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If m, n, and p are integers, is m + n odd?
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Updated on: 26 Jun 2013, 08:33
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If m, n, and p are integers, is m + n odd? (1) m = p^2 + 4p + 4 (2) n = p^2 + 2m + 1
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Originally posted by ichauhan.gaurav on 26 Jun 2013, 08:22.
Last edited by Bunuel on 26 Jun 2013, 08:33, edited 1 time in total.
RENAMED THE TOPIC.




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Re: If m, n, and p are integers, is m + n odd?
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26 Jun 2013, 08:32




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Re: If m, n, and p are integers, is m + n odd?
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26 Jun 2013, 08:42
If m, n, and p are integers, is m + n odd? (1) m = p^2 + 4p + 4 (2) n = p^2 + 2m + 1 Statement 1 If p is Odd then m  odd + even + even = Odd If p is Even then m  Even + even + even = Even Insufficient (still value of n is missing) Statement 2 If p is Odd then n  odd + even + odd = Even If p is Even then n  Even + even + odd = Odd Insufficient (still value of M is missing) Statement 1& 2 If p is Odd then m = Odd & n = Even M+ n = Odd If p is Even then m = Even & n = Odd M+ n = Odd Sufficient Thus answer C
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Re: If m, n, and p are integers, is m + n odd?
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06 Nov 2014, 16:44
Hi,
Why can't we factor M into (p+1)^2, which yields P = 1. Doesn't that lock in one of the variables to begin with? I realize that it won't give us a different answer but why isn't that a valid approach?



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Re: If m, n, and p are integers, is m + n odd?
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07 Nov 2014, 03:31



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Re: If m, n, and p are integers, is m + n odd?
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04 Sep 2015, 11:29
Bunuel, If we try 0 for p then m+n is even. So shouldn't the answer be E Could you clarify...
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Re: If m, n, and p are integers, is m + n odd?
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05 Sep 2015, 03:11



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Re: If m, n, and p are integers, is m + n odd?
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10 Nov 2016, 12:59
(1) m = p^2 +4p+4
p=0 > m=4 p=1 > m=9 p=2 > m=16
NOT SUFFICIENT
(2) n=p^2 +2p+1
p=0 > m=1 p=1 > m=4 p=2 > m=9
NOT SUFFICIENT
(1) + (2) p=0 > m+n=5 p=1 > m+n=13
SUFFICIENT



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Re: If m, n, and p are integers, is m + n odd?
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10 Nov 2016, 15:42
If m, n, and p are integers, is m + n odd?
(1) m = p^2 + 4p + 4 (2) n = p^2 + 2m + 1
1. m = p^2 + 4p + 4
This doesn't tell us anything about N so its insuff.
However if you'd like to factor it you get (p+2)(p+2)=m or p=m2
2. n = p^2 + 2m + 1
Here you can plug in numbrs. Depending on what you plug in n can be even or odd. Insuff
1+2 if you take the equation p=m2 and plug it into the equation for statement 2 you get m²4m+4+2m+1=n m²2m+5=n
try plugging an even number for m (4) 168+5=13 e+o=odd
Now plug in an odd (3)
96=3+5=even
n and m are opposites so the sum is always odd



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Re: If m, n, and p are integers, is m + n odd?
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27 Jan 2017, 18:12
Alternative answer:
1/ Rewrite m as (p+2)^2 2/ plug in m in n to express n solely in function of p: you get n=3p^2+8p+9 3/ Test for p=even if you get n+m=odd 4/ Test for p=odd if you get n+m=odd 5/ since 3 and 4 coincide (for p even and p odd we get n+m=odd), we can be sure using Statement 1 and 2 that m+n is odd.



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Re: If m, n, and p are integers, is m + n odd?
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21 Dec 2018, 21:02
m + n will be odd if one of them is odd. Statement 1. m = p2 + 4p + 4 = (p + 2)2 So, m is even if p is even and m is odd if p is odd. But we can’t say anything about m+n. Hence, Insufficient. Statement 2. n = p2 + 2m + 1. 2m is even because it is a multiple of 2. P2 + 1 will be even if p is odd and p2 +1 will be odd if p is even. So, n is even if p is odd and n is odd if p is even. But we can’t say anything about m +n. Hence, Insufficient. Statement 1 & 2 together. Using the results of statement 1 & 2, we can say that If p is even: m is even and n is odd. If p is odd: m is odd and n is even. Hence, m + n will always be odd. Hence, Sufficient.




Re: If m, n, and p are integers, is m + n odd? &nbs
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21 Dec 2018, 21:02






