1) 10^x = 4^y*5^z

2^x * 5^x = 2^2y * 5^z equating, we get x=2y (x will be even regardless whether y is even or odd) x=z ( x will be even if z is even and x will be odd if z is odd)

Insufficient

(2) 3^(x + 5) = 27^(y + 1)

3^(x + 5) = 3^3(y + 1) equating, we get

x + 5 = 3(y + 1) x = 3y - 2 (x will be even if y is even and x will be odd if y is odd)

Insufficient

Combining statements 1 and 2

we have below equations x=2y ------(1) x=z --------(2) x=3y-2 ----(3)

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2^x * 5^x = 2^2y * 5^z equating, we get x=2y (x will be even regardless whether y is even or odd) x=z ( x will be even if z is even and x will be odd if z is odd)

Looks like you have made an error in statement 1 (check highlighted part)

how can x be even and odd simultaneously

x = 2y = z i.e. x MUST be even because y is an Integer and therefore z will also be even

Hence, SUFFICIENT

I hope it helps!
_________________

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Re: If, x, y, and z are integers, is x even? [#permalink]

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07 Aug 2015, 14:58

I saw this question pop up today when I was studying my MGMAT book. In a recent post by mikemcgarry he encouraged me to not dismiss things and to look deeper to really ensure you understand the mechanics of the problem/question rather than just a surface understanding (something about icebergs comes to mind).

I see in the explanation here (and in the MGMAT book) that we are able to infer that \(4^y\) = \(2^2^y\). I'm certainly not going to argue that this is true as I have tested the theory with a few different numbers, and the rest of the problem makes sense to me. Rather than just dismiss this I would like to grasp the mechanics of why we are able to do this. I hope that if I understand this better I will be able to recognise this more easily in the future and in what cases I can and more importantly cannot make this inferance.

Thanks in advance for the help.

p.s. I know this is probably a very simple question for most of you around here but I guess we all get caught up on simple things from time to time
_________________

If you found my post useful, please consider throwing me a Kudos... Every bit helps

I saw this question pop up today when I was studying my MGMAT book. In a recent post by mikemcgarry he encouraged me to not dismiss things and to look deeper to really ensure you understand the mechanics of the problem/question rather than just a surface understanding (something about icebergs comes to mind).

I see in the explanation here (and in the MGMAT book) that we are able to infer that \(4^y\) = \(2^2^y\). I'm certainly not going to argue that this is true as I have tested the theory with a few different numbers, and the rest of the problem makes sense to me. Rather than just dismiss this I would like to grasp the mechanics of why we are able to do this. I hope that if I understand this better I will be able to recognise this more easily in the future and in what cases I can and more importantly cannot make this inferance.

Thanks in advance for the help.

p.s. I know this is probably a very simple question for most of you around here but I guess we all get caught up on simple things from time to time

Re: If, x, y, and z are integers, is x even? [#permalink]

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02 May 2017, 05:59

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

I searched high and low and could not find this question posted. Please redirect and lock thread if already posted. Also, I couldn't figure out how to format the (x+5) and (y+1) correctly. I read through the entire "Writing Mathematical Formulas on the Forum"...

I searched high and low and could not find this question posted. Please redirect and lock thread if already posted. Also, I couldn't figure out how to format the (x+5) and (y+1) correctly. I read through the entire "Writing Mathematical Formulas on the Forum"...

Hi... If you look down below in similar topics, this stands out.. Merging topics
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