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hellokimkim36
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Post subject: NP Guide (3rd Ed) - Divisibility & Primes p.106  Posted: Sun Aug 09, 2009 10:58 pm |
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I have a question regarding In Action Problem #25 on p.106 of the number properties (3rd Edition).
If x,y, and z are integers, is x even?
1) 10^x = (4^y)*(5^z)
--> I got (2^x)*(5^x) = (2^2y)*(5^z)
from this, I can infer that 2^x = 2^2y and 5^x = 5^z since 2 and 5 are primes.
Thus --> x=2y which i know x is for sure even;
BUT: -->x = z which i DO NOT know anything about z.
Therefore I think A is insufficient because x can be both even (2y) or odd (since z can be odd or even). However, the answer is that A is sufficient.
Please explain why A is sufficient.
Thanks.
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Ben Ku
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Post subject: Re: NP Guide (3rd Ed) - Divisibility & Primes p.106 Posted: Tue Aug 18, 2009 12:31 pm |
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Quote: If x,y, and z are integers, is x even?
1) 10^x = (4^y)*(5^z)
--> I got (2^x)*(5^x) = (2^2y)*(5^z)
from this, I can infer that 2^x = 2^2y and 5^x = 5^z since 2 and 5 are primes.
Thus --> x=2y which i know x is for sure even;
BUT: -->x = z which i DO NOT know anything about z.
Therefore I think A is insufficient because x can be both even (2y) or odd (since z can be odd or even). However, the answer is that A is sufficient.
I think that x = 2y (x is even) and x = z (z is an integer) do NOT contradict each other. Basically x must fit BOTH conclusions, so x must be even.
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Ben Ku
Instructor
ManhattanGMAT
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hellokimkim36
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Post subject: Re: NP Guide (3rd Ed) - Divisibility & Primes p.106 Posted: Tue Aug 18, 2009 7:04 pm |
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Thank you for your response. I agree with your explanation.
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Ben Ku
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Post subject: Re: NP Guide (3rd Ed) - Divisibility & Primes p.106 Posted: Wed Aug 19, 2009 12:07 pm |
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Glad it helped!
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Ben Ku
Instructor
ManhattanGMAT
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ankitp
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Post subject: Re: NP Guide (3rd Ed) - Divisibility & Primes p.106 Posted: Tue Dec 01, 2009 3:12 am |
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I have a question though I disagree with the solution.
Statement A by itself is NOT SUFFICIENT, x could = 0, which is not odd.
You need statement 1 and 2 to be sufficient , as statement 2 guarantees x != -
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Ben Ku
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Post subject: Re: NP Guide (3rd Ed) - Divisibility & Primes p.106 Posted: Thu Dec 03, 2009 2:16 am |
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ankitp wrote: I have a question though I disagree with the solution.
Statement A by itself is NOT SUFFICIENT, x could = 0, which is not odd.
You need statement 1 and 2 to be sufficient , as statement 2 guarantees x != - Can you expand on your thoughts? I don't really understand your question. The problem asks whether x is even. As we worked out above, we figured out that in statement (1), x must be even. You're right, x could be 0; this fits what we said about statement (1) and does not present a counterexample.
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Ben Ku
Instructor
ManhattanGMAT
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sudhir.18n
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Post subject: Re: NP Guide (3rd Ed) - Divisibility & Primes p.106 Posted: Fri May 13, 2011 2:41 pm |
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Hi ,
Reviving a very old thread..
Was just going through this problem on NPG 4 Ed.
Fairly easy one ; but the nly doubt I have is '
Do we have to assume in exponential questions that the integers are +ve? Bcoz the question stem says "If x, y, and z are integers, is x even?" cant X, Y , Z be negative?
Thanks
Sudhir
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jnelson0612
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Post subject: Re: NP Guide (3rd Ed) - Divisibility & Primes p.106 Posted: Sat May 14, 2011 10:33 pm |
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sudhir.18n wrote: Hi ,
Reviving a very old thread..
Was just going through this problem on NPG 4 Ed.
Fairly easy one ; but the nly doubt I have is '
Do we have to assume in exponential questions that the integers are +ve? Bcoz the question stem says "If x, y, and z are integers, is x even?" cant X, Y , Z be negative?
Thanks
Sudhir x, y, and z could possibly be negative, but the issue is whether x is even. We know that x=2y, so even if y=-1 and x=-2, x would still be even. Negative numbers can absolutely be distinguished as even and odd.
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Jamie Nelson
ManhattanGMAT Instructor
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